Designing a Channel Access Mechanism for Wireless Sensor Networkdownloads.hindawi.com/journals/wcmc/2017/7493269.pdf · 2019-07-30 · Cross-layer MAC protocol efforts Radio-triggered

Research ArticleDesigning a Channel Access Mechanism forWireless Sensor Network

Basma M Mohammad El-Basioni1 Abdellatif I Moustafa2

Sherine M Abd El-Kader1 and Hussein A Konber2

1Electronics Research Institute Cairo Egypt2Faculty of Engineering Al-Azhar University Cairo Egypt

Correspondence should be addressed to Basma M Mohammad El-Basioni bbasionieriscieg

Received 29 July 2016 Revised 6 November 2016 Accepted 23 November 2016 Published 17 January 2017

Academic Editor Stefano Savazzi

Copyright copy 2017 Basma M Mohammad El-Basioni et al This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

Although there are various Medium Access Control (MAC) protocols proposed for Wireless Sensor Network (WSN) there is noprotocol accepted as a standard specific to it This paper deals with completing the design of our previously proposed MAC forWSN by proposing a channel access mechanism (CAM) The CAM is based on developing a backoff mechanism which mainlydifferentiates nodesrsquo backoffs depending on their different identification numbers and it employs a performance tuning parameterfor reaching a required performance objective The probability distribution of the backoff period is constructed and Markov chainmodeling is used to analyze and evaluate the CAM against the IEEE802154 slotted CSMACA based on single- and multihopcommunication with respect to the reliability the average delay the power consumption and the throughput The analysis revealsthat the required performance of CAM against the IEEE slotted CSMACA can be obtained by choosing the maximum backoffstages number and the tuning parameter value and that CAM performs better than the IEEE with larger nodes number Themultihop scenario results in a good end-to-end performance of CAM with respect to the reliability and delay becomes betterwith lengthier paths at the expense of increasing the energy consumption

1 Introduction

MAC [1ndash3] is the rudiment for any wireless communicationsystem to function properly It coordinates access to andtransmission over the medium common to several nodesand puts rules to minimize interference and packet collisionsamong them under imposed constraints and desired perfor-mance goals

It is not highly true to say that the collision cause is theconcurrent transmissions because concurrent transmissionsmay not cause collision even if the transmitters reside in thesame radio range It is better not to point to the sender inclarifying the cause of the collision but referring it to thereceiver where the collision occurs at a receiver due to itsreception tomore than one signal at the same time because ofits residence in the common transmission area of more thanone transmitter whether it is the intended receiver of one ormore of them

The MAC protocols can be divided into two mainapproaches contention-based [4 5] (random assignmentprotocols) and contention-free [6 7] (schedule-based) ofwhich indoors may be classified into fixed-assignment pro-tocols and demand-assignment protocols Far from the badchannel utilization of the fixed-assignment and its othercons and far from the additional overhead of the demand-assignment through polling and reservation the contention-basedMACprotocol ismore logical for accessing the channelhowever it is more prone to fail in successful mediumallocation and collision prevention This depends on thecharacteristics of the contention-based MAC protocol itselfand another high importance factor which is the logicaltopology that determines the number of talkers who can talkto who when and where they can talk at what range and soforth

Based on that it is preferred to use a contention-basedMAC with a good performance works on a logical topology

HindawiWireless Communications and Mobile ComputingVolume 2017 Article ID 7493269 31 pageshttpsdoiorg10115520177493269

2 Wireless Communications and Mobile Computing

paved for it especially with respect to predictability andnumber of contending nodes where the condition underwhich these protocols may fail in preventing collisions is thesourcesrsquo number increase or the sourcesrsquo transmission rateincrease

The MAC layer design intended by the work proposed inthis paper is based on the physical layer of the IEEE802154standard [8ndash10] and composed of two techniques a timingstructure mechanism (TSM) proposed by our previous work[11] including the setup of the logical topology by dividing thenetwork into subnetworks (sub-NWs) using multichannelsand identifying the time structure of the sub-NW membersrsquowork and the contention-based CAM proposed in this paperThemain TSM ideawas to construct a receive schedule whichmakes at a time only one node from a group of nodes (sub-NW) listen to the channel and each node takes its turnsuccessively to listen for a small period At any time a nodewants to transmit it can turn its radio to the transmit stateand transmit directly in its maximum range or in a rangesuitable to the currently listening node using the CAM Thebackoff periods are aligned with a reference time common tothe nodes

The CAM is designed to be suitable to the proposed TSMand benefits from it and it is based on developing a backoffmechanism resorting to the common manner of increasingthe backoff stages (ie repeating the trials of accessing thechannel if it is found busy rather than announcing channelaccess failure and discarding the packet) and using a numberof transmission trials to cope with the transmission failurerather than discarding the packet

The rest of this paper is organized as follows Section 2includes a brief literature review for wireless MAC protocolsSection 3 begins with giving an overview of the beacon-enabled IEEE802154 slotted CSMACA then it illustratesthe proposed CAM idea and its modeling The performanceassessment of CAM is depicted in Section 4 where the CAMperformance is evaluated against the slotted CSMACA interms of single- andmultihop communication also the effectof different parameters on CAM performance and its tuningis considered Finally Section 5 concludes the paper andsuggests open issues for future work

2 Literature Review

The wireless medium access schemes used in different typesof wireless networks are based on carrier sensing backoffalgorithms andmechanisms for avoiding hidden and exposedterminal problems The Carrier Sense Multiple Access withCollision Avoidance (CSMACA) with its two versionsnonpersistent and 119901-persistent represents the basic formof channel access control In nonpersistent CSMA if thedevice senses the channel busy it backs off before tryingto transmit again When the channel is idle the devicetransmits immediately In 119901-persistent CSMA the devicecontinues sensing the busy channel until it becomes idle andin case of idle channel it transmits or defers transmissionaccording to a probability 119901 Keeping devices in the receivestate when not transmitting consumes a large amount ofenergy Multiple Access with Collision Avoidance (MACA)

[12] uses two additional packets Request-to-Send (RTS) andClear-to-Send (CTS) before the transmission to reduce theoccurrence of the hidden and exposed terminal problemsThe RTS is sent by the sender and the receiver willing toaccept data responds with CTS the other devices hear theRTS or the CTS and avoid interfering the involved devicesuntil end of transmission The RTSCTS represents overloadon the network and causes additional delay

Modifications to these schemes were then proposed suchas using acknowledgment using Request-for-Request-to-Send packet by a busy RTS receiver after finishing its transac-tion employing waiting intervals other than the backoff timeproviding priority levels for wireless channel access as usedin the IEEE80211 [13] distributed coordination function andusing variations in backoff time computation method suchas binary exponential backoff multiplicative increase andlinear decrease balanced backoff algorithm andwaiting timebased backoffWireless networks do not only use contention-based schemes but also use contention-free access such as thepoint coordination function defined in IEEE80211 in whicha coordinator device polls other devices for data

Due to the energy constraint in WSN the design ofWSN MAC considers other mechanisms in addition to thatused in coordinating the shared medium allocation andcontrols nodesrsquo activation to allow them to sleep saving theirenergy wasted in idle listening and overhearing The usedmedium allocation scheme itself should be energy-efficientfor example it does not employ large overhead The MACprotocols proposed in literature for WSN can be broadlyclassified according to the scheme depicted in Figure 1

The contention-based synchronous sleep-scheduling [14]can be through having each node following a periodicactivesleep cycle the nodes that are close to one anothersynchronize their active cycles together and if the next hop ofa transmission overhears it it remains awake until receivingthe forwarded data rather than sleeping and delaying dataforwarding up to its next active cycle But this is not alwaysthe case the next-hop node may be out of the hearing rangeof both the sender and the receiver making data forwardinginterruption problem unavoidable the staggered wake-upscheduling [15 16] is used to address this problem whichcreates a pipeline for data propagation based on the depth-level of nodes in a data-gathering tree where the active periodof one level partially overlaps with that of the lower level

In the asynchronous sender-initiated MAC [17 18] thesender transmits a preamble to indicate a pending trans-mission The receiver wakes up occasionally to listen tosuch a preamble for appropriately responding In receiver-initiated schemes [19] instead of long preambles the senderlistens to the channel waiting for the receiver small bea-cons transmitted in duty cycle fashion to synchronizewith the receiver The asynchronous schemes are simpler toimplement than the synchronous but it may result in verylong delay WSN MAC can be contention-free using TimeDivision Multiple Access (TDMA) or Frequency DivisionMultiple Access (FDMA) or hybrid In multichannel MAC[20 21] some issues are raised such as limited number ofavailable channels channel selection and assignment policyand recursive channel switching overhead Radio-triggered

Wireless Communications and Mobile Computing 3

MAC protocols

Cross-layer MACprotocol efforts

Radio-triggeredMAC protocols

Sleep-based MACprotocols

Integrating MAC design with otherlayers to improve the performance

Trying to reduce the energy a node consumesin idle listening by concerning and dealing with

node HW itself

Intermediate powerlevel-based

On-demand wake-up(two channel wake-

up radio)

Optimizing the radio sleep capabilitiesusing existing node HW

Adding a circuit of passive radio sensor hardwareor separate low power wake-up receiver to the nodes

responsible for waking up the ordinary RF transceiver

DistributedCentralized

More efficient than distributedbut less suitable to WSN

More simple to implement scalable and robust than centralized

Contention-freeContention-based

CDMAFDMATDMA

The most usedfor WSN

Not suitablefor WSN

AsynchronousSynchronous

Sender-initiated(preamble sampling-based)

Receiver-initiated(wakeup beacons-based)

Activendashsleep dutycycling

Staggered wake-upscheduling

Figure 1 Different approaches for WSNMAC protocols

MAC [22 23] and cross-layer MAC [24 25] designs areother approaches proposed for WSN which can be employedwith different types of channel access mechanisms If radio-triggered ID [26 27] is used an additional wake-up hardwarecorresponding to each used frequency and a transmitter ableto transmit at different frequencies simultaneously will berequired

IEEE 802154 is the de facto physical and MAC layersstandard specification used forWSNs In IEEE 802154MACthe channel time is bounded using a superframe structurebounded by periodic transmission of a beacon frame Thesuperframe has activeinactive portions a CSMA-basedCon-tention Access Period (CAP) and an optional reservation-based Guaranteed Time Slot (GTS) scheme intended to sup-port devices requiring dedicated bandwidth or low latencytransmission through a Contention-Free Period (CFP) Inour previous work [11] the channel time bounding mecha-nism of the proposed MAC is implemented and evaluatedagainst the IEEE 802154 MAC superframe structure in acomplete network form using the same contention-basedchannel access mechanism used in the standard and illus-trated in the next section In this paper a design for the

proposedMAC contention-based channel access mechanismis implemented and evaluated against the standard

3 CAM Idea ImplementationEvaluation and Modeling

This section firstly gives an explanation and insight on theIEEE802154 contention-based channel access mechanismand then it proceeds to explain the new backoff method ofthe proposed CAM which represents the difference betweenit and the standard channel access mechanism This sectionalso includes a simple simulation-based evaluation of CAMas a proof of concept and it ends with introducing the CAMmodeling

31 Overview of the Beacon-Enabled IEEE802154 SlottedCSMACA The IEEE802154 standard specifies the physicallayer and media access control layer for low-rate wirelesspersonal area networks (LR-WPANs) and based on it otherstandards which define the upper layers of the stack are devel-oped such as ZigBee [28] ISA10011a [29] WirelessHART[30] MiWi [31] and 6LoWPAN [32]


The IEEE802154 network can operate in two modesof operation beacon- or nonbeacon-enabled modes Innonbeacon-enabled mode the peer-to-peer data transfermodel in which the devices wishing to communicate need toreceive constantly and simply transmit its data using unslot-ted CSMACA is employed Indeed this consumes morenodesrsquo energy as undesirable manner for battery-powerednodesThebeacon-enabledmode ismore suitable for battery-powered nodes where in this mode a star topology isformed between devices and a single central controller calledthe coordinator these devices are allowed to sleep mostof their times while the coordinator listens to the channelfor a longer time but also is allowed to sleep periodicallyThe coordinator bounds its channel time using a super-frame structure bounded by the transmission of a beaconframe

In beacon-enabled mode the slotted CSMACA channelaccess mechanism in which units of time called backoffperiods (backoff slots) are alignedwith the start of the beacontransmission and each time a device wishes to transmit dataframes it shall locate the boundary of the next backoff slotand then wait for a random number of backoff slots If thechannel is idle the device can begin transmitting on thenext available backoff slot boundary otherwise followingthis randombackoff the device shall wait for another randomnumber of backoff slots before trying to access the channelagain Each device shall maintain three variables for eachtransmission attempt119873119861 119862119882 and 119861119864119873119861 holds the number of times the CSMACA algorithmattempts to access the channel to transmit the current packetand it is initialized to zero before every new transmissionThe value of the attributemacMaxCSMABackoffs determinesthe maximum value for this variable that is it determinesthe number of allowed attempts for CSMACA algorithm toaccess the channel to send a packet before reporting channelaccess failure if the value of 119873119861 is greater than macMaxCS-MABackoffs the CSMACA algorithm shall terminate with aCHANNEL ACCESS FAILURE status119862119882 defines the fixed number of backoff periods that thechannel has to be idle before a node can start to transmit andin the standard it is set to 2 backoff periods According to thatit is initialized to 2 before each transmission attempt and resetto 2 each time the channel is assumed to be busy119861119864 refers to the backoff exponent a basis of two is raisedto the119861119864 power (2119861119864) to indicate the count of possible backoffperiods number and the CSMACA can randomly chooseone from them to wait this chosen backoff periods numberbefore attempting to assess the channel This count (2119861119864)represents a range of consecutive numbers of backoff periodsbeginning from 0 backoff period and so ending with (2119861119864 minus1) backoff period Each channel access attempt failure for atransmission 119861119864 is incremented by one to double the rangeof possible backoff periods numbers but up to a maximumvalue equal to the value of the aMaxBE constant beyondwhich its value is frozen and also it has a minimum valuemacMinBE (referred in the paper as1198980)

The slotted CSMACA purposes making the performingof the Clear Channel Assessment (CCA) and starting of

Time

CCA(8 symbols) (12 symbols)

aTurnaroundTime

Backoff period (20 symbols)

The start of the transmission if the channel assessed idle

Figure 2 Illustration of the backoff period

Node 2

Node 1

Node 3

Figure 3 The effect of a backoff period smaller than 20 symbols

packet transmission operations of nodes be aligned con-sequently overlap of CCA operations will not occur andneither false idle channel assessment nor collisions mayoccur Not only does the synchronization of backoff periodsachieve that but also the choice of the unit backoff periodvalue affects this aim The value of the backoff period isselected to be equal to aCCAduration plus a turnaround timefor changing the transceiver to the transmit state which is thetime taken by the node to be ready for the transmission startSo the backoff period equals 20 symbol as shown in Figure 2

If it is said that small backoff period is better to decreasethe delay the reply will be that if the backoff period is smallerthan 20 symbols there will be an overlap among the CCAand turnaround times of nodes as shown in Figure 3 Node2 sensed the channel idle and started to turn its transmitteron during that Node 1 was assessing the channel and itsassessment ended before or on or just after the time Node2 began to send and it did not hear its transmission andproceeded to transmit The same thing can happen betweenNode 1 and Node 3 Although the nodes started to assess thechannel in different backoff periods they collided

The backoff period should not also be greater than20 symbols A greater period as illustrated in Figure 4increases the delay which resulted from the backoff time andfrom locating the next backoff slot boundary without anyadditional beneficial effect on preventing the channel sensingoverlap and collisions

The 119862119882 is selected to be 2 backoff periods that is thenode should be sure that two idle CCA operations wereperformed before the beginning to transmit for preventingpotential collisions of acknowledgement frames If the recep-tion of a packet had been completed at a node before thebackoff period boundary at which it began to perform its


Node 2

Node 1

Figure 4 The effect of a backoff period greater than 20 symbols

CCA and accordingly its reception had been completed atits destination node before the same backoff boundary (thispacket can be undeliverable by this node which wants totransmit while its acknowledgement is deliverable that isthe source node of the acknowledged packet can be out ofthe range of the node wants to transmit but the node wantsto transmit and its intended receiver fall in the range of thedestination node) an overlap would occur between the delayconsumed by the destination node computed starting fromthe time of packet reception completion and representedin the turnaround time and the backoff period boundarylocating delay to start sending the required acknowledgementand the CCA of the node wants to transmit which sensedthe channel idle while an acknowledgement was going to betransmitted If this node does not perform a second CCAit will start to transmit its packet with the destination nodeacknowledgement transmission and a collision would occuras illustrated in the Figure 5

32 Backoff Method Explanation In the proposed backoffmethod the node computes the backoff time in each backoffstage from

bf (119904) = (119868119863 + intuniform (0 119877119868119863mod (119904 + 1)))sdotmod (2119898119887 minus 119906) + (119904minus1sum119895=0

(bf (119895) + cca (119895)))sdotmod (119906 + 1) (1)

where bf(119904) is the function used by a node to computeits backoff time in a backoff stage 119904 119904 is the index of thebackoff stage in range [0 119898] 119868119863 refers to the identificationof the node computes the backoff period 119877119868119863 refers to theidentification of a receiving node and cca(119904) is a functionwhich gives the time spent in channel sensing in stage 119904 Inthe analysis the clause sum119904minus1

119895=0(bf(119895) + cca(119895)) is referred to asldquothe backoff sumrdquo and denoted by bfsum(119904)

The first term of the equation aims to make the backofftime of each node different from the others by making itdependent on their different identification numbers so thatif more than one node have data to send at the same timethey wait different time periods before starting to sense thechannel

The integer uniform random number intuniform(0119877119868119863mod(119904 + 1)) used in the first term depends on theidentification of the receiving node The purpose of thisis to differentiate the backoff time of a certain node with

the passage of time taking advantage of the presence ofdifferent receiving nodes so that no node always has to waita bigger time than its competitors and this prevents the errorrepeating by backing off the same period each backoff trialafter an overlapped sensing is done But this random numberis limited to a certain range by considering the modulus of119877119868119863 and a certain value made to be dependent on the indexof the backoff stage also in order to differentiate the backoffwith time and so that the possible range to a node is allowedto become greater each backoff trial

The second term of the equation considers the fact thatthe nodes may have data to send already in different timesbut their different computed backoff delays make them startsensing the channel at the same time Therefore this termmakes the backoff times chosen by the nodes depends ontheir starting time of having the datawhich is different amongthem in this case this is achieved by taking the sum ofthe delays which resulted from the previously encounteredbackoff stages for this data (if any)

For limiting the backoff time to a certain maximumlimit regardless of the values of nodesrsquo IDs the modulararithmetic is involved in the two terms of the equation andthe maximum limit is selected to be as the maximum limit ofbackoff in the IEEE standard which equals (2119898119887 minus 1) where119898119887 is the maximum backoff exponent

The moduli of the modular operations determine therange of each equationrsquos term resultant values therefore itis made to be dependent on a parameter 119906 which controlsthe maximum value of each term The increase in 119906 valueincreases the maximum value of the second term whiledecreasing that of the first term and vice versa by thesame logic 119906 is used as a tuning parameter for performancemetrics The range of 119906 is [0 2119898119887 minus 1] the values of the twovariables 119868119863 and 119877119868119863 fall in the range [1119873] where119873 is thenumber of nodes in the sub-NW assumed to fall within range[2infin)33 Using R Language to Simulate Nodesrsquo Backoff A codein R language [33] was written to simulate the nodesrsquobackoffs upon (1) and quickly manifest their correspondingbehavior and its impact on star topology data transmissionspecially with respect to the eventuating of collisions andchannel access overlap at different simple assumption-basedscenarios

The code assumes that each node takes its turn as astar topology receiver upon a predetermined schedule for aperiod equal to a complete transaction (13-backoff unit) Thenode does not start a transmission process until it finishes itsreceiving slot Packet generation is exponentially distributedover nodes with rate equal to 1 and limited to be 1 packet pernode over the simulation time The packet generation timefor all nodes is limited to be within a certain period from thestart time to guarantee that all nodes will have data to sendduring the test period There is only one transmission trialbut a number of backoff stages are allowed The consideredparameters are computed by averaging the outputs of anumber of code runs (in each run the time of having datafor each node is changed)


Transmitted Ack

0000192

00001920000128

Received data Pkt Transmitted data Pkt

1st CCA 2nd CCA

Destinationnode

Node wants to transmit

Received data Pkt

Figure 5 Illustration of the importance of performing two CCAs

10 20 30 40 50 60 700Number of nodes

0

05

1

15

2

25

3

35

4

45

Avg

num

ber o

f col

lisio

ns

Figure 6 CAM average number of collisions versus number ofnodes

By setting 119898 to 5 119898119887 to 5 119906 to 5 and the time withinwhich each node will generate a packet to 1240 backoff unitFigure 6 shows that the average number of collisions increasespolynomially with the increase of the number of contendingnodes with instantaneous rate of change linearly increaseswith increasing nodes number This increase of collisionsnumber and the inherent increase of nodes number whichcause the collisionrsquos conflict result in the increase of the losspercentage due to collisions occurrence as shown in Figure 7the loss percentage reached approximately 13 when nodesnumber is 70

Figure 8 shows the percentages of both the total num-ber of time slots which encounter overlap in transmissionattemptsrsquo starts and the number of time slots which causeconcurrent channel access and accordingly collisions withrespect to the total number of channel access attemptsWhileFigure 9 draws the number of collision-prone transmissionattempts which encounter conflict at the start of backoffcomputation and the number of collision-raiser time slotsthis is computed with restricting the time of nodesrsquo startdata generation to a small period to increase the chances ofconcurrent transmission and channel access attempts

0

2

4

6

8

10

12

14

Loss

per

cent

age d

ue to

colli

sion

()

10 20 30 40 50 60 700Number of nodes

Figure 7 CAM loss percentage due to collision versus number ofnodes

Collision-prone situationsCollisions

Perc

enta

ge fr

om to

tal c

hann

el ac

cess

atte

mpt

s (

)

20 30 40 50 60 7010Number of nodes

0

5

10

15

20

25

30

Figure 8 CAM percentages of collision-prone and collision-raisersituations


10 20 30 40 50 60 70Number of nodes


0

10

20

30

40

50

60

70

80

90

100

Num

ber o

f occ

urre

nces

Figure 9 CAM number of collision-prone and collision-raisersituations

It is apparent from Figure 9 that the number of collisionshappened is smaller with a big percentage than the numberof chances that would cause them if the conflicting nodesselect similar backoff periods It could be said that thebackoff method solves approximately on average 808 ofthe channel access conflict situations encountered actuallysome of these situations are originally caused by the backoffmethod itself due to its incapability to perfectly preventconflicts but it is able to mend from thismdashif the channelis found busy and no collision occurmdashby preventing therepeating of the conflict at the following concurrent startsof transmission attempts of the conflicting nodes whichdecreases the number of collisions However generally thepercentage of the total number of eventuated conflicts withrespect to the total number of channel access attemptsis not considered to be a big percentage as shown inFigure 8

Figure 10 indicates the fairness of the backoff methodwith respect to the backoff delay computed as the standarddeviation of the average backoff delay encountered by eachnode As indicated by Figure 10 the 119906 value has a noticeableimpact on the backoff delay fairness among nodes as itcontrols modulating high values computed for the backoffto lower values specially the ID-dependent values and theeffect of the integer uniform random number used in the firstterm of the backoff equation will be more apparent when 119906is big or 119906 is small and 119873 is big When 119906 is small and 119873less than 2119898119887 minus 119906 the backoff delay fairness is better at lower119873 values while when 119873 exceeds 2119898119887 minus 119906 a worse fairnessobtained changes between fall and rise with increasing119873 butwith small amount When 119906 is big the ID-dependent valuewhich is main contributor in differentiating backoff delaysis modulated to small range of values which causes morefairness at higher 119906 values decreases when 119873 increases dueto the effect of the second term of the equation

20 30 40 50 60 7010Number of nodes

Stan

dard

dev

iatio

n of

the a

vera

ge b

acko

ff de

lay

2

3

4

5

6

7

8

u = 25

u = 5

Figure 10 CAM fairness with respect to backoff delay

After clarifying and proving the idea using simpleassumption-based simulation scenarios the subsequent sec-tions consider a precious general modeling and evaluation ofthe CAM

34 CAM Modeling In this section a Markov chain [34]model for the CAM will be implemented Regarding theIEEE802154 slotted CSMACA the generalized model pre-sented in [35] is used for its implementation also thismodel is used as a basis for CAM modeling this workrepresents a generalized accurate model which can be usedfor effective analysis in terms of reliability delay and energyconsumption It takes into account the full functionality of theprotocol the core of IEEE802154 which is the exponentialbackoff process which is modeled backoff stages limit retrylimits acknowledgements and unsaturated traffic

The state transition model represents the proposed CAMwhich is depicted in Figure 11 As indicated in the modelthe three-dimensional Markov chain is described using threestochastic processes 119892(119905) 119888(119905) and 119910(119905) which represent thebackoff stage at time 119905 the state of the backoff counter attime 119905 and the state of retransmission counter at time 119905respectively The states from (119894 1 119895) to (119894 2119898119887 minus 1 119895) are thebackoff states the states (1198760 1198761198710minus1

) consider the idlestate when the queue is empty and the node is waiting fora new packet arrival states (119894 0 119895) and (119894 minus1 119895) representthe first and second CCA respectively and states (minus1 119896 119895)and (minus2 119896 119895) model the successful transmission and packetcollision respectively

The MAC queue is assumed to be a first-in-first-outMM1 queue for both CAM and slotted CSMACA Thegenerated packets arrive at the queue with rate of 120582 packetsper second (pps) The mean service rate 120583 of the queuepackets equals the reciprocal of themean packet service timeSome of the notations used in the analysis throughout thepaper are present in Notations

341 Computation of the Backoff Probability DistributionIn this section we are going to construct the probability


11

11

11

11

11

11

q0

q0q0Q0

Q1

minus2 0 n minus2 Lc minus 1 n

minus1 Ls minus 1 0

minus1 0 0 1 minus q0

1 minus q0 1 minus q0

P

1 minus P 1 minus 0 minus1 0 0 0 0 0 10 0 2m minus 2 0 0 2m minus 1 0

1 minus

P

1 minus P 1 minus 0 minus1 0 m 0 0 m 1 0 m 2m minus 2 0 m 2m minus 1 0

1 minus

minus2 0 0 minus2 Lc minus 1 0

P

1 minus P

1 minus

0 minus1 1 0 0 1 0 1 1

m 11m 0 1

0 2m minus 2 1 0 2m minus 1 1

1 minus

minus2 0 1

minus1 Ls minus 1 1

minus2 Lc minus 1 1

minus1 0 1

P

1 minus P

1 minus

1 minus

0 minus1 1

m 2m minus 2 1 m 2m minus 1 1

P

1 minus P 1 minus 1 minus

minus1 0 n

minus1 Ls minus 1 n


0 minus1 n 0 0 n 0 1n 0 2m minus 2 n 0 2m minus 1 n

P

m 2m minus 2 n m 2m minus 1 nm 0 n m 1 n0 minus1 n

pK(k | I = 0)

pK(k | I = 0)

pK(k | I = 0)

pK(k | I = 0)

pK(k | I = 1)

pK(k | I = 1)

pK(k | I = 1)

pK(k | I = m)

pK(k | I = m)

pK(k | I = m)

QL0minus1

Figure 11 State transition model for CAM


distribution of the backoff period generated by a node indifferent backoff stages 119901119870(119896 | 119868 = 119894) in case the nodecommunicates with its sub-NW members and in case thenode communicates with the Base Station (BS) To achievethat the following definitions are introduced which arederived from generating the set of all possible backoff periodvalues with experiments which consider all the possiblecombinations of the backoff equation variablesrsquo values underspecified conditions The R language is used to generatethese experiments outcome and the relations which describethe probability distribution are derived from observing thepattern of these outcomes

In CAM the receiving node identification 119877119868119863 valuemay vary through the successive backoff stages especiallyaccording to the previously proposed TSM the receivingnode in each receiving slot of the time frame is differentthus the possible 119877119868119863 values in different backoff stagesencountered by a node can be represented by a permutation(with repetition) The effect of the 119877119868119863 value on the value ofthe backoff periods computed by a node in different stagesappears in the integer uniform random number clause inthe first term of the backoff equation as an added value tothe node 119868119863 This added value referred to as ADV fallswithin a range its lower bound is 0 and its upper bounddepends on the 119877119868119863 value in the considered backoff stagewith a maximum possible value equal to the number of the

backoff stage based on that the range of ADV is indicatedin the following definitions by its variable upper bound(119880119861)

The following definitions find the probability of a certainbackoff period value computed by a node in terms ofthe number of times this node computes it and the totalnumber of the backoff periods computed by the node Themathematical formulation of the backoff period probabilitydepends on exploiting the recurrence of the combinations ofvariables cause a backoff value through a calculable numberof repeating times rather than iteratively computes all thebackoff values and then extracts the required informationfrom them This treats the problem of the long time con-sumed in iterative computation which may be consideredas an almost infinite with the huge number of iterationscorresponding to the huge number of variablesrsquo combinationswhich increases inflation with increasing the nodes numberand the backoff stages number Simpler expressions to takesmaller time for computing the number of occurrence timesof a backoff value under certain conditions are depicted inAppendix A

Definition 1 Let r(119880119861 119904) be a function used to compute thenumber of 119877119868119863 values which result in a specific range of theADV in a backoff stage 119904 Then r(119880119861 119904) is a function of thisrange 119880119861 and it can be computed as follows

r (119880119861 119904) = lfloor 119873119904 + 1rfloor if condition1 and condition2 are both true or falselfloor 119873119904 + 1rfloor + 1 if condition1 is true and condition2 is falselfloor 119873119904 + 1rfloor minus 1 if condition1 is false and condition2 is true (2)

where condition1 is equivalent to 119873mod(119904 + 1) ge 119880119861 gt 0condition2 is equivalent to 119880119861 = 119868119863mod(119904 + 1) and lfloorsdot sdot sdot rfloor isthe floor function

Definition 2 Let rnum(119880119861 119904) denote the number of occur-rence times of a specific range 119880119861 in a backoff stage 119904 Thenrnum(119880119861 119904) equals the number of 119877119868119863 values which resultin the 119880119861 in the backoff stage 119904 multiplied by the number ofoccurrence times of a119877119868119863 value in a stage and it is computedas follows

rnum (119880119861 119904) = r (119880119861 119904) (119873 minus 1)119878 (3)

where 119878 is the stage at which we want to compute the backoffperiod 119878 isin [0119898] and 119904 isin [0 119878]Definition 3 Let 119862 be a two-dimensional array which repre-sents the combinations of ADV through all stages from 0 to119878 The array 119862 has number of rows equal to (119878 + 1) indexedby 119903119900 one row for each combination accordingly the numberof the columns of 119862 equals 119878 + 1 indexed by 119888119900

Let 119881 be a set of 119878 + 1 vectors where 119881 = V0 V1 V119878Vector V119904 represents the maximum range of ADV in stage 119904which is [0 119904]

If we denote the number of occurrence times of one com-bination corresponding to a row 119903119900 in 119862 by cnum(119903119900) thencnum(119903119900) equals the maximum number of occurrence timesof a combination corresponding to a row in 119862 multiplied bythe probability of occurrence of the intended combinationcorresponding to a row 119903119900cnum (119903119900)= max (rnum) 119878+1prod

119911=1

( 119911sum119890=1

119888119903119900119911leV119911minus1119890

rnum (V119911minus1119890 119911 minus 1)(119873 minus 1)119878+1 )= (119873 minus 1)119878+1 119878+1prod

119911=1

( 119911sum119890=1

119888119903119900119911leV119911minus1119890

rnum (V119911minus1119890 119911 minus 1)(119873 minus 1)119878+1 )(4)

where 119888119903119900119911 is the element of the array 119862 at the row number 119903119900and column number 119911 and V119911minus1119890 is the element number 119890 inthe vector V which corresponds to stage number 119911 minus 1


Definition 4 Let the total number of occurrence times of theset of all possible backoff period values of an experiment out-come be denoted by the notation tknum(119878) Then tknum(119878)equals the sum of the number of occurrence times of all theADV combinations which constitute the rows of119862multipliedby the number of the combinations of the time units used toperform CCA through a number of 119878 stages namely

tknum (119878) = 2119878 (119878+1)sum119903119900=1

cnum (119903119900) (5)

for every 119868119863 isin [1119873] 119906 isin [0 2119898119887 minus 1] and 119878 isin [0119898]Definition 5 Let the number of occurrence times of a possiblebackoff period value 119896 of an experiment outcome be denotedby the notation knum(119896 119878) and let the 2119878-by-119878 matrix 119860represent all the combinations of the number of the time unitsused to performCCA in all stages then for every 119868119863 isin [1119873]119906 isin [0 2119898119887 minus 1] 119878 isin [0119898] and 119860119886119903119900 isin 119860

knum (119896 119878) = (119878+1)sum119903119900=1

119896=bf119903119900(119878)

cnum (119903119900) (6)

where

bf119903119900 (119878) = (119868119863 + 119888119903119900119878+1)mod (2119898119887 minus 119906)+ (bfsum (119878))mod (119906 + 1) bfsum (0) = 0bfsum (119878) = 119878sum

119888119900=1

(119868119863 + 119888119903119900119888119900)mod (2119898119887 minus 119906)+ (bfsum (119888119900 minus 1))mod (119906 + 1)+ 119886119886119903119900119888119900when 119878 gt 0

(7)

The previous definitions relate the communicationwithinthe sub-NW the following definitions Definitions 6 and 7consider the communication with the BS distinguished bythe existence of only one possible receiver which is the BSidentified by 0 therefore in this case 119877119868119863 always equals 0

Definition 6 Let the total number of occurrence times ofthe set of all possible backoff period values of an experimentoutcome due to the communication with the BS be denotedby the notation bstknum(119878) then bstknum(119878) is defined as

bstknum (119878) = 2119878 (8)

for every 119868119863 isin [1119873] 119906 isin [0 2119898119887 minus 1] and 119878 isin [0119898]Definition 7 Let the number of occurrence times of a possiblebackoff period value 119896 of an experiment outcome due tothe communication with the BS be denoted by the notationbsknum(119896 119878) and let the 2119878-by-119878 matrix 119860 represent all thecombinations of the number of the timeunits used to perform

CCA in all stages then for every 119868119863 isin [1119873] 119906 isin [0 2119898119887 minus1]119878 isin [0119898] and 119860119886119903119900 isin 119860bsknum (119896 119878) = sum

119896=bf(119878)1 (9)

where

bf (119878) = 119868119863mod (2119898119887 minus 119906)+ (bfsum (119878))mod (119906 + 1) bfsum (0) = 0bfsum (119878) = 119878sum

119888119900=1

119868119863mod (2119898119887 minus 119906)+ (bfsum (119888119900 minus 1))mod (119906 + 1)+ 119886119886119903119900119888119900when 119878 gt 0

(10)

Definition 8 The probability distribution of the backoffperiod generated by a node in different backoff stages 119901119870(119896 |119868 = 119894) is computed as follows for every 119896 isin [0 2119898119887 minus 1] and119894 isin [0 119898]119901119870 (119896 | 119868 = 119894) = 1119873 119873sum

119868119863=1

knum (119896 119894)tknum (119894)for sub-NW communication119901119870 (119896 | 119868 = 119894) = 1119873 119873sum

119868119863=1

bsknum (119896 119894)bstknum (119894)

for communicating BS(11)

342 Deriving the Stationary Distribution Thenonzero statetransition probabilities associated with the CAM Markovchain of Figure 11 represent the state transition due todecrementing the backoff counter by one the transition fromone backoff stage to the next one due to sensing the channelbusy the transition from one transmission trail to the nextone due to collision occurrence the transition after channelaccess failure to the queue idle state the transition aftertransmission failure to the queue idle state the transition tothe queue idle state after the maximum backoff stage in thelast transmission trial and finally the transition from the idlestate to the first backoff stage in the first transmission trialthese probabilities are described by (12)ndash(18)

P (119894 119896 119895 | 119894 119896 + 1 119895) = 1 for 2119898119887 minus 1 ge 119896 ge 0 (12)

P (119894 119896 119895 | 119894 minus 1 0 119895) = (120572 + (1 minus 120572) 120573) 119901119870 (119896 | 119868 = 119894)for 119894 le 119898 (13)


P (0 119896 119895 | 119894 0 119895 minus 1)= 119875 (1 minus 120572) (1 minus 120573) 119901119870 (119896 | 119868 = 0) for 119895 le 119899 (14)

P (1198760 | 119898 0 119895) = 1199020 (120572 + (1 minus 120572) 120573) for 119895 lt 119899 (15)

P (1198760 | 119894 0 119899) = 1199020 (1 minus 120572) (1 minus 120573) for 119894 lt 119898 (16)

P (1198760 | 119898 0 119899) = 1199020 (17)

P (0 119896 0 | 1198760) = (1 minus 1199020) 119901119870 (119896 | 119868 = 0)for 2119898119887 minus 1 ge 119896 ge 0 (18)

The following analysis is concerned with finding the closedform for the stationary distribution of the CAM Markovchain (119887119894119896119895) where 119887119894119896119895 = lim119905rarrinfinP(119892(119905) = 119894 119888(119905) = 119896 119910(119905) =119895) 119894 isin (minus2119898) 119896 isin (minus1max(2119898119887 minus 1 119871 119904 minus 1 119871119888 minus 1)) and119895 isin (0 119899) Using (12)ndash(18) and due to the regularity of thechain from (13) for 0 lt 119894 le 119898 0 le 119895 le 119899 2119898119887 minus 1 ge 119896 ge 0we have119887119894119896119895 = 119887119894minus10119895 (120572 + (1 minus 120572) 120573) 2119898119887minus1sum

119903=119896

119901119870 (119903 | 119868 = 119894) (19)1198871198940119895 = (120572 + (1 minus 120572) 120573) 119887119894minus10119895 (20)

and then by recursive application and substitution of (20) forsuccessive backoff stages we can conclude that1198871198940119895 = (120572 + (1 minus 120572) 120573)119894 11988700119895 (21)

let 120572 + (1 minus 120572)120573 = 119909 from (19) (20) and (21) we have119887119894119896119895 = 11990911989411988700119895 2119898119887minus1sum119903=119896

119901119870 (119903 | 119868 = 119894) (22)

From (14) we have1198870119896119895 = 119875 (1 minus 120572) (1 minus 120573) 2119898119887minus1sum119903=119896

119901119870 (119903 | 119868 = 0) 119898sum119894=0

1198871198940119895minus1= 11988700119895 2119898119887minus1sum

119903=119896

119901119870 (119903 | 119868 = 0) (23)

and then from (22) and (23) for 0 le 119894 le 119898 0 le 119895 le 119899 2119898119887 minus1 ge 119896 ge 0 119887119894119896119895 = 11990911989411988700119895 2119898119887minus1sum119903=119896

119901119870 (119903 | 119868 = 119894) (24)

From (14) and (21) we have11988700119895 = (1 minus 119909) 119875 119898sum119894=0

11990911989411988700119895minus1 = (1 minus 119909119898+1) 11987511988700119895minus1 (25)

let (1 minus 119909119898+1)119875 = 119910 and by recursive application andsubstitution of (25) for successive transmission trials we canconclude that 11988700119895 = 119910119895119887000 (26)

then from (24) and (26) (24) can be rewritten as

119887119894119896119895 = 119909119894119910119895119887000 2119898119887minus1sum119903=119896

119901119870 (119903 | 119868 = 119894) (27)

We next derive the expression of 119887000 by applying thenormalization condition

119899sum119895=0

2119898119887minus1sum119896=0

119898sum119894=0

119887119894119896119895 + 119898sum119894=0

119899sum119895=0

119887119894minus1119895+ 119899sum119895=0

(119871119904minus1sum119896=0

119887minus1119896119895 + 119871119888minus1sum119896=0

119887minus2119896119895) + 1198710minus1sum119897=0

119876119897 = 1 (28)

after deriving the expression of each term in (28) in termsof the probability 119887000 and substituting with them on it weobtain

119887000 = [(1 minus 119910119899+11 minus 119910 )sdot 2119898119887minus1sum119896=0

119898sum119894=0

(119909119894 2119898119887minus1sum119903=119896

119901119870 (119903 | 119868 = 119894)) + (1 minus 120572)sdot 1 minus 119909119898+11 minus 119909 1 minus 119910119899+11 minus 119910 + (1 minus 119909119898+1) ((1 minus 119875) 119871 119904+ 119875119871119888) (1 minus 119910119899+11 minus 119910 ) + 1198710 11990201 minus 1199020 (1 minus 119910119899+11 minus 119910 119909119898+1+ 119875 (1 minus 119909119898+1) 119910119899+ (1 minus 119875) (1 minus 119909119898+1) 1 minus 119910119899+11 minus 119910 )]minus1

(29)

35 Single-Hop Communication Analysis The single-hopcommunication scenario considers a number of nodes 119873which are reachable from each other when each node hasdata to transmit it contends with the others in accessingthe shared channel according to the behavior described bythe employed Markov chain models for slotted CSMACAand CAM This section concerns the derivation of therequired performancemetrics expressions startingwith find-ing expressions for some of the modelsrsquo related probabilitiesrequired in the performance analysis implementation

351 Deriving Expressions for the Modelsrsquo Different AssociatedProbabilities Thederivations of 120591120572120573 and119875 for both slottedCSMACA and CAM are the same as done in [35] where120591 = 119898sum

119894=0

119899sum119895=0

1198871198940119895 = (1 minus 119909119898+11 minus 119909 )(1 minus 119910119899+11 minus 119910 ) 119887000119875 = 1 minus (1 minus 120591)119873minus1

12 Wireless Communications and Mobile Computing120572 = P (1st CCA busy due to data transmission)+ P (1st CCA busy due to ACK transmission)= 119871 (1 minus (1 minus 120591)119873minus1) (1 minus 120572) (1 minus 120573) + 119871119886119888119896sdot 119873120591 (1 minus 120591)119873minus11 minus (1 minus 120591)119873 (1 minus (1 minus 120591)119873minus1) (1 minus 120572) (1 minus 120573) 120573 = 1 minus (1 minus 120591)119873minus1 + 119873120591 (1 minus 120591)119873minus12 minus (1 minus 120591)119873 + 119873120591 (1 minus 120591)119873minus1

(30)

The mean packet service time 119864[119878] takes into account theprobability that the serviced packet may be transmittedsuccessfully or discarded due to reaching transmission retrylimit or channel access failure and the average time taken ineach case from the instant the packet is at the head of thequeue is differentthere4 119864 [119878] = 119877119864 [119863] + 119875119888119903 (119899 + 1) (119871119888 + 119864 [119879ℎ])+ 119875119888119891 [[ 119899sum

119895=0

1 minus 1199101 minus 119910119899+1119910119895(119895 (119871119888 + 119864 [119879ℎ])+ 119898sum

119894=0

2119898119887minus1sum119903=0

119903119901119870 (119903 | 119868 = 119894) + 119879119878119862 2119898+1sum119890=1

119862119890120572120573 (119898 + 1)sdot (119873119890

120572 (119898 + 1) + 2119873119890120573 (119898 + 1)))]]

(31)

The Matlab is used for solving the nonlinear system ofequations represented by 120591 120572 120573 and 1199020 expressions352 Reliability Analysis The derivation of the reliabilitywhich is the probability of successful packet reception forboth slottedCSMACA andCAM is the same as done in [35]where119877 = 1 minus 119875119888119891 minus 119875119888119903 = 1 minus 119909119898+1 (1 minus 119910119899+1)1 minus 119910 minus 119910119899+1 (32)

353 Delay Analysis The average delay is defined as the timeinterval from the instant at which the data packet is at thehead of the MAC queue ready to be transmitted until itsacknowledgement is received The derivation of the averagedelay expression is the same as done in [35] for both slottedCSMACA and CAM except for the term in the equation of119864[119879ℎ]which refers to the backoff time in CAM case this termequals (for complete derivation see [35])1sum119898

119894=0 119862120572120573 (119894) 119898sum119894=0

( 2119894sum119890=1

119862119890120572120573 (119894) 119894sum119897=0

2119898119887minus1sum119903=0

119903119901119870 (119903 | 119868 = 119897)) (33)

354 Energy ConsumptionAnalysis Theaverage energy con-sumption is computed from (34) where119864119894119864119904119888119864119905119864119903 and119864119904119901

are the average energy consumption in idle-listen channelsensing transmit receive and sleep states respectively 119864119904119901term is neglected119864 = 119864119894 119898sum

119894=0

2119898119887minus1sum119896=1

119899sum119895=0

119887119894119896119895 + 119864119904119888 119898sum119894=0

119899sum119895=0

(1198871198940119895 + 119887119894minus1119895)+ 119864119905 119899sum

119895=0

119871minus1sum119896=0

(119887minus1119896119895 + 119887minus2119896119895)+ 119864119894 119899sum

119895=0

(119887minus1119871119895 + 119887minus2119871119895)+ 119899sum119895=0

119871+119871119886119888119896+1sum119896=119871+1

(119864119903119887minus1119896119895 + 119864119894119887minus2119896119895) + 119864119904119901 1198710minus1sum119897=0

119876119897(34)

355Throughput Analysis The throughput which is definedas the fraction of channel time used to successfully transmitdata payload bits in unit time is computed from119879119867= 119875119904119906119888119888119890119904119904119875119887119906119904119910119871(1 minus 119875119887119906119904119910) 119878119887 + 119875119904119906119888119888119890119904119904119875119887119906119904119910119871 119904 + 119875119887119906119904119910 (1 minus 119875119904119906119888119888119890119904119904) 119871119888 (35)

where 119875119887119906119904119910 is the probability that there is at least onetransmission in the considered unit time and it equals (1minus(1minus120591)119873) 119875119904119906119888119888119890119904119904 is the probability of successful data transmissionconditioned by the fact that the channel is busy and it equals(119873120591(1 minus 120591)119873minus1)119875119887119906119904119910 the denominator of 119879119867 considers thatthe channel time has different probabilities of being free orbusy with failed or successful transmission

36 Multihop Communication Analysis The aim of thissection is to analyze the end-to-end performance of theproposed CAM when the packet is forwarded through inter-mediate node(s) to reach the final destination for comparingthe CAM performance against the slotted CSMACA inmultihop topologyThe algorithmic technique of ldquodivide andconquerrdquo is used for finding the end-to-end performancewhere the multihop path is partitioned into a number ofsingle-hops solved using the previous analysis with adjustingthe model parameters and may be with some modificationsaccording to the employed topology then the solutionsobtained for each single-hop are appropriately merged toobtain the end-to-end multihop performance

Figure 12 presents examples for the employed topologyfor each protocol the topology of the slotted CSMACAis the logical topology for it which is the cluster-tree Theproposed CAM topology is constructed by dividing thenetwork into subnetworks each one works on a differentfrequency channel some members are BS-neighbors andits members work on our previously proposed TSM [11]The time slot equals the time of one transmission and nointeraction between the sub-NWs is assumedThe number ofthe BS-neighbors in all the sub-NWs is approximately equaland the number of the non-BS-neighbors in all the sub-NWs


0 10 20 30 40 50

P

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BSBS-neighborNon-BS-neighborGelatinous shape encloses a sub-NW members

(a)

0 10 20 30 40 50

1

45

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6

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1412

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919

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BSCoordinatorDeviceConnection between coordinatorsConnection between devices and coordinators

(b)

Figure 12 Multihop network topologies (a) for CAM network and (b) for slotted CSMACA cluster-tree network

is also approximately equal In CAM no attention is given toa specific routing technique that is no determinants of thenext hop also in CSMACA no determinants imposed forselecting the parent coordinator from the discovered ones

In the two topologies when a node has a packet at thehead of the queue ready to be sent it can immediately startits transmission process to the currently listening receiverthat is all the intended receivers in any time are available nosleeping schedule causes deferring of a transmission processsuch that only the effect of the medium access method isconsidered The nodes are deployed uniformly the nodeswhich have the capability of coordinator represent 25 ofthe total nodes number and are deployed independentlyuniformly throughout the area

The starts of the first packet generation of all the sub-NWmembers are separated by an ignorable time accordinglythe generation repetitions will be separated by an ignorabletime The cluster-tree formation and communication as wellas the communication between sub-NWsrsquo BS-neighbors andthe BS are performed using minus15 dBm while the commu-nication among sub-NWsrsquo members is performed using agreater transmission power level minus10 dBm for assuring thereachability of the receiving node at any time

The following sections concern deriving expressions forthe multihop performance metrics for both the slottedCSMACA network and the CAM network The multihopnetwork topology imposes changes in each node variablesand the communication conditions from one network to theother ormay be fromone hop to another in the samenetworksuch as the existence of different degrees of neighborhoodto a transmitting node which raises the existence of hiddennodes different packet arrival rates and different number of

contended nodes Section 361 analyzes the effect ofmultihopcommunication on the two networksrsquo models associatedprobabilities Sections 362 to 365 analyze the end-to-end reliability delay energy consumption and throughputthe same definitions and computation are used for findingthese slotted CSMACA and CAM end-to-end performancemetrics except few indicated differences

361 Deriving Expressions for the Modelsrsquo Different AssociatedProbabilities In this section the derivations of120572120573 and119875 forboth slotted CSMACA and CAM will be introduced

(1) Slotted CSMACA End-to-End Analysis In the cluster-treeslotted CSMACA network and by assuming that the numberof each cluster end devices members I119889 is approximatelyequal and the number of children coordinators I119888 variesfrom 0 to a constant maximum limit for each coordinatorthe packet arrival rate at the MAC queue differs from theend device 120582119889 to the coordinator 120582119888 also if no aggregation isassumed it will differ for coordinators at different levels but itmay differ in case of aggregation employed from coordinatorto another one if their I119888 values are different The packetgeneration rate 120582 at each node is equal in each time unitthe network will have the number of packets described by 120582generated fromeachnode and in computing the approximatevalue of the packet arrival rate at a node it is assumed thatall the transmitted packets to this node will be deliveredsuccessfullyThe packet arrival rates are computed as follows120582119889 = 120582120582119888119894 = 120582 (1 +I119889 +I119888119894

) if aggregation is assumed

14 Wireless Communications and Mobile Computing120582119888119894 = 120582 (1 +I119889 +Itotal119888119894

(1 +I119889))if no aggregation is assumed

(36)

whereItotal119888119894

represents the number of the coordinators belowthe coordinator 119894 in its tree branch its children coordinatorsits grandchildren coordinators the children of its grandchil-dren coordinators and so on

According to the packet arrival rate and the differentneighborhood of each node and its neighbors the node willhave its own probabilities of 120591 120572 120573 and 119875 The neighbor-hood of a transmitting node its receiverrsquos neighborhoodand the neighborhood of its receiverrsquos neighbors are dis-tinguished by defining some sets of nodes each one hasan effect on the transmitting node packet these sets areΦ119905 Φ119905119888

Φ119905119903 Φℎ119905119903 Φℎ119888119905119903 120595119888 119862119905 and 119862The set Φ119905 defines the neighborhood of a node 119905 which

are the nodes surrounding this node that can hear itstransmissions and likewise it can hear their transmissions(the neighbor coordinators are discriminated by Φ119905119888

andincorporate the BS) the set Φ119905119903 defines the common neigh-borhood of the nodes 119905 and 119903 (Φ119905119903 = (Φ119905 cap Φ119903)) the setΦℎ119905119903 defines the hidden nodes from the node 119905 with respectto the transmission to node 119903 including the BS the set Φℎ119888119905119903

defines the hidden coordinators from the node 119905 with respectto the transmission to node 119903 including the BS the set 120595119888defines the set of coordinator 119888 children from devices andcoordinators the set 119862119905 is a set of one element correspondingto the coordinator of node 119905 and the set 119862 defines the set ofall coordinators in the network

(a) The Collision Probability The collision probability relatedto node 119905 is the probability that node 119905 encounters a collisionon a transmitted packet to its coordinator and it is denotedby 119875119905 The collision probability 119875119905 is given by119875119905 = 119875119862119904119890119899119904119890119905 + (1 minus 119875119862119904119890119899119904119890119905) 119875119862ℎ119863119886119905119886119905+ (1 minus 119875119862119904119890119899119904119890119905) (1 minus 119875119862ℎ119863119886119905119886119905) 119875119862ℎ119860119888119896119905 (37)

where 119875119862119904119890119899119904119890119905 is the collision probability of a transmittedpacket from 119905 to 119903 due to concurrent channel sensing119875119862ℎ119863119886119905119886119905 is the collision probability of a transmitted packetfrom 119905 to 119903 due to hidden data transmission starts before orafter the beginning of the packet transmission and 119875119862ℎ119860119888119896119905is the collision probability of a transmitted packet from 119905 to119903 due to hidden acknowledgement transmission starts beforeor after the beginning of the packet transmission

The probability 119875119862119904119890119899119904119890119905 considers the probability thatat least one node from the common neighborhood of thetransmitter and the receiver (except the BS) transmits at thesame time slot If each node in the common neighborhoodsenses the channel with its own probability 120591 119875119862119904119890119899119904119890119905 iscomputed from119875119862119904119890119899119904119890119905 = 1 minus prod

119895isinΦ119905119903 119895 =BS(1 minus 120591119895) (38)

Hidden acknowledgements to the transmitter 119905 resultedfrom successful data reception at the hidden coordinatorsfrom 119905 uponwhich they transmit acknowledgements receivedat its receiver 119903 and collide with its data The probability119875119862ℎ119860119888119896119905 is given by119875119862ℎ119860119888119896119905 = 119875119878119877ℎ1199051 minus prod119896isin⋃ℎisinΦℎ119888119905119903

120595ℎ(1 minus 120591119896)

sdot | ⋃ℎisinΦℎ119888119905119903 120595ℎ|sum119902=1

| ⋃ℎisinΦℎ119888119905119903120595ℎ|119862119902sum

119898=1

( prod119894isin119889119898

119889119898=1198891198981 1198891198982 119889119898119902

120591119894sdot prod119895isin⋃ℎisinΦℎ119888119905119903

120595ℎ119889119898

(1 minus 120591119895)sdot(1 minus prod

119899isin119889119898119889119898=1198891198981 1198891198982119889119898119902

(120572119899 + (1 minus 120572119899) 120573119899)))(39)

where | ⋃ℎisinΦℎ119888119905119903120595ℎ| stands for the size of the set of nodes

which represents the union of all the sets which containthe children of the hidden coordinators from 119905 | ⋃ℎisinΦℎ119888119905119903 120595ℎ|119862119902represents the number of combinations of size 119902 from the set| ⋃ℎisinΦℎ119888119905119903

120595ℎ| 119889119898 represents the combination number 119898 ofsize 119902 and they are used in (39) to calculate the probabilityof at least one node from the set | ⋃ℎisinΦℎ119888119905119903

120595ℎ| which beginsa transmissionThe notation 119875119878119877ℎ119905 represents the probabilityof successful data reception at the hidden coordinators from119905 and it is defined in Appendix B

The probability 119875119862ℎ119863119886119905119886119905 is the probability of at least onefrom the hidden nodes to 119905 which begins a transmission inany time unit of a time duration equal to the average channeloccupation of a data transmission before the beginning of119905 transmission and one after it The probability 119875119862ℎ119863119886119905119886119905 iscalculated from119875119862ℎ119863119886119905119886119905

= 2119871 |Φℎ119905119903BS|sum119902=1

|Φℎ119905119903BS|119862119902sum119898=1

( prod119894isin119896119898

119896119898=1198961198981 1198961198982 119896119898119902

120591119894sdot prod119895isinΦℎ119905119903(119896119898cupBS)


119899isin119896119898119896119898=1198961198981 1198961198982 119896119898119902

(120572119899 + (1 minus 120572119899) 120573119899)))(40)

where |Φℎ119905119903BS|119862119902 represents the 119902-combinations from thehidden nodes to 119905 excluding the BS and it equals the numberof rows of thematrixK where each row contains one differentcombination


(b) Probability of Finding the 1st CCA Busy The equation of120572119905 which is the probability of node 119905 finds the 1st CCA busywhich comprises the probability to find it busy due to datatransmission (1205721119905) and the probability to find it busy due toacknowledgement transmission 1205722119905120572119905 = 1205721119905 + (1 minus 1205721119905) 12057221199051205721119905 = 119871 |Φ119905BS|sum

119902=1

|Φ119905BS|119862119902sum119898=1

( prod119894isin119896119898

119896119898=1198961198981 1198961198982 119896119898119902

120591119894sdot prod119895isinΦ119905(119896119898cupBS)


119899isin119896119898119896119898=1198961198981 1198961198982 119896119898119902

(120572119899 + (1 minus 120572119899) 120573119899)))1205722119905 = 1198751198781198771199051 minus prod119896isin⋃ℎisinΦ119905119888

120595ℎ119905(1 minus 120591119896)

sdot | ⋃ℎisinΦ119905119888 120595ℎ119905|sum119902=1

| ⋃ℎisinΦ119905119888120595ℎ119905|119862119902sum

119898=1

( prod119894isin119889119898

119889119898=1198891198981 1198891198982119889119898119902

120591119894sdot prod119895isin⋃ℎisinΦ119905119888

120595ℎ(119889119898cup119905)


119899isin119889119898119889119898=1198891198981 1198891198982 119889119898119902

(120572119899 + (1 minus 120572119899) 120573119899)))

(41)

where |Φ119905BS|119862119902 and | ⋃ℎisinΦ119905119888120595ℎ119905|119862119902 represent the 119902-

combinations from all the neighbors of 119905 excluding theBS and all the children of the neighbor coordinatorsof 119905 excluding 119905 itself respectively The notation 119875119878119877119905represents the probability of successful data reception at thecoordinators of node 119905 neighborhood and it is defined inAppendix B

(c) Probability of Finding the 2nd CCA Busy The probability120573119905 which is the probability of node 119905 finding the 2ndCCA slot(denoted as CCA2) busy given that the 1st CCA slot (denotedas CCA1) was idle is derived in the same fashion used in [36]but with considering the different neighborhood and otherdifferent values the nodes have

The node can assess its 2nd CCA busy in two cases thefirst one occurs if some other nodes in the medium weresensing their 2nd CCA during this node 1st CCA and starteda new transmission in the nodersquos 2nd CCA slot This canonly happen if the other node started sensing in the slotjust before the intended node 1st CCA slot (denoted as slot1)and the channel was then idle The second case of assessing

the 2nd CCA busy occurs when the 1st CCA idle slot wasthe slot between data transmission and acknowledgement(the probability of the second case occurrence is denoted by119875119887119890119905119886119860119862119870) then120573119905 = P (1198681199041198971199001199051 | 1198681198621198621198601)P (1198781199041198971199001199051) + 119875119887119890119905119886119860119862119870 (42)

where 1198681199041198971199001199051 and 1198681198621198621198601 are the events of finding slot1 andCCA1idle respectively the event 1198781199041198971199001199051 is the event of start sensingin slot1

The conditional probability P(1198681199041198971199001199051 | 1198681198621198621198601) is the proba-bility that a given idle slot is preceded by another idle slot

P (1198681199041198971199001199051 | 1198681198621198621198601) = 1 minus P (1198611199041198971199001199051 cap 1198681198621198621198601)P (1198681198621198621198601)= 1 minus P (1198611199041198971199001199051 cap 1198681198621198621198601)

P (1198611199041198971199001199051 cap 1198681198621198621198601) + P (1198681199041198971199001199051 cap 1198681198621198621198601) (43)

where 1198611199041198971199001199051 it the event of finding slot1 busy then 120573119905 can berewritten as120573119905 = (1 minus P (1198611199041198971199001199051 cap 1198681198621198621198601)

P (1198611199041198971199001199051 cap 1198681198621198621198601) + P (1198681199041198971199001199051 cap 1198681198621198621198601))sdot P (1198781199041198971199001199051) + 119875119887119890119905119886119860119862119870 (44)

The event 1198681198621198621198601 occurs in four cases

Case 1 A busy slot before the idle CCA1 because of a failedpacket transmission due to collision this is represented by theprobability 119875119887119906119904119910119865119905 for node 119905Case 2 A busy slot before the idle CCA1 because of anacknowledgement following a successful data transmissionthis is represented by the probability 119875119887119906119904119910119860119905 for node 119905Case 3 A busy slot before the idle CCA1 because of asuccessful packet transmission where the idle slot is theinterframe space in between data and acknowledgement thisis represented by the probability 119875119887119906119904119910119878119905 for node 119905Case 4 An idle slot before the idle CCA1 happened afteran acknowledged successful transmission or an unacknowl-edged unsuccessful transmission this is represented by theprobability 119875119894119889119897119890119905 for node 119905

Substituting with these probabilities in (44) we have120573119905 = (1 minus 119875119887119906119904119910119865119905 + 119875119887119906119904119910119860119905 + 119875119887119906119904119910119878119905119875119887119906119904119910119865119905 + 119875119887119906119904119910119860119905 + 119875119887119906119904119910119878119905 + 119875119894119889119897119890119905 )sdot (1 minus prod119895isinΦ119905 119895 =BS

(1 minus 120591119895))+ 119875119887119906119904119910119860119905119875119887119906119904119910119865119905 + 119875119887119906119904119910119860119905 + 119875119887119906119904119910119878119905 + 119875119894119889119897119890119905

(45)

and the expressions which define these probabilities arepresented in Appendix B


(2) CAMEnd-to-EndAnalysis InCAM the packet generationrate 120582 at each node is equal in each time unit the network willhave the number of packets described by 120582 generated fromeach node the time unit described by 120582 equals multiples ofthe TSM frame greater than 120582multiplied by maximum num-ber of allowed hops through a sub-NW and in computingthe approximate value of the packet arrival rate at a node it isassumed that all the transmitted packets to this node will bedelivered successfully It is assumed that if the BS-neighborsnumber does not represent the larger share in a sub-NW theytransmit their packets directly to BS and are not allowed touse multihops The topology does not imply a specific formof doing aggregation the routing may determine that so noaggregation is assumed

Thenumber of the sub-NWnon-BS-neighbormembers isdenoted byI119900 and the number of the BS-neighbor membersis denoted by IBS The average packet arrival rate at the BS-neighbors 120582BS is greater than that of the non-BS-neighbors120582119900 as they represent the critical zone around the BS andit depends on both I119900 and IBS The whole path taken bya transmitted packet lies in a specific sub-NW except thelast hop where the last hop source which is a BS-neighborswitches its working channel to the working channel of theBS

Assume that a one hop of packets transmitted from eachnon-BS-neighbor node is completed approximately withina TSM frame time and when each node succeeds to sendits packet whether generated or forwarded it sends it toa receiver different from whom its peers send to whetherthis receiver is a BS-neighbor or not According to that atthe completion of one packet transmission from each nodethe non-BS-neighbor node will receive a number of packetsranges from 0 to (119897max minus 2) where 119897max is the maximum pathlength The final intermediate node is a BS-neighbor andthe average number of packets received by a BS-neighborin a completion of each non-BS-neighbor nodes one packettransmission is approximately equal to the number of non-BS-neighbors divided by the number of BS-neighbors in thesub-NW Based on the previous considerations the averagepacket arrival rates 120582119900 and 120582BS are computed as follows120582119900 = 120582(1 + lceilsum119897maxminus2

119909=0 119909119897max minus 1 rceil) 120582BS = 120582(1 + lceil I119900

IBSrceil) (46)

(a) Deriving Non-BS-Neighbor Different Associated Proba-bilities The probability of collision of a non-BS-neighbortransmitted packet depends on the number of non-BS-neighbors in its receiver neighborhood in its sub-NW andtheir values of 120591 For simplicity and to encounter the problemof hidden nodes to the transmitter it is assumed that all thenon-BS-neighbormembers always transmitwith its full range(or a range enough for covering the whole employed field)therefore no hidden nodes to the transmitter In case thereceiving node is a BS-neighbor the number of competingnodes119873119888119901 with a node tries to transmit will be equal to (I119900 minus

1) and in case of its being a non-BS-neighbor 119873119888119901 equals(I119900 minus 2) Under the previous assumptions the derivation of120572 120573 and 119875 for a non-BS-neighbor is turned to be the sameas followed in the single-hop communication analysis withnotations and values of variables indicate a non-BS-neighborin a sub-NW119875119900 = 1 minus (1 minus 120591119900)119873119888119901 120572119900 = (119871 + 119871119886119888119896(I119900120591119900 (1 minus 120591119900)I119900minus11 minus (1 minus 120591119900)I119900 ))

sdot (1 minus (1 minus 120591119900)I119900minus1) (1 minus 120572119900) (1 minus 120573119900) 120573119900 = 1 minus (1 minus 120591119900)I119900minus1 +I119900120591119900 (1 minus 120591119900)I119900minus12 minus (1 minus 120591119900)I119900 +I119900120591119900 (1 minus 120591119900)I119900minus1 (47)

(b) Deriving BS-Neighbor Different Associated ProbabilitiesThe probability of collision of a BS-neighbor transmittedpacket depends on the number of BS-neighbors in all thesub-NWs and their values of 120591 If the number of sub-NWsis denoted by 119873119904 then the number of BS-neighbors equalsIBS119873119904 some of them may be hidden to others where Φ119905BSrepresents the common neighbors between the BS-neighbor119905 and the BS andΦℎ119905BS represents the hidden BS-neighbors tothe BS-neighbor 119905 The probabilities 120572 120573 and 119875 are derivedin the same fashion as they are derived in case of slottedCSMACA except here there is no hidden acknowledgementthe set of all the children of the neighbor coordinatorscontains only the BS-neighbors and is defined by Φ119905BS cupΦℎ119905BS and successful concurrent transmissions from eventwo nodes do not exist

362 End-to-End Reliability Analysis The end-to-end relia-bility 119877e-to-e is the ANDing and in other words the productof the probabilities of successful packet reception at eachintermediate node in the considered path then to the BS

119877e-to-e = 119897prod119899=1

119877119899 (48)

where 119897 is the path length in terms of its incorporated nodesnumber excluding the final destination which is the BS 119877119899is the single-hop reliability of the transmitted packet by thenode number 119899 in the path then 1198771 is corresponding to thefirst node in the path which is the source node and 119877119897 iscorresponding to the last node in the path which is a BS childcoordinator

363 End-to-End Delay Analysis By ignoring the processingdelay the average end-to-end delay 119863e-to-e is the summationof the average delays for successfully delivering the packet(119863) at each node in the path including the PAN coordinator(BS) and the average queuing delay (119908 = (120582120583)(120583 minus 120582))at each intermediate node in the path where 120582 here refers


to the queue packet arrival rate and 120583 is the packet servicerate 119863e-to-e = 119897sum

119899=1

(119908119899 + 119863119899) (49)

The channel switching time is added to the end-to-enddelay in CAM case to incorporate the effect of a BS-neighborswitching to the BS channel to send its data to it (channelswitching time is approximately the transmission time of a32 byte (sim1ms) [37])

364 End-to-End Energy Consumption Analysis The totalenergy consumed to relay the packet through the pathtowards the BS is assumed to be the summation of the totalenergy consumed by each node in transmitting the packetto the next-hop node For simplicity the switching betweenfrequency channels is assumed to consume ignorable energy

119864e-to-e = 119897sum119899=1

119864119899 (50)

365 Network Throughput Analysis The normalized systemthroughput is defined and calculated here in the same wayused for single-hop analysis the difference is in the definitionof 119875119887119906119904119910 and 119875119904119906119888119888119890119904119904 If we denote the set of all nodes in thenetwork (except BS and PAN coordinator) byΦ119905119900119905119886119897 here119875119887119906119904119910 = 1 minus prod

119894isinΦ119905119900119905119886119897

(1 minus 120591119894) 119875119904119906119888119888119890119904119904 = sum119894isinΦ119905119900119905119886119897

119875119878119879119894119875119887119906119904119910 (51)

where 119875119878119879119896 as defined in Appendix B is the probability ofsuccessful transmission by a node

Anothermetric used tomeasure the network productivityis the goodput defined as the data bits successfully received atthe BS in one time unit The network goodput 119866 (in bitssec)is the summation of all nodes goodputs let 119874119899 be the set ofall possible paths for delivering data from node 119899 to the BSthen 119866 = (119871 times 20 times 4) sum

119899isinΦ119905119900119905119886119897

sum119903isin119874119899

119877e-to-e (119899 119903)119863e-to-e (119899 119903) (52)

4 Performance Assessment

This section assesses the performance of the proposedCAM First it tests the effect of different parameters on itsperformance then the performance of the proposed CAMis compared to the beacon-enabled IEEE802154 slottedCSMACA based on single-hop communication and finallythe multihop communication performance is consideredThe testsrsquo results were analyzed for better understanding fordifferent behaviors and getting observations and conclusionscan be used for modifications and optimizations

510

1520

25

12

34

= 3

= 4 = 5um

0

001

002

003

004

005

Relia

bilit

y

Figure 13119898 119906 and 120582 effect on CAM reliability

510

1520

25

12

34

= 3 = 4 = 5

um

5

10

15

20

25

30

Avg

del

ay (m

s)

Figure 14119898 119906 and 120582 effect on CAM avg delay

41 Effect of Parameters on the Proposed CAM PerformanceThe effect of the parameters 119898 traffic load represented by120582 and the tuning parameter 119906 on the average delay thereliability and the power consumption of the proposed CAMis studied in this section considering a sub-NW communica-tion example with number of nodes equal to 50 node119898119887 = 5and1198980 = 3

Figures 13 and 14 show that both the average delay and thereliability increase with the increase in119898 value while tuning119906 to a higher value decreases both of them For example whenthe value of119898 is increased from 1 to 4 at 120582 = 5 and 119906 = 5 thereliability increased by about 16781 at the same time thedelay is increased by about 1077 with adjusting the valueof 119906 the delay increment percentage could be reduced tobe 553 while the reliability still higher but with a smallerpercentage about 20 when 119906 equals 25

The change of 119906 value affects the possible values range ofthe backoff equation first term and causes the inverse effectto the range of the second term When 119906 is small the firstterm range is bigger than the second term range which resultsin higher reliability because the events of modulating thevalue of this ID-dependent term of the 50 different nodes tothe same value are smaller in this case and a greater spaceis left for different nodesrsquo IDs to differentiate their backoffsthe main principle that the backoff equation used to improvereliability even though the sum of the delays encounteredin backoff and channel sensing during the previous stages


510

1520

25

12

34

= 3 = 4

= 5

um

15

2

25

Pow

er co

nsum

ptio

n (m

W)

Figure 15119898 119906 and 120582 effect on CAM power consumption

(the backoff sum) is modulated in the second term to asmall range of possible values resulting in a higher percentageof recurrence for this term value This is at the expense ofincreasing the delay

Changing 119906 to higher values reduces the range of thefirst term value and increases the second term range whichaccording to the previously mentioned illustration decreasesboth reliability and delay by a percentage decreases with119898 increase The reduction percentage is decreased with 119898increase due to the salience of the second term effect ofimproving reliability at higher 119898 values also the delay isincreased in this case because the sum of the delays whichresulted from the previously encountered backoff stages isincreased and the modulus of the modulo operation deter-mines its range becomes greater

Changing 119906 to higher values increases the first term valuerecurrence percentage and decreases the second term valuerecurrence percentage When the second term recurrencepercentage approaches the first term recurrence percentageand then becomes less than it the reliability changes itsbehavior from the decrease to the increase this appearsas a convex curvature in the decayed reliability and delaycurvesWhen themaximumbackoff sum is decreased behindthe modulus of the second term and continues to decreasewith increasing 119906 at this point the reliability continues todecrease As shown in Figures 13 and 14 the increase of thetraffic load slightly decreases the reliability and very slightlyincreases the delay (almost no effect on the delay appears inthe figure)

With regard to the energy consumption the proposedCAM energy consumption takes the inverse behavior of thereliability with respect to 119906 such that under the conditionsof higher probability of collisions higher traffic load andhigher number of retransmissions the main componentswhich affect the total energy consumption are of the packettransmission stage which cause its increase The effect of theidle backoff state energy consumption appears when the timespent in backoff highly decreases when 119898 is small (119898 equals1 or less) 119906 is high and the traffic load is low

Generally from Figure 15 the energy consumptionincreases when 119898 increases from 1 to 2 due to the con-siderable increase of the backoff time (as 1198980 = 3 and

0

002

004

006

008

01

012

014

Relia

bilit

y

40 50 60 70 8030Number of nodes

Slotted CSMACA (m = 1)Slotted CSMACA (m = 2)Slotted CSMACA (m = 3)Slotted CSMACA (m = 4)

CAM (m = 1)CAM (m = 2)CAM (m = 3)CAM (m = 4)

Figure 16 Slotted CSMACA and CAM reliability versus numberof nodes

119898119887 = 5 the third backoff stage results in double therange of possible backoff periods of the second stage whilethe backoff periods are maintained on that range in thesubsequent backoff stages) and the increase in the numberof transmissionsretransmissions especially when the trafficload is low The increase of the 119898 value from the value 2increases the reliability and decreases the power consumedin the transaction states while increasing the backoff powerconsumption (with lower rate) making the total energy con-sumption amount tend to have converged magnitudes andbecome approximately steady with increasing119898 regardless ofthe traffic load and 11990642 Performance Assessment Based on Single-Hop Communi-cation Figure 16 shows the reliability of the proposed CAMand the IEEE802154 slotted CSMACA at different backoffstages drawn versus the number of nodes119873 Also Figures 1920 and 21 represent the same comparison but with respect tothe average delay the average energy consumption and thethroughput of the two protocols All values are correspondingto 119906 = 5 119898119887 = 5 1198980 = 3 119899 = 3 119871 = 7119878119887 and119871119886119888119896 = 17119878119887 As shown in Figure 16 the reliability of CAMwhich resulted from a certain value of 119898 is greater than theslotted CSMACA reliability which resulted from the same119898value with a big percentage on average 177 this percentageincreases when 119873 increases For example at 119898 equal to 3the reliability is increased by about 683 when 119873 is 30this percentage increases until it becomes greater than 200when 119873 exceeds 60 Also it could be noticed that lower119898 values cause in CAM network more reliability than thatcaused by higher119898 values in slotted CSMACA but rather asthe number of nodes increases the reliability of high119898 valuesin the slotted CSMACA is turned to be not only smaller thanits lower 119898 values CAM reliability but also smaller than thereliability of the two backoff stages CAM


30 40 50 60 70 80

Prob

abili

ty o

f disc

ardi

ng p

acke

ts

Number of nodes

075

08

085

09

095

1

due t

o ch

anne

l acc

ess f

ailu

re



Figure 17 119875119888119891 of slotted CSMACA and CAM versus number ofnodes

It is expectable to achieve more reliable communicationusing the proposed CAM as the implemented backoff mech-anism is designed to decrease the channel sensing overlapamong contending nodesThe CAM actually reduces the firstcarrier sensing probability in a randomly chosen time slot (120591)therefore the collision probability is reduced and accordinglythe probability of a packet being discarded due to reachingretry limits is reduced

Regarding the probability of discarding packets due tochannel access failure as shown in Figure 17 at a certain119898 value it is also reduced in CAM case with percentagedecreases with 119873 increase The approaching of the CAMand slotted CSMACA collision probability and probabilityof unsuccessful channel access (119909) in a backoff stage at higher119873 values causes the approaching of the CAM and CSMACAprobability of discarding packets due to channel access failureat higher119873 values As shown in Figure 18 119909 in CAM turns tobe greater than its CSMACA peer at higher 119873 values Thisis referred to the approaching of both of them 120572 value athigher119873 while the 120573 of CAM is greater than CSMACA dueto higher occurrence of acknowledgement transmissions

Figures 19 and 20 reveal that besides the increase of CAMreliability with fixing119898 value the energy consumptionwhichresulted from CAM network is smaller than CSMACA byon average 11 except for 119898 equal to 1 where CSMACAconsumes the less energy but this is at the expense of increasein the CAM average delay over CSMACA by on average426 The range of backoff values the nodes pick from inCSMACA is doubled each backoff stage until its maximumlimit reaches 2119898119887 minus 1 and then it stabilizes on this range InCAM the range of backoff values possible for nodes has theupper limit 2119898119887 minus 1 from the first stage (the same 119898119887 valueis reinvolved in both of them) which increases its averagedelay over CSMACA average delay corresponding to thesame119898 value However the decrease of CAM loss percentageappears in improving the throughput of the CAM networkeven though its delay is greater as shown in Figure 21 with

0875

0877

0879

0881

0883

0885

0887

0889

0891

Prob

abili

ty o

f uns

ucce

ssfu

l cha

nnel

acce

ss at

tem

pt




Figure 18 Slotted CSMACA and CAM probability of unsuccessfulchannel access versus number of nodes

0

5

10

15

20

25

30

35

40

Avg

del

ay (m

s)


Slotted CSMACA (m = 2)Slotted CSMACA (m = 1)Slotted CSMACA (m = 3) Slotted CSMACA (m = 4)

CAM (m = 2)CAM (m = 1)CAM (m = 3) CAM (m = 4)

Figure 19 Slotted CSMACA and CAM avg delay versus numberof nodes

fixing 119898 value and the CAM network throughput is greaterthan CSMACA by on average 1174

The increase percentage of the CAM average delay couldbe reduced by choosing the 119898 and 119906 values For exampleconsidering 119898 equal to 3 for slotted CSMACA in theprevious comparison setup as the reliability due to using 4backoff stages CAM is greater than the reliability of slottedCSMACA in the considered case by on average 1958 asshown in Figure 16 also the 3 backoff stages CAM resultsin reliability greater than it Then from Figures 16 19 and20 setting 119898 equal to 2 in CAM results in greater reliabilitygreater average delay and lower power consumption than 119898equal to 3 slotted CSMACA by on average 1363 84 and


30 40 50 60 70 80Number of nodes

0

05

1

15

2

25

Ener

gy co

nsum

ptio

n (m

w)



Figure 20 Slotted CSMACA and CAM energy consumption ver-sus number of nodes


0

005

01

015

02

025

03

Thro

ughp

ut



Figure 21 Slotted CSMACA and CAM throughput versus numberof nodes

145 respectively this means setting 119898 equal to 2 in theCAM results in small percentage of average delay increasewhile the reliability is high with a big percentage

Furthermore tuning the 119906 parameter via increasing itsvalue could reduce the delay more Figures 22 23 24 and 25compare theCSMACAperformance andCAMperformancecomputed for different higher values of 119906 at 119898119887 = 5 1198980 = 3119899 = 3 119871 = 7119878119887 and 119871119886119888119896 = 17119878119887 From Figure 22 itcould be noticed that when 119906 is set to 8 the CAM delay ison average greater by 49 and this percentage is reducedto be 225 when 119906 equals 11 while the average reliabilityin this case is still greater by about 984 and the average

35 40 45 50 55 60 65 70 75 8030Number of nodes

12

13

14

15

16

17

18

19

Avg

del

ay (m

s)

Slotted CSMACA (m = 3)CAM (m = 2 u = 5)CAM (m = 2 u = 8)

CAM (m = 2 u = 11)CAM (m = 2 u = 14)CAM (m = 2 u = 17)

Figure 22 Slotted CSMACA and CAM avg delay at different 119906values versus number of nodes

0

001

002

003

004

005

006

007

008

Relia

bilit

y

35 40 45 50 55 60 65 70 75 8030Number of nodes



Figure 23 Slotted CSMACA and CAM reliability at different 119906values versus number of nodes

energy consumption is 1317 lower Setting 119906 to 14 resultsin reducing the average delay of the CAM by about 212while the CAM reliability is still greater by 725 and CAMenergy consumption is less by 1194 Further increasing 119906more decreases CAM average delay as well as reliability forexample at 119906 equal to 17 we can obtain with CAMon averagea 6135 greater reliability 45 less delay 114 less powerconsumption and 878 greater throughput

Also the CAM delay which resulted from setting119898 equalto 3 could be tuned to be close to CSMACA delay but therest of CAM performance would be worse than that reachedfrom tuning CAM two backoff stages performance becausethe delay in this case is higher with a bigger percentage


14

15

16

17

18

19

2

21

22

Ener

gy co

nsum

ptio

n (m

w)

35 40 45 50 55 60 65 70 75 8030Number of nodes



Figure 24 Slotted CSMACA and CAM power consumption atdifferent 119906 values versus number of nodes

35 40 45 50 55 60 65 70 75 8030Number of nodes

0

005

01

015

02

025

Thro

ughp

ut



Figure 25 Slotted CSMACA and CAM throughput at different 119906values versus number of nodes

about 376 When 119906 is set to 23 the delay reaches 49increase percentage and the CAM reliability increase andenergy consumption reduction percentages are 212 and212 respectively Setting 119906 to 26 decreases both the delayand the reliability and increases the energy consumption ofthe CAM over the CSMACA

43 Tuning the 119906 Value For finding the best 119906 value to agiven performance objective the following analysis describeswith more details the effect of the whole range of possible119906 values which is [0 31] for 119898119887 = 5 on the performanceof CAM at different parametersrsquo values and compares itto the CSMACA performance under the same conditions

Each subfigure in Figure 26 sketches one performancemetricfor both CAM indicated by solid lines and the slottedCSMACA indicated by dashed lines computed for differentvalues of 119906 and119898 at certain value of119873 The variability of thebackoff time values has the biggest effect in determining thebehavior of CAM reliability and accordingly the delay andenergy consumption For the communication not to BS thereis no recurrence of the possible values of the backoff equationfirst term without modulation due to the modulation used init up to a certain limit 119906119871 equal to (32minus119873minus119898) After this limitthe range of the possible values for the first termdecreases andthe recurrence of backoff values among nodes increases

The recurrence in the second term of the equation ismaximal at 119906 = 0 then it takes to decrease as 119906 increasesup to a certain limit 1199061015840119871 equal to the minimum value greaterthan the maximum backoff sum minus one subtracted fromit one Thus for 119873 less than or equal to 32 minus 119898 the generaltendency of the reliability curve is to increase with increasing119906 at lower 119906 values and decreases with increasing 119906 at higher119906 values

Between the start with increase and the ending withdecrease the reliability behavior at intermediate 119906 valuesdepends on 119906119871 and 1199061015840119871 If 1199061015840119871 is less than 119906119871 the reliabilityincreases up to 1199061015840119871 then over the values of 119906 between the twolimits the reliability stabilizes on a constant value because inthis case there is no recurrence neither in the first term valuenor in the second term value and the maximum backoff sumis constant after 119906119871 the reliability decreases This could benoticed in the constant reliability between 1199061015840119871 and 119906119871 for 119873less than or equal to 15 at 119898 equal to 1 and 119873 less than orequal to 6 at119898 equal to 2

When 119906119871 is less than 1199061015840119871 the interval between themencounters an increase in first term value recurrence and adecrease in the second term value recurrence this causeswith general decaying behavior the previously mentionedcurvatures in the reliability curve depending on the relativevalues of the recurrence percentage in the two terms and themaximum backoff sum values or in better words dependingon the probability of being in the backoff state

The 119898 = 1 backoff stage causes the existence of 119906119871 itsvalue decreases by 1 for each 119873 increment until it reaches 0at 119873 equal to 31 The value of 119906119871 in each subsequent valueof 119898 is less by one than its value at the direct previous 119898value that is the 119906119871 value reaches 0 at119873 equal to 30 when119898equals 2119873 equal to 29when119898 equals 3 and so forth1199061015840119871 valueincreases with119873 increase and up to a certain119873 it stabilizeson its reached value When 119898 equals 1 1199061015840119871 increases until 119873equals 15 then it takes a constant value of 16 At119898 equal to 2and119873 equal to 6 1199061015840119871 stabilizes on the value of 24The limit 1199061015840119871at119898 equal to 3 and 4 is always constant on the values 28 and30 respectively

Exception to the previously mentioned general behaviorit is noticed that at high 119906 values when 119898 equals 1 (alsowhen 119898 = 2 but with feeble emergence) the reliabilityincreases rather than its expected decrease As stated beforethe backoff state is the dominant factor which determinesthe reliability behavior when it increases the first carriersensing probability in a randomly chosen time slot decreasesas a result the sensing overlap decreases and the reliability


transmission not to BSAt N = 5 = 3 pps




transmission not to BSAt N = 32 = 3 pps transmission not to BSAt N = 32 = 3 pps transmission not to BSAt N = 32 = 3 pps

transmission not to BSAt N = 15 = 3 pps transmission not to BSAt N = 15 = 3 pps




5 10 15 20 25 300u

05055

06065

07075

08085

Relia

bilit

y

5 10 15 20 25 300u

456789

1011121314

Avg

del

ay (m

s)

3638

442444648

552

Avg

ener

gy co

nsum

ptio

n (m

w)

5 10 15 20 25 300u

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10121416

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442444648

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5 10 15 20 25 300u

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02025

03035

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del

ay (m

s)

5 10 15 20 25 300u

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222242628

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ener

gy co

nsum

ptio

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w)

0002004006008

01012014

Relia

bilit

y

5 10 15 20 25 300u

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20

25

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del

ay (m

s)

5 10 15 20 25 300u

5 10 15 20 25 300u

112141618

222242628

3

Avg

ener

gy co

nsum

ptio

n (m

w)

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2 m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 3

m = 3 m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 4

m = 4

m = 4m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4m = 4

m = 4

m = 4

m = 4

Figure 26 CAM and slotted CSMACA performance over the whole range of the 119906 valueof the transmitting node increases and vice versa This isespecially when119898 is higher that is the node stays more timein backoff states The staying in the idle state at the queuein contrary to the staying in the backoff state increases withincreasing 119906 as themean packet service times of the nodes are

decreased At high119906 values low119898 values (119898 = 1) and small120582(this exception is vanishing with increasing 120582) the queue idlestate dominates affecting the first carrier sensing probabilityin a randomly chosen time slot therefore this probabilityis decreased even though the backoff times variability is


decreased this illustrates the exceptional increase behavior ofthe reliability at high 119906 values and119898 equal to 1 which gives thepossibility in some cases to have higher reliability while boththe delay and energy consumption are highly decreasing

The CAM performance behavior can be described forthe nodes to be used as an indication for the expected per-formance under certain conditions to help for dynamicallychanging performance settings by using lookup tables curvefitting approximation based on the determinable behaviormentioned before for the reliability with the backoff timevalues or by some other means For example let 119873 equal10 and reliability delay and energy consumption curvescan be fitted to construct their representative mathematicalfunctions for best fit each curve can be considered uponmore than one interval of 119906 values For example the whole 119906range is divided into four intervals each curve correspondingto an interval is fitted in a separate equationwith a low degreeFrom these equations the node computes the performanceindications corresponding to certain 119898 and 119906 and optimizesthe performance upon given requirements such as a referenceperformance values a specific metric to be optimized andpercentages for optimizing the specified metric and permit-ting for resultant degradation in the other metrics

Let the reference performance be the correspondent tothe current values of 119898 = 2 and 119906 = 20 and forsome reasons such as frequent loss of acknowledgementsa need for increasing reliability becomes desirable with aspecified percentage 5 on condition that the delay andenergy consumption do not increasewithmore than the samepercentage other performance variations and tolerances canbe employed to deal with the situation where the mainlyrequired performance specification cannot be achieved Inthis case the resultant values of 119898 and 119906 which achievethe required or the acceptable performance are 3 and 25respectivelyWhen the delay is the parameter to be optimizedutilizing the same previous percentages the resultant valuesof 119898 and 119906 in this case are 3 and 27 respectively Alsofor some reasons such as the falling of the battery levelbelow a threshold or the occurrence of a deviation from adetermined power consumption behavior the optimizationcould be directed for example to reach the lesser energyconsumption value possible regardless of the other metricsvalues which in this case is corresponding to 119898 = 1 and119906 = 3144 Performance Assessment Based on Multihop Communica-tion Theprevious evaluation reveals that the required single-hop performance of CAM against the slotted CSMACAcan be obtained by choosing the 119898 and 119906 values andthat CAM performs more better than slotted CSMACA inlarger number of nodes The comparisons performed in thissection are based on the analysis presented in Section 36 formultihop performance and on the small network examples ofFigure 12 For example Node 16 in the cluster-tree network iscorresponding to the following setsΦ16= 1 3 4 5 8 9 12 13 14 15 17 19 20 22

Φ16119888= 1 3 4 5 Φ16 4= 1 3 5 8 9 12 13 14 15 17 19 20 22 Φℎ16 4 = 0 2 21 Φℎ11988816 4 = 0 2 11986216 = 4 1205950 = 1 4 1205951 = 12 14 15 1205952 = 7 11 18 1205953 = 6 13 22 24 1205954 = 5 8 16 17 1205955 = 2 3 9 19 20

(53)

The transmission level used in the employed networkexample for the sub-NWsrsquo BS-neighbors communicationwith the BS results in the existence of no hidden nodes Noaggregation is assumed The nodes were deployed randomlytherefore their IDs are randomly distributed throughoutthe area ditto the aliases of a sub-NWrsquos members are alsorandomly distributed throughout its area The CAM backoffperiods are computed within a sub-NW using the aliasesrather than the IDs while the IDs are used in backoffcomputation for the communication with the BS to cope withthe repetition of aliases in different sub-NWs It is worthnoting that the communication to the BS in the CAM hasa different backoff probability distribution as indicated inSection 341 in Definitions 6 and 7

The following analysis compares the end-to-end perfor-mance of CAM and the slotted CSMACA In CSMACAnetwork different samples of the whole network members(14 15 16 or 17 node) are considered in computing its per-formance for decreasing computation time and coping withthe limitation of the used function nchoosek for computingneighborsrsquo different combinations which is only practical forsituations where the input vector length is less than about 15then for each node the performance corresponding to thelowest reliability is taken into account

The value of 119898 in the CSMACA network is randomlyselected to be 2 the CAM network needs identification of119898 and 119906 values which achieve a required performance withrespect to this setting of the CSMACA network Accordingto the network example the values of I119900 IBS and119873119904 are 62 and 3 respectively 119897max was chosen to be 4 and 120582 was setto 3 pps Other parameters were set like that 119898119887 = 5 119899 = 3119871 = 7119878119887 and 119871119886119888119896 = 17119878119887 By setting these parameters tothese values in the analysis computing and comparing theperformance of CSMACA and CAM over the whole rangeof possible 119906 values based on one-hop communication asdone in Section 43 that is the same number of competing


nodes used in CAM is used for CSMACA the same 120582 isused and no hidden terminal is considered for both Theobtained results are used as guiding values for determiningthe values of 119898 and 119906 for the employed example whichincorporates variations on the communication parametersnot only between the two networks but also for differentnodes in each network due to the nature of multihopcommunication

For the communication between the BS-neighbors andthe BS two combinations of 119898 and 119906 are chosen to achievethe acceptable CAM performance with respect to CSMACAregarding the reliability and delay 4 and 31 respectively thiscombination is found to increase CAM reliability by about13 over CSMACA while its delay is greater by only about22 The other combination is 6 and 31 this combinationis found to increase CAM reliability by about 434 but atthe same time increases CAM delay by about 409 thiscan be considered to be acceptable as the reliability metricat the BS is more important and this large delay can bedealt with decreasing the previous hops delay along theremaining multihop path For the communication amongthe sub-NW members when the receiver is a BS-neighborsix combinations for 119898 and 119906 are chosen 1 and 31 4 and31 4 and 30 3 and 29 3 and 26 and 2 and 22 Whenthe receiver is a non-BS-neighbor four combinations for119898 and 119906 are chosen 1 and 31 4 and 31 4 and 30 and3 and 30 The effects of these combinations vary amongreducing both CAM reliability with small percentage anddelay with high percentage increasing both with a relativelyhigher percentage for the reliability very slightly increasingreliability while decreasing delay with a relatively higherpercentage and very slightly decreasing delay with increasingreliability by a relatively higher percentageThis optimizationis only based on the reliability and delay regardless of thepower consumption

Mixtures of these 119898 and 119906 combinations were used inthe considered example analysis and the following figureswere obtainedwhich represent the different variations of theirbehavior for one-hop path up to four-hop path Each valuecorresponding to 119899-hop path represents the average of valuesof all the possible 119899-hop paths in the network

As mentioned before the CAM offers communicationreliability greater than IEEE slotted CSMACA exposed tothe same conditions while the multihop communicationintroduces additional loads on the IEEE network representedby a wider neighborhood even though the used transmissionrange is smaller than CAM and the collisions due to hiddenterminals These factors participate in decreasing the IEEEslotted CSMACA reliability more than the estimated whenthe values of119898 and 119906 were being selected The one-hop pathdelay of CAM is greater than its value of slotted CSMACAas the concentration was on increase the reliability at the BSeven at the expense of the delay also the channel switchingtime at the BS-neighbor contributes in increasingCAMdelayAs the length of the path in terms of hops number becomesgreater the CAM end-to-end delay falls below the slottedCSMACA the start and percentage of this falling dependon the 119898 and 119906 combinations used for sub-NW membersrsquocommunication

1 2 3 4Number of hops

IEEE slotted CSMACA

0

01

02

03

04

05

06

07

08

End-

to-e

nd re

liabi

lity

CAM 431-131-131CAM 431-430-131

CAM 631-430-131CAM 631-131-131

Figure 27 End-to-end reliability versus number of hops

As shown in Figure 27 CAM 631-430-131 where eachpair represents 119898 and 119906 for BS-neighbor to BS-neighborand not BS-neighbor communications respectively resultsin the higher reliability percentage over all path lengthsstarting with a percentage greater than 100 for one-hoppath increases for lengthier paths But the CAM delay inthis case is also greater by about 54 for one-hop paththis percentage decreases until it reaches 20 less than IEEEslotted CSMACA delay From Figures 27 and 28 the CAM431-131-131 could be chosen to be the combinations whichachieve the most preferable CAM performance with respectto end-to-end reliability and delay where the reliability of theone-hop path is greater by about 46 and this percentageincreases more than 100 for more lengthier paths at thesame time theCAMend-to-enddelay is greater only by 147for the one-hop path from the two-hop path it starts todecrease with percentage which reaches 41 for the four-hoppath

Also under the selected 119898 and 119906 values for best per-formance Figures 29 and 30 declare that CAM networkutilizes on average 80 of the channel time in transmittinguseful data while slotted CSMACA network utilizes about42 of the time besides that the CAM multihop networkdelivers data bits to the BS with rate equal to multiples of theCSMACA network data delivery rate The subnetworkingnature of CAM network and its support for multipathcommunication aid more in improving its performance withrespect to throughput and goodput

The CAM exhausts more energy to achieve this per-formance in channel sensing waiting acknowledgementreceiving acknowledgement and longer backoff time at theBS-neighbors The most important factor which increasesCAM energy consumption over the IEEE slotted CSMACAas shown in Figure 31 is the energy consumed in transmis-sion in IEEE network the probability of successful channelaccess is smaller which decreases transmission chances and



000E + 00

100E + 01

200E + 01

300E + 01

400E + 01

500E + 01

600E + 01

End-

to-e

nd d

elay

(ms)

IEEE slotted CSMACACAM 431-131-131CAM 431-430-131

CAM 631-430-131CAM 631-131-131

Figure 28 Avg end-to-end delay versus number of hops

Slotted CSMACAnetwork example

CAM network example0

01

02

03

04

05

06

07

08

09

Aver

age n

etw

ork

thro

ughp

ut

Figure 29 Multihop network throughput

accordingly the energy consumed in the transmit state Alsothe refuge of the non-BS-neighbors in CAM to transmit witha greater transmission level contributes in increasing its end-to-end energy consumption

5 Conclusion and Future Work

This paper deals with completing the design of our previouslyproposed MAC by designing a contention-based channelaccess mechanism (CAM) suitable to the previously estab-lished logical topology and timing structure mechanismTheCAM is based on developing a backoff mechanism whichcan be performed via multiple stages and allowing multipletransmission trialsThe backoff equation differentiates nodesrsquobackoff times depending on their different identificationnumbers (IDs) bearing a consideration for achieving fairnessamong nodes and taking into account the avoidance of errorrepeating after a sensing overlap increasing the possiblebackoff values range each backoff stage and the possibleoccurrence of sensing overlap due to the computed backoffvalues themselves while the times of having data are different



50

100

150

200

250

Net

wor

k go

odpu

t (bi

tms)

Figure 30 Multihop network goodput


IEEE slotted CSMACA

000E + 00

500E + 00

100E + 01

150E + 01

200E + 01

End-

to-e

nd p

ower

cons

umpt

ion

(mW

)

CAM 431-131-131CAM 431-430-131

CAM 631-430-131CAM 631-131-131

Figure 31 Avg end-to-end power consumption versus number ofhops

and limiting the backoff time to a certain maximum limitregardless of the IDs and other incorporated variablesrsquo valuesA performance tuning parameter ldquo119906rdquo which controls themaximum value of each term of the backoff equation isemployed

This backoff idea is clarified using simple assumption-based simulation scenarios then the probability distributionof the backoff period generated by a node in different backoffstages is constructed and theMarkov chain modeling is usedto analyze and evaluate the CAM against the IEEE802154slotted CSMACA based on single-hop and multihop com-munication with respect to the reliability the average delaythe power consumption and the throughput

Changing the value of the parameter 119906 is already foundto tune these mentioned performance metrics tradeoffsmaking it possible to reach a required performance objectiveor set different modes of operation for example a directtransmission mode a zero-backoff mode and a highest-reliability mode by choosing variablesrsquo values such as backoffstages number 119906 and CCAs number Likewise adaptability


and dynamic performance adjustment could be achieved bydescribing the computed CAM performance to nodes insome way

The CAM analysis reveals that the required performanceof CAM against the IEEE slotted CSMACA can be obtainedby choosing the backoff stages number and 119906 values andthat CAM performs richly better than the IEEE with largernumber of nodes In the single-hop communication scenarioselecting the backoff stages number to be 3 for slottedCSMACA and selecting the CAM backoff stages numberand 119906 to be 2 and 11 respectively and with increasingnodes number achieve average of 984 higher reliability and1317 smaller energy consumption of CAM while CAMdelay is greater by 225 Tuning 119906 to higher values furtherreduces the delay when 119906 is 17 we can obtain with CAM a6135 greater reliability 45 less delay and 114 less powerconsumption

New analysis implementation is derived for the multihopnetwork considering the effect of different classes of neigh-borhood the probability of collision due the hidden terminalsdata and acknowledgements and different packet arrival ratefor each node The solutions obtained for each single-hopare appropriately merged to obtain the end-to-end multihopperformance Mixtures of chosen backoff stages number and119906 combinations are used in the multihop scenario for thecommunication between the BS-neighbors and the BS andthe communication among subnetwork members One ofthese mixtures is chosen to be of the most preferable CAMperformance where the reliability of one-hop path is greaterby about 46 and this percentage increases more than 100for more lengthier paths at the same time the CAM end-to-end delay is greater only by 147 for one-hop path fromtwo-hop path it starts to decrease with percentage reaches41 for four-hop path but this is achieved at the expense ofconsuming more energy

Other optimizations on the proposed CAM can be direc-tions for future workThe formulation of the backoff equationitself can be optimized for offering better performance Themodeling and analysis of CAM can be enhanced to considerfor example different values for the 119898119887 variable The testsrsquoconditions would be varied The devised model supportsusing different 119906 values only per single-hop supportingdifferent 119906 values per node which would be a possiblefuture optimization enhances the dynamism of performanceadjustment Also more accurate comprehensive and simplerepresentation to the nodes of the derived performance tun-ing schemes is an enhancementwhich needs to be researched

Appendix

A Simpler Representation of BackoffPeriodsrsquo Occurrence Number

The backoff values computed from the proposed backoffequation under certain conditions can take a simpler and

regular pattern facilitates finding a simple relation betweenthe number of backoff valuesrsquo occurrence times and the othervariables such that this number can be computed from itdirectly without experiencing looping computation or withattenuating the obligation for using loops

Up on the observation on the pattern of the num-ber of backoff valuesrsquo occurrence times when the backoffstage number equals 0 for both the communication to BS(bsknum(119896 0)) and within the sub-NW (knum(119896 0)) thefollowing equations are derived

range (119873) = 119873 if 119873 lt 21198981198872119898119887 otherwise (A1)

For every 119906 lt 2119898119887 minus 119873 we have

knum (119896 0) = 119873 minus 1 if 119896 isin [1 range (119873)]0 otherwise (A2)

for every 119906 = 2119898119887 minus 119873 we have

knum (119896 0) = 119873 minus 1 if 119896 le range (119873) minus 10 otherwise (A3)

for every 119906 gt 2119898119887 minus 119873 we have

knum (119896 0)= (119873 minus 1) (1 + lfloor119873+119906 minus 2

1198981198872119898119887 minus 119906 rfloor) + f (119896) if 119896 le 2119898119887 minus119906minus10 otherwise (A4)

where

f (119896)= 119873 minus 1 if 0 lt 119896 le (119873 + 119906 minus 2119898119887)mod (2119898119887 minus 119906)0 otherwise (A5)

The following equations are derived for computing thenumber of backoff valuesrsquo occurrence times in the secondthird and forth backoff stages 119878 isin [1 3] in case thecommunication is to BS (bsknum(119896 119878))


bsknum (119896 119878) = 2119878sum119862119862119860119888119900119898119887=1

1 iff 119896 = 119868119863mod (2119898119887 minus 119906) + (sumfn (119878 119862119862119860119888119900119898119887 119868119863))mod (119906 + 1) (A6)

where

sumfn (119878 119862119862119860119888119900119898119887 119868119863)=

119872119894119899119861119865119904119906119898119879119890119903119898 if 119862119862119860119888119900119898119887 == 1 and 119868119863mod (2119898119887 minus 119906) == 1sumfn (119878 2119878 119868119863 minus 1) if 119862119862119860119888119900119898119887 == 1 and 119868119863mod (2119898119887 minus 119906) gt 1119879119903119894119892119892119890119903119861119865119904119906119898119879119890119903119898 if 119862119862119860119888119900119898119887 == 1 and 119868119863mod (2119898119887 minus 119906) == 0sumfn (119878 119862119862119860119888119900119898119887 minus 1 119868119863) + even (119862119862119860119888119900119898119887) + h (119862119862119860119888119900119898119887 119878) otherwise

119872119894119899119861119865119904119906119898119879119890119903119898 =

2 if 119878 == 1 and 119906 = 2119898119887 minus 12119878 + 119878minus1sum119899=1

f (119899) if 119878 = 1 and 119906 = 2119898119887 minus 11 if 119878 == 1 and 119906 == 2119898119887 minus 1119878 + 12 119878minus1sum119899=1

f (119899) if 119878 = 1 and 119906 == 2119898119887 minus 1f (119899) = (f (119899 minus 1) + 2119899)mod (119906 + 1) f (0) = 0119879119903119894119892119892119890119903119861119865119904119906119898119879119890119903119898 =

1 if 119878 = 1119878 + 119878minus1sum119899=1

g (119899) otherwiseg (119899) = (g (119899 minus 1) + 119899)mod (119906 + 1) g (0) = 0h (119862119862119860119888119900119898119887 119878) = (119878 == 3) times ((119862119862119860119888119900119898119887 == 3) times (1199001 minus 119906 times (1199002 + 1199003)) + (119862119862119860119888119900119898119887 == 5) times (minus119906 times (1199005 + 1199006 + 1199007) minus 1199004)minus (119862119862119860119888119900119898119887 == 7) times 119906 times (1199008 + 1199009)) minus (119878 == 2) times (119862119862119860119888119900119898119887 == 3) times 11990010 times 119906 + (119878 == 3) times ((119862119862119860119888119900119898119887 == 3)times ( (1199001 + 1199002 + 1199003)) + (119862119862119860119888119900119898119887 == 5) times ( (1199004 + 1199005 + 1199006 + 1199007)) + (119862119862119860119888119900119898119887 == 7) times ( (1199008 + 1199009))) + (119878 == 2)times (119862119862119860119888119900119898119887 == 3) times (11990010) 1199001 = 1 if 3 | (119906 minus 2)0 otherwise1199002 = 1 if (119906 + 1) | (119868119863mod (2119898119887 minus 119906) + (23) (119906 + 3)) and 3 | 1199060 otherwise1199003 = 1 if (119906 + 1) | (119868119863mod (2119898119887 minus 119906) + (13) (119906 + 5)) and 3 | (119906 minus 1)0 otherwise


1199004 = 1 if 119906 = 00 otherwise1199005 = 1 if (119906 + 1) | (119868119863mod (2119898119887 minus 119906) + 2) and 119906 = 00 otherwise1199006 = 1 if (119906 + 1) | (119868119863mod (2119898119887 minus 119906) (13) (2119906 + 7)) and 3 | (119906 minus 1)0 otherwise1199007 = 1 if (119906 + 1) | (119868119863mod (2119898119887 minus 119906) + (13) (119906 + 6)) and 3 | (119906 minus 3)0 otherwise1199008 = 1 if (119906 + 1) | (119868119863mod (2119898119887 minus 119906) + 2) and 3 ∤ (119906 minus 2)0 otherwise1199009 = 1 if ((119906 + 1)3 ) | (119868119863mod (2119898119887 minus 119906) + 2) and 3 | (119906 minus 2)0 otherwise11990010 = 1 if (119906 + 1) | (119868119863mod (2119898119887 minus 119906) + 2)0 otherwise

(A7)

The symbols and | ∤ and indicate ldquological andrdquo ldquodividesrdquoldquodoes not dividerdquo and ldquological negationrdquo respectively

B Derivation and Representation ofSome Terms

First we define the notation 119875119878119877ℎ119905 in the equation of 119875119862ℎ119860119888119896119905which represents the probability of successful data receptionat the hidden coordinators from a transmitter 119905 the probabil-ity 119875119878119877ℎ119905 is given by (B1) where 119875119878119879119896 represents the proba-bility that a node 119896 transmits to its coordinator (or its receivergenerally) successfully without collision due to concurrentchannel sensing hidden data or hidden acknowledgementThe 119875119878119877ℎ119905 equation considers the fact that there may be

more than one successful reception at the coordinators at thesame time that is more than one child can send to theircoordinators successfully at the same time if each one doesnot exist in the neighborhood of the other coordinators

Also the equation considers the different degrees ofnodes with respect to a transmitting node some nodes willrepresent its neighborhood Φ119905 some others are hidden fromit Φℎ119905119903 and the others are neither neighbors (notin Φ119905) norhidden (notin Φℎ119905119903) for each node degree the event representsa transmission causing a hidden acknowledgement collisionwhich occupies from the channel time different averageperiods accordingly the combinations of such events ofdifferent degrees occurring at the same time occupy differentaverage periods determined by the smallest period occupiedby an involved event

119875119878119877ℎ119905 = (119871119886119888119896 + 119871) sum119899isinΦℎ119888119905119903

sum119896isin120595119899119896notinΦ119905119896notinΦℎ119905119903

119875119878119879119896 + 119871119886119888119896 sum119899isinΦℎ119888119905119903

sum119896isin(120595119899capΦℎ119905119903)

119875119878119879119896 + sum119899isinΦℎ119888119905119903

sum119896isin(120595119899capΦ119905)

119875119878119879119896 minus (119871119886119888119896 + 119871) |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1

prod119899isinℎ119898

ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902

sequence of terms=119902

( sum119896isin120595119899 119896notinΦ119905119896notinΦℎ119905119903

119896notin((Φℎ1198981cupΦℎ1198982cupsdotsdotsdotcupΦℎ119898119902 )Φ119899)

119875119878119879119896)minus 119871119886119888119896 |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1

sum119899isinℎ119898

ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902

summation term=119902 product terms

(( sum119896isin(120595119899capΦℎ119905119903)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911 119896notinΦ119905


119875119878119879119896))


minus |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


(( sum119896isin(120595119899capΦ119905)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911


119875119878119879119896))(B1)

119875119878119879119896 = 120591119896 prod119895isinΦ119896119899

(1 minus 120591119895) (1 minus 119875119862ℎ119863119886119905119886119896) (1 minus 119875119862ℎ119860119888119896119896) (B2)

The 119875119878119877119905 in the equation of 1205722119905 represents the probabilityof successful data reception at the coordinators in transmitter119905 neighborhood that is the probability of at least one of the nonmutually exclusive events of children successful transmis-

sions to the transmitter 119905 neighborhood coordinators occursThe probability 119875119878119877119905 is given by

119875119878119877119905 = 119871119886119888119896( sum119899isinΦ119905119888

sum119896isin120595119899119896 =119905

119875119878119879119896 minus |Φ119905119888 |sum119902=2

(minus1)119902 |Φ119905119888 |119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


( sum119896isin120595119899 119896 =119905


119875119878119879119896)) (B3)

where |Φ119905119888 |119862119902 represent the 119902-combinations from neighborcoordinators of 119905

Last expressions presented in this appendix are related tothe probabilities deriving 120573119905 and they are

119875119887119906119904119910119878119905 = sum119896isinΦ119905119896 =BS

119875119878119879119896 minus |119862|sum119902=2

(minus1)119902sdot |119862|119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982ℎ119898119902


( sum119896isin(120595119899capΦ119905)


119875119878119879119896)119875119887119906119904119910119865119905 = (1 minus prod

119895isinΦ119905119895 =BS(1 minus 120591119895))

sdot (1 minus 1198751198871199061199041199101198781199051 minus prod119895isinΦ119905119895 =BS (1 minus 120591119895)) = 1 minus prod119895isinΦ119905119895 =BS

(1 minus 120591119895)minus 119875119887119906119904119910119878119905 119875119887119906119904119910119860119905 = 119875119878119877119905119871119886119888119896

(B4)

The probability 119875119894119889119897119890119905 of an idle slot1 before the idleCCA1 happened when slot 119894 1 le 119894 lt infin is preceded by

a transmission and no node senses the channel from slot 119894until CCA1 then119875119894119889119897119890119905 = (1 minus prod

119895isinΦ119905119895 =BS(1 minus 120591119895))

sdot infinsum119894=1

((1 minus 120591119905) prod119895isinΦ119905119895 =BS

(1 minus 120591119895))119894minus1

= 1 minus prod119895isinΦ119905119895 =BS (1 minus 120591119895)1 minus (1 minus 120591119905)prod119895isinΦ119905119895 =BS (1 minus 120591119895) (B5)

Notations120572 The probability of finding the channel busyin the 1st clear channel assessment (CCA1)120573 The probability of finding the channelbusy in the 2nd clear channel assessment(CCA2)120591 The probability that a node attempts a firstcarrier sensing in a random time slot1199020 The probability of going back to state 1198760120582 Packet generation rate used with anappropriate subscript to indicate thepacket arrival rate at the MAC queue120583 Packet service rate119875 The probability that a transmitted packetencounters a collision

30 Wireless Communications and Mobile Computing119877 The reliability119875119888119891 The probability that the packet is discardeddue to channel access failure119875119888119903 The probability of a packet being discardeddue to retry limits119863 The average delay119864 The average energy consumption

P() Probability of an event119871 119904 The time period for successful transmission119871119888 The time period for failed transmission1198710 The idle state length without generatingpackets119871 The length of data packet119871119886119888119896 The length of acknowledgement119878119887 The time unit aUnitBackoffPeriod119898 The maximum backoff stages number119864[119879ℎ] The expected total backoff delay119864[119878] Mean packet service time119862120572120573(119894) All possibilities of choosing 119894 elements from aset of busy channel probabilities (1 minus 120572)120573 120572119862119890120572120573(119894) One of the elements in the set 119862120572120573(119894)119873119890

120572(119894)119873119890120573(119894) Return the number of 120572 and (1 minus 120572)120573 in119862119890120572120573(119894) respectively119879119904119888 The CCA time

I Used to indicate the size of a specific subsetof nodes such as number of end devices in acluster and the number of the BS-neighborsin a sub-NW with a subscript whichidentifies this subset informationΦ Used to define sets of nodes distinguish thedifferent degrees and effects of neighborhood(neighbor common neighbor hidden etc)with a subscript which identifies this setinformation120595119888 The set of coordinator 119888 children119862119905 119862 The coordinator of node 119905 and the set of allcoordinators respectively

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] R Adhikari ldquoA meticulous study of various medium accesscontrol protocols for wireless sensor networksrdquo Journal ofNetwork and Computer Applications vol 41 no 1 pp 488ndash5042014

[2] A Ali H Wang H Lv and X Chen ldquoA survey of MACprotocols design strategies and techniques in wireless ad hocnetworksrdquo Journal of Communications vol 9 no 1 pp 30ndash382014

[3] D Wong Q Chen and F Chin ldquoDirectional Medium AccessControl (MAC) protocols in wireless ad hoc and sensor net-works a surveyrdquo Journal of Sensor and Actuator Networks vol4 no 2 pp 67ndash153 2015

[4] M Doudou D Djenouri N Badache and A BouabdallahldquoSynchronous contention-based MAC protocols for delay-sensitive wireless sensor networks a review and taxonomyrdquoJournal of Network and Computer Applications vol 38 no 1 pp172ndash184 2014

[5] C K Sonkar O P Sangwan and A M Tripathi ldquoComparativeanalysis of contention based medium access control protocolsforwireless sensor networksrdquo inQuality Reliability Security andRobustness in Heterogeneous Networks vol 115 of Lecture Notesof the Institute for Computer Sciences Social Informatics andTelecommunications Engineering pp 86ndash103 Springer BerlinGermany 2013

[6] T S Lin H Rivano and F Le Mouel ldquoPerformance com-parison of contention- and schedule-based mac protocols inurban parking sensor networksrdquo in Proceedings of the ACMInternational Workshop on Wireless and Mobile Technologies forSmart Cities (WiMobCity rsquo14 ) pp 39ndash48 Philadelphia PaUSAAugust 2014

[7] P K Pal and P Chatterjee ldquoA survey on TDMA-based MACprotocols for wireless sensor networkrdquo International Journal ofEmerging Technology and Advanced Engineering vol 4 no 6pp 219ndash230 2014

[8] T Adamson D Archer D Avery et al IEEE Standard 802154for Information TechnologymdashTelecommunications and Informa-tion Exchange between SystemsmdashLocal and Metropolitan AreaNetworksmdashSpecific Requirements Part 154 Wireless MediumAccess Control and Physical Layer Specification vol 802154 ofEdited by Michael P G McInnis D Gutierrez J A BourgeoisM Moridi S Jamieson P Breen G Callaway The Institute ofElectrical and Electronics Engineers NewYork NY USA 2003

[9] M M Chandane S G Bhirud and S V Bonde ldquoPerformanceanalysis of IEEE 802154rdquo International Journal of ComputerApplications vol 40 no 5 pp 23ndash29 2012

[10] W Yuan X Wang J-P M G Linnartz and I G MM Niemegeers ldquoCoexistence performance of IEEE 802154wireless sensor networks under IEEE 80211bg interferencerdquoWireless Personal Communications vol 68 no 2 pp 281ndash3022013

[11] B M El-Basioni A I Moustafa S M El-Kader and HA Konber ldquoTiming Structure Mechanism of Wireless SensorNetworkMAC layer forMonitoringApplicationsrdquo InternationalJournal of Distributed Systems and Technologies vol 7 no 3 pp1ndash20 2016

[12] P Karn ldquoMACAmdasha new channel access method for packetradiordquo in Proceedings of the 9th ARRL Computer NetworkingConference pp 134ndash140 London Canada September 1990

[13] B Bellalta L Bononi R Bruno and A Kassler ldquoNext genera-tion IEEE 80211 Wireless Local Area Networks current statusfuture directions and open challengesrdquo Computer Communica-tions vol 75 pp 1ndash25 2016

[14] Vikas and P Nand ldquoContention based energy efficient wire-less sensor networkmdasha surveyrdquo in Proceedings of the Interna-tional Conference onComputing CommunicationampAutomation(ICCCA rsquo15) pp 546ndash551 Greater Noida India May 2015

[15] A Keshavarzian H Lee and L Venkatraman ldquoWakeupscheduling inwireless sensor networksrdquo inProceedings of the 7thACM International Symposium on Mobile Ad Hoc Networkingand Computing (MobiHoc rsquo06) pp 322ndash333 Florence ItalyMay2006

[16] G Lu B Krishnamachari and C S Raghavendra ldquoAn adaptiveenergy-efficient and low-latency MAC for tree-based data


gathering in sensor networksrdquo Wireless Communications andMobile Computing vol 7 no 7 pp 863ndash875 2007

[17] F Alfayez M Hammoudeh and A Abuarqoub ldquoA surveyon MAc protocols for duty-cycled wireless sensor networksrdquoProcedia Computer Science vol 73 pp 482ndash489 2015

[18] W H Rajani Muraleedharan I Demirkol O Yang H Ba andS Ray ldquoSleeping techniques for reducing energy dissipationrdquo inThe Art of Wireless Sensor Networks Volume 1 FundamentalsPart II H M Ammari Ed pp 163ndash197 Springer BerlinGermany 2014

[19] X Fafoutis A Di Mauro M D Vithanage and N DragonildquoReceiver-initiated medium access control protocols for wire-less sensor networksrdquo Computer Networks vol 76 pp 55ndash742015

[20] M D Jovanovic G L Djordjevic G S Nikolic and B DPetrovic ldquoMulti-channel media access control for wireless sen-sor networks a surveyrdquo in Proceedings of the 10th InternationalConference on Telecommunications in Modern Satellite Cableand Broadcasting Services (TELSIKS rsquo11) pp 741ndash744 IEEE NisSerbia October 2011

[21] R Diab G Chalhoub and M Misson ldquoOverview on multi-channel communications in wireless sensor networksrdquoNetworkProtocols and Algorithms vol 5 no 3 p 112 2013

[22] P Sthapit and J-Y Pyun ldquoEffects of radio Triggered SensorMAC protocol over wireless sensor networkrdquo in Proceedingsof the 11th IEEE International Conference on Computer andInformation Technology (CIT rsquo11) and 11th IEEE InternationalConference on Scalable Computing andCommunications (SCAL-COM rsquo11) pp 546ndash551 IEEE Pafos Cyprus September 2011

[23] M I Brownfield T Nelson S Midkiff and N J DavisIV ldquoWireless sensor network radio power management andsimulation modelsrdquo Open Electrical amp Electronic EngineeringJournal vol 4 no 1 pp 21ndash31 2010

[24] S Jagadeesan and V Parthasarathy ldquoCross-layer design inwireless sensor networksrdquo in Advances in Computer ScienceEngineering amp amp Applications vol 166 of Advances inIntelligent and Soft Computing pp 283ndash295 Springer BerlinGermany 2012

[25] U Khatri and S Mahajan ldquoCross-layer design for wireless sen-sor networks a surveyrdquo in Proceedings of the 2nd InternationalConference on Computing for Sustainable Global Development(INDIACom rsquo15) pp 73ndash77 New Delhi India 2015

[26] L Gu and J A Stankovic ldquoRadio-triggeredwake-up forwirelesssensor networksrdquo Real-Time Systems vol 29 no 2-3 pp 157ndash182 2005

[27] J Ansari D Pankin and P Mahonen ldquoRadio-triggered wake-ups with addressing capabilities for extremely low powersensor network applicationsrdquo International Journal of WirelessInformation Networks vol 16 no 3 pp 118ndash130 2009

[28] ZigBee Alliance httpwwwzigbeeorg[29] Nivis Wireless Sensor Networks ldquoNetworks ISA10011a

Technology Standardrdquo 2009 httpwwwniviscomtechnolo-gyISA10011aphp

[30] S Petersen and S Carlsen ldquoComparison of WirelessHART andISA10011a for wireless instrumentationrdquo in Industrial Commu-nication Technology Handbook R Zurawski Ed chapter 33 pp1ndash15 CRC Press 2nd edition 2014

[31] S Chhajed M Sabir and K P Singh ldquoWireless Sensor Net-work implementation using MiWi wireless protocol stackrdquo inProceedings of the 4th IEEE International Advance ComputingConference (IACC rsquo14) pp 239ndash244 Gurgaon India February2014

[32] Texas InstrumentsWireless Connectivity Overview for 6LoW-PAN httpwwwticomlsdstiwireless connectivity6lowpanoverviewpage

[33] The R Project for Statistical Computing httpswwwr-projectorg

[34] P Bremaud Markov Chains Gibbs Fields Monte Carlo Sim-ulation and Queues vol 31 of Texts in Applied MathematicsSpringer New York NY USA 1999

[35] P Park P Di Marco P Soldati C Fischione and K HJohansson ldquoA generalized Markov chain model for effectiveanalysis of slotted IEEE 802154rdquo in Proceedings of the IEEE 6thInternational Conference on Mobile Adhoc and Sensor Systems(MASS rsquo09) pp 130ndash139 Macau China October 2009

[36] S Pollin M Ergen S C Ergen et al ldquoPerformance analysis ofslotted carrier Sense IEEE 802154 acknowledged uplink trans-missionsrdquo in Proceedings of the IEEE Wireless Communicationsand Networking Conference (WCNC rsquo08) pp 1559ndash1564 IEEELas Vegas Nev USA April 2008

[37] P H Chou C-J Chen S F Jenks and S-J Kim ldquoHiperSensean integrated system for dense wireless sensing and massivelyscalable data visualizationrdquo in Software Technologies for Embed-ded andUbiquitous Systems S Lee and P Narasimhan Eds vol5860 pp 252ndash263 Springer Berlin Germany 2009

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpswwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



paved for it especially with respect to predictability andnumber of contending nodes where the condition underwhich these protocols may fail in preventing collisions is thesourcesrsquo number increase or the sourcesrsquo transmission rateincrease

The MAC layer design intended by the work proposed inthis paper is based on the physical layer of the IEEE802154standard [8ndash10] and composed of two techniques a timingstructure mechanism (TSM) proposed by our previous work[11] including the setup of the logical topology by dividing thenetwork into subnetworks (sub-NWs) using multichannelsand identifying the time structure of the sub-NW membersrsquowork and the contention-based CAM proposed in this paperThemain TSM ideawas to construct a receive schedule whichmakes at a time only one node from a group of nodes (sub-NW) listen to the channel and each node takes its turnsuccessively to listen for a small period At any time a nodewants to transmit it can turn its radio to the transmit stateand transmit directly in its maximum range or in a rangesuitable to the currently listening node using the CAM Thebackoff periods are aligned with a reference time common tothe nodes

The CAM is designed to be suitable to the proposed TSMand benefits from it and it is based on developing a backoffmechanism resorting to the common manner of increasingthe backoff stages (ie repeating the trials of accessing thechannel if it is found busy rather than announcing channelaccess failure and discarding the packet) and using a numberof transmission trials to cope with the transmission failurerather than discarding the packet

The rest of this paper is organized as follows Section 2includes a brief literature review for wireless MAC protocolsSection 3 begins with giving an overview of the beacon-enabled IEEE802154 slotted CSMACA then it illustratesthe proposed CAM idea and its modeling The performanceassessment of CAM is depicted in Section 4 where the CAMperformance is evaluated against the slotted CSMACA interms of single- andmultihop communication also the effectof different parameters on CAM performance and its tuningis considered Finally Section 5 concludes the paper andsuggests open issues for future work

2 Literature Review

The wireless medium access schemes used in different typesof wireless networks are based on carrier sensing backoffalgorithms andmechanisms for avoiding hidden and exposedterminal problems The Carrier Sense Multiple Access withCollision Avoidance (CSMACA) with its two versionsnonpersistent and 119901-persistent represents the basic formof channel access control In nonpersistent CSMA if thedevice senses the channel busy it backs off before tryingto transmit again When the channel is idle the devicetransmits immediately In 119901-persistent CSMA the devicecontinues sensing the busy channel until it becomes idle andin case of idle channel it transmits or defers transmissionaccording to a probability 119901 Keeping devices in the receivestate when not transmitting consumes a large amount ofenergy Multiple Access with Collision Avoidance (MACA)

[12] uses two additional packets Request-to-Send (RTS) andClear-to-Send (CTS) before the transmission to reduce theoccurrence of the hidden and exposed terminal problemsThe RTS is sent by the sender and the receiver willing toaccept data responds with CTS the other devices hear theRTS or the CTS and avoid interfering the involved devicesuntil end of transmission The RTSCTS represents overloadon the network and causes additional delay

Modifications to these schemes were then proposed suchas using acknowledgment using Request-for-Request-to-Send packet by a busy RTS receiver after finishing its transac-tion employing waiting intervals other than the backoff timeproviding priority levels for wireless channel access as usedin the IEEE80211 [13] distributed coordination function andusing variations in backoff time computation method suchas binary exponential backoff multiplicative increase andlinear decrease balanced backoff algorithm andwaiting timebased backoffWireless networks do not only use contention-based schemes but also use contention-free access such as thepoint coordination function defined in IEEE80211 in whicha coordinator device polls other devices for data

Due to the energy constraint in WSN the design ofWSN MAC considers other mechanisms in addition to thatused in coordinating the shared medium allocation andcontrols nodesrsquo activation to allow them to sleep saving theirenergy wasted in idle listening and overhearing The usedmedium allocation scheme itself should be energy-efficientfor example it does not employ large overhead The MACprotocols proposed in literature for WSN can be broadlyclassified according to the scheme depicted in Figure 1

The contention-based synchronous sleep-scheduling [14]can be through having each node following a periodicactivesleep cycle the nodes that are close to one anothersynchronize their active cycles together and if the next hop ofa transmission overhears it it remains awake until receivingthe forwarded data rather than sleeping and delaying dataforwarding up to its next active cycle But this is not alwaysthe case the next-hop node may be out of the hearing rangeof both the sender and the receiver making data forwardinginterruption problem unavoidable the staggered wake-upscheduling [15 16] is used to address this problem whichcreates a pipeline for data propagation based on the depth-level of nodes in a data-gathering tree where the active periodof one level partially overlaps with that of the lower level

In the asynchronous sender-initiated MAC [17 18] thesender transmits a preamble to indicate a pending trans-mission The receiver wakes up occasionally to listen tosuch a preamble for appropriately responding In receiver-initiated schemes [19] instead of long preambles the senderlistens to the channel waiting for the receiver small bea-cons transmitted in duty cycle fashion to synchronizewith the receiver The asynchronous schemes are simpler toimplement than the synchronous but it may result in verylong delay WSN MAC can be contention-free using TimeDivision Multiple Access (TDMA) or Frequency DivisionMultiple Access (FDMA) or hybrid In multichannel MAC[20 21] some issues are raised such as limited number ofavailable channels channel selection and assignment policyand recursive channel switching overhead Radio-triggered


MAC protocols






node HW itself



up radio)








CDMAFDMATDMA


Not suitablefor WSN

















Time


aTurnaroundTime




Node 2

Node 1

Node 3







Node 2

Node 1





(bf (119895) + cca (119895)))sdotmod (119906 + 1) (1)











Transmitted Ack

0000192

00001920000128


1st CCA 2nd CCA

Destinationnode


Received data Pkt


10 20 30 40 50 60 700Number of nodes

0

05

1

15

2

25

3

35

4

45

Avg

num

ber o

f col

lisio

ns




0

2

4

6

8

10

12

14

Loss

per

cent

age d

ue to

colli

sion

()

10 20 30 40 50 60 700Number of nodes



Perc

enta

ge fr

om to

tal c

hann

el ac

cess

atte

mpt

s (

)

20 30 40 50 60 7010Number of nodes

0

5

10

15

20

25

30



10 20 30 40 50 60 70Number of nodes


0

10

20

30

40

50

60

70

80

90

100

Num

ber o

f occ

urre

nces




20 30 40 50 60 7010Number of nodes

Stan

dard

dev

iatio

n of

the a

vera

ge b

acko

ff de

lay

2

3

4

5

6

7

8

u = 25

u = 5









11

11

11

11

11

11

q0

q0q0Q0

Q1


minus1 Ls minus 1 0



P


1 minus

P


1 minus


P

1 minus P

1 minus

0 minus1 1 0 0 1 0 1 1

m 11m 0 1


1 minus

minus2 0 1

minus1 Ls minus 1 1

minus2 Lc minus 1 1

minus1 0 1

P

1 minus P

1 minus

1 minus

0 minus1 1


P


minus1 0 n

minus1 Ls minus 1 n



P


pK(k | I = 0)

pK(k | I = 0)

pK(k | I = 0)

pK(k | I = 0)

pK(k | I = 1)

pK(k | I = 1)

pK(k | I = 1)

pK(k | I = m)

pK(k | I = m)

pK(k | I = m)

QL0minus1











rnum (119880119861 119904) = r (119880119861 119904) (119873 minus 1)119878 (3)




119911=1

( 119911sum119890=1

119888119903119900119911leV119911minus1119890


119911=1

( 119911sum119890=1

119888119903119900119911leV119911minus1119890





tknum (119878) = 2119878 (119878+1)sum119903119900=1

cnum (119903119900) (5)


knum (119896 119878) = (119878+1)sum119903119900=1

119896=bf119903119900(119878)

cnum (119903119900) (6)

where


119888119900=1


(7)



bstknum (119878) = 2119878 (8)



119896=bf(119878)1 (9)

where


119888119900=1


(10)


119868119863=1


119868119863=1

bsknum (119896 119894)bstknum (119894)



P (119894 119896 119895 | 119894 119896 + 1 119895) = 1 for 2119898119887 minus 1 ge 119896 ge 0 (12)




P (1198760 | 119898 0 119895) = 1199020 (120572 + (1 minus 120572) 120573) for 119895 lt 119899 (15)


P (1198760 | 119898 0 119899) = 1199020 (17)



119903=119896

119901119870 (119903 | 119868 = 119894) (19)1198871198940119895 = (120572 + (1 minus 120572) 120573) 119887119894minus10119895 (20)



119901119870 (119903 | 119868 = 119894) (22)


119901119870 (119903 | 119868 = 0) 119898sum119894=0

1198871198940119895minus1= 11988700119895 2119898119887minus1sum

119903=119896

119901119870 (119903 | 119868 = 0) (23)


119901119870 (119903 | 119868 = 119894) (24)





119887119894119896119895 = 119909119894119910119895119887000 2119898119887minus1sum119903=119896

119901119870 (119903 | 119868 = 119894) (27)


119899sum119895=0

2119898119887minus1sum119896=0

119898sum119894=0

119887119894119896119895 + 119898sum119894=0

119899sum119895=0

119887119894minus1119895+ 119899sum119895=0

(119871119904minus1sum119896=0

119887minus1119896119895 + 119871119888minus1sum119896=0

119887minus2119896119895) + 1198710minus1sum119897=0

119876119897 = 1 (28)



119898sum119894=0

(119909119894 2119898119887minus1sum119903=119896


(29)



119894=0

119899sum119895=0



(30)


119895=0

1 minus 1199101 minus 119910119899+1119910119895(119895 (119871119888 + 119864 [119879ℎ])+ 119898sum

119894=0

2119898119887minus1sum119903=0

119903119901119870 (119903 | 119868 = 119894) + 119879119878119862 2119898+1sum119890=1

119862119890120572120573 (119898 + 1)sdot (119873119890

120572 (119898 + 1) + 2119873119890120573 (119898 + 1)))]]

(31)



119894=0 119862120572120573 (119894) 119898sum119894=0

( 2119894sum119890=1

119862119890120572120573 (119894) 119894sum119897=0

2119898119887minus1sum119903=0

119903119901119870 (119903 | 119868 = 119897)) (33)



119894=0

2119898119887minus1sum119896=1

119899sum119895=0

119887119894119896119895 + 119864119904119888 119898sum119894=0

119899sum119895=0

(1198871198940119895 + 119887119894minus1119895)+ 119864119905 119899sum

119895=0

119871minus1sum119896=0

(119887minus1119896119895 + 119887minus2119896119895)+ 119864119894 119899sum

119895=0

(119887minus1119871119895 + 119887minus2119871119895)+ 119899sum119895=0

119871+119871119886119888119896+1sum119896=119871+1


119876119897(34)






0 10 20 30 40 50

P

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(a)

0 10 20 30 40 50

1

45

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1412

1520

919

8

16

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22

21

1324

23

10

18 7

11

0

10

20

30

40

50


(b)












(36)











119895isinΦ119905119903 119895 =BS(1 minus 120591119895) (38)


120595ℎ(1 minus 120591119896)


| ⋃ℎisinΦℎ119888119905119903120595ℎ|119862119902sum

119898=1

( prod119894isin119889119898

119889119898=1198891198981 1198891198982 119889119898119902


120595ℎ119889119898


119899isin119889119898119889119898=1198891198981 1198891198982119889119898119902

(120572119899 + (1 minus 120572119899) 120573119899)))(39)






= 2119871 |Φℎ119905119903BS|sum119902=1

|Φℎ119905119903BS|119862119902sum119898=1

( prod119894isin119896119898

119896119898=1198961198981 1198961198982 119896119898119902



119899isin119896119898119896119898=1198961198981 1198961198982 119896119898119902

(120572119899 + (1 minus 120572119899) 120573119899)))(40)




119902=1

|Φ119905BS|119862119902sum119898=1

( prod119894isin119896119898

119896119898=1198961198981 1198961198982 119896119898119902



119899isin119896119898119896119898=1198961198981 1198961198982 119896119898119902


120595ℎ119905(1 minus 120591119896)

sdot | ⋃ℎisinΦ119905119888 120595ℎ119905|sum119902=1

| ⋃ℎisinΦ119905119888120595ℎ119905|119862119902sum

119898=1

( prod119894isin119889119898

119889119898=1198891198981 1198891198982119889119898119902


120595ℎ(119889119898cup119905)


119899isin119889119898119889119898=1198891198981 1198891198982 119889119898119902

(120572119899 + (1 minus 120572119899) 120573119899)))

(41)









P (1198611199041198971199001199051 cap 1198681198621198621198601) + P (1198681199041198971199001199051 cap 1198681198621198621198601) (43)


P (1198611199041198971199001199051 cap 1198681198621198621198601) + P (1198681199041198971199001199051 cap 1198681198621198621198601))sdot P (1198781199041198971199001199051) + 119875119887119890119905119886119860119862119870 (44)




(1 minus 120591119895))+ 119875119887119906119904119910119860119905119875119887119906119904119910119865119905 + 119875119887119906119904119910119860119905 + 119875119887119906119904119910119878119905 + 119875119894119889119897119890119905

(45)







IBSrceil) (46)






119877e-to-e = 119897prod119899=1

119877119899 (48)





119899=1

(119908119899 + 119863119899) (49)



119864e-to-e = 119897sum119899=1

119864119899 (50)


119894isinΦ119905119900119905119886119897

(1 minus 120591119894) 119875119904119906119888119888119890119904119904 = sum119894isinΦ119905119900119905119886119897

119875119878119879119894119875119887119906119904119910 (51)



119899isinΦ119905119900119905119886119897

sum119903isin119874119899

119877e-to-e (119899 119903)119863e-to-e (119899 119903) (52)



510

1520

25

12

34

= 3

= 4 = 5um

0

001

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003

004

005

Relia

bilit

y


510

1520

25

12

34

= 3 = 4 = 5

um

5

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s)






510

1520

25

12

34

= 3 = 4

= 5

um

15

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Pow

er co

nsum

ptio

n (m

W)







0

002

004

006

008

01

012

014

Relia

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30 40 50 60 70 80

Prob

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ts

Number of nodes

075

08

085

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1

due t

o ch

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l acc

ess f

ailu

re







0875

0877

0879

0881

0883

0885

0887

0889

0891

Prob

abili

ty o

f uns

ucce

ssfu

l cha

nnel

acce

ss at

tem

pt





0

5

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s)









0

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1

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0

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35 40 45 50 55 60 65 70 75 8030Number of nodes

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35 40 45 50 55 60 65 70 75 8030Number of nodes







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35 40 45 50 55 60 65 70 75 8030Number of nodes




35 40 45 50 55 60 65 70 75 8030Number of nodes

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5 10 15 20 25 300u

05055

06065

07075

08085

Relia

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5 10 15 20 25 300u

456789

1011121314

Avg

del

ay (m

s)

3638

442444648

552

Avg

ener

gy co

nsum

ptio

n (m

w)

5 10 15 20 25 300u

04045

05055

06065

07075

Relia

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5 10 15 20 25 300u

468

10121416

Avg

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ay (m

s)

5 10 15 20 25 300u

332343638

442444648

Avg

ener

gy co

nsum

ptio

n (m

w)

5 10 15 20 25 300u

02025

03035

04045

05055

Relia

bilit

y

5 10 15 20 25 300u

5

10

15

20

Avg

del

ay (m

s)

5 10 15 20 25 300u

2

25

3

35

Avg

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gy co

nsum

ptio

n (m

w)

5 10 15 20 25 300u

01015

02025

03035

04

Relia

bilit

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5 10 15 20 25 300u

468

1012141618202224

Avg

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5 10 15 20 25 300u

5 10 15 20 25 300u

1618

222242628

332

Avg

ener

gy co

nsum

ptio

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w)

0002004006008

01012014

Relia

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5 10 15 20 25 300u

5

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15

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25

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Avg

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ay (m

s)

5 10 15 20 25 300u

5 10 15 20 25 300u

112141618

222242628

3

Avg

ener

gy co

nsum

ptio

n (m

w)

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2 m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 3

m = 3 m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 4

m = 4

m = 4m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4m = 4

m = 4

m = 4

m = 4







Φ16119888= 1 3 4 5 Φ16 4= 1 3 5 8 9 12 13 14 15 17 19 20 22 Φℎ16 4 = 0 2 21 Φℎ11988816 4 = 0 2 11986216 = 4 1205950 = 1 4 1205951 = 12 14 15 1205952 = 7 11 18 1205953 = 6 13 22 24 1205954 = 5 8 16 17 1205955 = 2 3 9 19 20

(53)










IEEE slotted CSMACA

0

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End-

to-e

nd re

liabi

lity

CAM 431-131-131CAM 431-430-131

CAM 631-430-131CAM 631-131-131







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CAM 631-430-131CAM 631-131-131




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(mW

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CAM 431-131-131CAM 431-430-131

CAM 631-430-131CAM 631-131-131










Appendix













where




bsknum (119896 119878) = 2119878sum119862119862119860119888119900119898119887=1


where

sumfn (119878 119862119862119860119888119900119898119887 119868119863)=


119872119894119899119861119865119904119906119898119879119890119903119898 =




1 if 119878 = 1119878 + 119878minus1sum119899=1




(A7)






119875119878119877ℎ119905 = (119871119886119888119896 + 119871) sum119899isinΦℎ119888119905119903


119875119878119879119896 + 119871119886119888119896 sum119899isinΦℎ119888119905119903

sum119896isin(120595119899capΦℎ119905119903)

119875119878119879119896 + sum119899isinΦℎ119888119905119903

sum119896isin(120595119899capΦ119905)

119875119878119879119896 minus (119871119886119888119896 + 119871) |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902




119875119878119879119896)minus 119871119886119888119896 |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


(( sum119896isin(120595119899capΦℎ119905119903)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911 119896notinΦ119905


119875119878119879119896))


minus |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


(( sum119896isin(120595119899capΦ119905)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911


119875119878119879119896))(B1)

119875119878119879119896 = 120591119896 prod119895isinΦ119896119899




119875119878119877119905 = 119871119886119888119896( sum119899isinΦ119905119888

sum119896isin120595119899119896 =119905

119875119878119879119896 minus |Φ119905119888 |sum119902=2

(minus1)119902 |Φ119905119888 |119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


( sum119896isin120595119899 119896 =119905


119875119878119879119896)) (B3)



119875119887119906119904119910119878119905 = sum119896isinΦ119905119896 =BS

119875119878119879119896 minus |119862|sum119902=2

(minus1)119902sdot |119862|119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982ℎ119898119902


( sum119896isin(120595119899capΦ119905)


119875119878119879119896)119875119887119906119904119910119865119905 = (1 minus prod

119895isinΦ119905119895 =BS(1 minus 120591119895))


(1 minus 120591119895)minus 119875119887119906119904119910119878119905 119875119887119906119904119910119860119905 = 119875119878119877119905119871119886119888119896

(B4)



119895isinΦ119905119895 =BS(1 minus 120591119895))



(1 minus 120591119895))119894minus1







Competing Interests


References










































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










MAC protocols






node HW itself



up radio)








CDMAFDMATDMA


Not suitablefor WSN

















Time


aTurnaroundTime




Node 2

Node 1

Node 3







Node 2

Node 1





(bf (119895) + cca (119895)))sdotmod (119906 + 1) (1)











Transmitted Ack

0000192

00001920000128


1st CCA 2nd CCA

Destinationnode


Received data Pkt


10 20 30 40 50 60 700Number of nodes

0

05

1

15

2

25

3

35

4

45

Avg

num

ber o

f col

lisio

ns




0

2

4

6

8

10

12

14

Loss

per

cent

age d

ue to

colli

sion

()

10 20 30 40 50 60 700Number of nodes



Perc

enta

ge fr

om to

tal c

hann

el ac

cess

atte

mpt

s (

)

20 30 40 50 60 7010Number of nodes

0

5

10

15

20

25

30



10 20 30 40 50 60 70Number of nodes


0

10

20

30

40

50

60

70

80

90

100

Num

ber o

f occ

urre

nces




20 30 40 50 60 7010Number of nodes

Stan

dard

dev

iatio

n of

the a

vera

ge b

acko

ff de

lay

2

3

4

5

6

7

8

u = 25

u = 5









11

11

11

11

11

11

q0

q0q0Q0

Q1


minus1 Ls minus 1 0



P


1 minus

P


1 minus


P

1 minus P

1 minus

0 minus1 1 0 0 1 0 1 1

m 11m 0 1


1 minus

minus2 0 1

minus1 Ls minus 1 1

minus2 Lc minus 1 1

minus1 0 1

P

1 minus P

1 minus

1 minus

0 minus1 1


P


minus1 0 n

minus1 Ls minus 1 n



P


pK(k | I = 0)

pK(k | I = 0)

pK(k | I = 0)

pK(k | I = 0)

pK(k | I = 1)

pK(k | I = 1)

pK(k | I = 1)

pK(k | I = m)

pK(k | I = m)

pK(k | I = m)

QL0minus1











rnum (119880119861 119904) = r (119880119861 119904) (119873 minus 1)119878 (3)




119911=1

( 119911sum119890=1

119888119903119900119911leV119911minus1119890


119911=1

( 119911sum119890=1

119888119903119900119911leV119911minus1119890





tknum (119878) = 2119878 (119878+1)sum119903119900=1

cnum (119903119900) (5)


knum (119896 119878) = (119878+1)sum119903119900=1

119896=bf119903119900(119878)

cnum (119903119900) (6)

where


119888119900=1


(7)



bstknum (119878) = 2119878 (8)



119896=bf(119878)1 (9)

where


119888119900=1


(10)


119868119863=1


119868119863=1

bsknum (119896 119894)bstknum (119894)



P (119894 119896 119895 | 119894 119896 + 1 119895) = 1 for 2119898119887 minus 1 ge 119896 ge 0 (12)




P (1198760 | 119898 0 119895) = 1199020 (120572 + (1 minus 120572) 120573) for 119895 lt 119899 (15)


P (1198760 | 119898 0 119899) = 1199020 (17)



119903=119896

119901119870 (119903 | 119868 = 119894) (19)1198871198940119895 = (120572 + (1 minus 120572) 120573) 119887119894minus10119895 (20)



119901119870 (119903 | 119868 = 119894) (22)


119901119870 (119903 | 119868 = 0) 119898sum119894=0

1198871198940119895minus1= 11988700119895 2119898119887minus1sum

119903=119896

119901119870 (119903 | 119868 = 0) (23)


119901119870 (119903 | 119868 = 119894) (24)





119887119894119896119895 = 119909119894119910119895119887000 2119898119887minus1sum119903=119896

119901119870 (119903 | 119868 = 119894) (27)


119899sum119895=0

2119898119887minus1sum119896=0

119898sum119894=0

119887119894119896119895 + 119898sum119894=0

119899sum119895=0

119887119894minus1119895+ 119899sum119895=0

(119871119904minus1sum119896=0

119887minus1119896119895 + 119871119888minus1sum119896=0

119887minus2119896119895) + 1198710minus1sum119897=0

119876119897 = 1 (28)



119898sum119894=0

(119909119894 2119898119887minus1sum119903=119896


(29)



119894=0

119899sum119895=0



(30)


119895=0

1 minus 1199101 minus 119910119899+1119910119895(119895 (119871119888 + 119864 [119879ℎ])+ 119898sum

119894=0

2119898119887minus1sum119903=0

119903119901119870 (119903 | 119868 = 119894) + 119879119878119862 2119898+1sum119890=1

119862119890120572120573 (119898 + 1)sdot (119873119890

120572 (119898 + 1) + 2119873119890120573 (119898 + 1)))]]

(31)



119894=0 119862120572120573 (119894) 119898sum119894=0

( 2119894sum119890=1

119862119890120572120573 (119894) 119894sum119897=0

2119898119887minus1sum119903=0

119903119901119870 (119903 | 119868 = 119897)) (33)



119894=0

2119898119887minus1sum119896=1

119899sum119895=0

119887119894119896119895 + 119864119904119888 119898sum119894=0

119899sum119895=0

(1198871198940119895 + 119887119894minus1119895)+ 119864119905 119899sum

119895=0

119871minus1sum119896=0

(119887minus1119896119895 + 119887minus2119896119895)+ 119864119894 119899sum

119895=0

(119887minus1119871119895 + 119887minus2119871119895)+ 119899sum119895=0

119871+119871119886119888119896+1sum119896=119871+1


119876119897(34)






0 10 20 30 40 50

P

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0

10

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(a)

0 10 20 30 40 50

1

45

2

6

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1412

1520

919

8

16

17

22

21

1324

23

10

18 7

11

0

10

20

30

40

50


(b)












(36)











119895isinΦ119905119903 119895 =BS(1 minus 120591119895) (38)


120595ℎ(1 minus 120591119896)


| ⋃ℎisinΦℎ119888119905119903120595ℎ|119862119902sum

119898=1

( prod119894isin119889119898

119889119898=1198891198981 1198891198982 119889119898119902


120595ℎ119889119898


119899isin119889119898119889119898=1198891198981 1198891198982119889119898119902

(120572119899 + (1 minus 120572119899) 120573119899)))(39)






= 2119871 |Φℎ119905119903BS|sum119902=1

|Φℎ119905119903BS|119862119902sum119898=1

( prod119894isin119896119898

119896119898=1198961198981 1198961198982 119896119898119902



119899isin119896119898119896119898=1198961198981 1198961198982 119896119898119902

(120572119899 + (1 minus 120572119899) 120573119899)))(40)




119902=1

|Φ119905BS|119862119902sum119898=1

( prod119894isin119896119898

119896119898=1198961198981 1198961198982 119896119898119902



119899isin119896119898119896119898=1198961198981 1198961198982 119896119898119902


120595ℎ119905(1 minus 120591119896)

sdot | ⋃ℎisinΦ119905119888 120595ℎ119905|sum119902=1

| ⋃ℎisinΦ119905119888120595ℎ119905|119862119902sum

119898=1

( prod119894isin119889119898

119889119898=1198891198981 1198891198982119889119898119902


120595ℎ(119889119898cup119905)


119899isin119889119898119889119898=1198891198981 1198891198982 119889119898119902

(120572119899 + (1 minus 120572119899) 120573119899)))

(41)









P (1198611199041198971199001199051 cap 1198681198621198621198601) + P (1198681199041198971199001199051 cap 1198681198621198621198601) (43)


P (1198611199041198971199001199051 cap 1198681198621198621198601) + P (1198681199041198971199001199051 cap 1198681198621198621198601))sdot P (1198781199041198971199001199051) + 119875119887119890119905119886119860119862119870 (44)




(1 minus 120591119895))+ 119875119887119906119904119910119860119905119875119887119906119904119910119865119905 + 119875119887119906119904119910119860119905 + 119875119887119906119904119910119878119905 + 119875119894119889119897119890119905

(45)







IBSrceil) (46)






119877e-to-e = 119897prod119899=1

119877119899 (48)





119899=1

(119908119899 + 119863119899) (49)



119864e-to-e = 119897sum119899=1

119864119899 (50)


119894isinΦ119905119900119905119886119897

(1 minus 120591119894) 119875119904119906119888119888119890119904119904 = sum119894isinΦ119905119900119905119886119897

119875119878119879119894119875119887119906119904119910 (51)



119899isinΦ119905119900119905119886119897

sum119903isin119874119899

119877e-to-e (119899 119903)119863e-to-e (119899 119903) (52)



510

1520

25

12

34

= 3

= 4 = 5um

0

001

002

003

004

005

Relia

bilit

y


510

1520

25

12

34

= 3 = 4 = 5

um

5

10

15

20

25

30

Avg

del

ay (m

s)






510

1520

25

12

34

= 3 = 4

= 5

um

15

2

25

Pow

er co

nsum

ptio

n (m

W)







0

002

004

006

008

01

012

014

Relia

bilit

y







30 40 50 60 70 80

Prob

abili

ty o

f disc

ardi

ng p

acke

ts

Number of nodes

075

08

085

09

095

1

due t

o ch

anne

l acc

ess f

ailu

re







0875

0877

0879

0881

0883

0885

0887

0889

0891

Prob

abili

ty o

f uns

ucce

ssfu

l cha

nnel

acce

ss at

tem

pt





0

5

10

15

20

25

30

35

40

Avg

del

ay (m

s)









0

05

1

15

2

25

Ener

gy co

nsum

ptio

n (m

w)





0

005

01

015

02

025

03

Thro

ughp

ut






35 40 45 50 55 60 65 70 75 8030Number of nodes

12

13

14

15

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17

18

19

Avg

del

ay (m

s)




0

001

002

003

004

005

006

007

008

Relia

bilit

y

35 40 45 50 55 60 65 70 75 8030Number of nodes







14

15

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18

19

2

21

22

Ener

gy co

nsum

ptio

n (m

w)

35 40 45 50 55 60 65 70 75 8030Number of nodes




35 40 45 50 55 60 65 70 75 8030Number of nodes

0

005

01

015

02

025

Thro

ughp

ut






















5 10 15 20 25 300u

05055

06065

07075

08085

Relia

bilit

y

5 10 15 20 25 300u

456789

1011121314

Avg

del

ay (m

s)

3638

442444648

552

Avg

ener

gy co

nsum

ptio

n (m

w)

5 10 15 20 25 300u

04045

05055

06065

07075

Relia

bilit

y

5 10 15 20 25 300u

468

10121416

Avg

del

ay (m

s)

5 10 15 20 25 300u

332343638

442444648

Avg

ener

gy co

nsum

ptio

n (m

w)

5 10 15 20 25 300u

02025

03035

04045

05055

Relia

bilit

y

5 10 15 20 25 300u

5

10

15

20

Avg

del

ay (m

s)

5 10 15 20 25 300u

2

25

3

35

Avg

ener

gy co

nsum

ptio

n (m

w)

5 10 15 20 25 300u

01015

02025

03035

04

Relia

bilit

y

5 10 15 20 25 300u

468

1012141618202224

Avg

del

ay (m

s)

5 10 15 20 25 300u

5 10 15 20 25 300u

1618

222242628

332

Avg

ener

gy co

nsum

ptio

n (m

w)

0002004006008

01012014

Relia

bilit

y

5 10 15 20 25 300u

5

10

15

20

25

30

Avg

del

ay (m

s)

5 10 15 20 25 300u

5 10 15 20 25 300u

112141618

222242628

3

Avg

ener

gy co

nsum

ptio

n (m

w)

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2 m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 3

m = 3 m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 4

m = 4

m = 4m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4m = 4

m = 4

m = 4

m = 4







Φ16119888= 1 3 4 5 Φ16 4= 1 3 5 8 9 12 13 14 15 17 19 20 22 Φℎ16 4 = 0 2 21 Φℎ11988816 4 = 0 2 11986216 = 4 1205950 = 1 4 1205951 = 12 14 15 1205952 = 7 11 18 1205953 = 6 13 22 24 1205954 = 5 8 16 17 1205955 = 2 3 9 19 20

(53)










IEEE slotted CSMACA

0

01

02

03

04

05

06

07

08

End-

to-e

nd re

liabi

lity

CAM 431-131-131CAM 431-430-131

CAM 631-430-131CAM 631-131-131







000E + 00

100E + 01

200E + 01

300E + 01

400E + 01

500E + 01

600E + 01

End-

to-e

nd d

elay

(ms)


CAM 631-430-131CAM 631-131-131




01

02

03

04

05

06

07

08

09

Aver

age n

etw

ork

thro

ughp

ut







50

100

150

200

250

Net

wor

k go

odpu

t (bi

tms)



IEEE slotted CSMACA

000E + 00

500E + 00

100E + 01

150E + 01

200E + 01

End-

to-e

nd p

ower

cons

umpt

ion

(mW

)

CAM 431-131-131CAM 431-430-131

CAM 631-430-131CAM 631-131-131










Appendix













where




bsknum (119896 119878) = 2119878sum119862119862119860119888119900119898119887=1


where

sumfn (119878 119862119862119860119888119900119898119887 119868119863)=


119872119894119899119861119865119904119906119898119879119890119903119898 =




1 if 119878 = 1119878 + 119878minus1sum119899=1




(A7)






119875119878119877ℎ119905 = (119871119886119888119896 + 119871) sum119899isinΦℎ119888119905119903


119875119878119879119896 + 119871119886119888119896 sum119899isinΦℎ119888119905119903

sum119896isin(120595119899capΦℎ119905119903)

119875119878119879119896 + sum119899isinΦℎ119888119905119903

sum119896isin(120595119899capΦ119905)

119875119878119879119896 minus (119871119886119888119896 + 119871) |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902




119875119878119879119896)minus 119871119886119888119896 |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


(( sum119896isin(120595119899capΦℎ119905119903)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911 119896notinΦ119905


119875119878119879119896))


minus |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


(( sum119896isin(120595119899capΦ119905)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911


119875119878119879119896))(B1)

119875119878119879119896 = 120591119896 prod119895isinΦ119896119899




119875119878119877119905 = 119871119886119888119896( sum119899isinΦ119905119888

sum119896isin120595119899119896 =119905

119875119878119879119896 minus |Φ119905119888 |sum119902=2

(minus1)119902 |Φ119905119888 |119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


( sum119896isin120595119899 119896 =119905


119875119878119879119896)) (B3)



119875119887119906119904119910119878119905 = sum119896isinΦ119905119896 =BS

119875119878119879119896 minus |119862|sum119902=2

(minus1)119902sdot |119862|119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982ℎ119898119902


( sum119896isin(120595119899capΦ119905)


119875119878119879119896)119875119887119906119904119910119865119905 = (1 minus prod

119895isinΦ119905119895 =BS(1 minus 120591119895))


(1 minus 120591119895)minus 119875119887119906119904119910119878119905 119875119887119906119904119910119860119905 = 119875119878119877119905119871119886119888119896

(B4)



119895isinΦ119905119895 =BS(1 minus 120591119895))



(1 minus 120591119895))119894minus1







Competing Interests


References










































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













Time


aTurnaroundTime




Node 2

Node 1

Node 3







Node 2

Node 1





(bf (119895) + cca (119895)))sdotmod (119906 + 1) (1)











Transmitted Ack

0000192

00001920000128


1st CCA 2nd CCA

Destinationnode


Received data Pkt


10 20 30 40 50 60 700Number of nodes

0

05

1

15

2

25

3

35

4

45

Avg

num

ber o

f col

lisio

ns




0

2

4

6

8

10

12

14

Loss

per

cent

age d

ue to

colli

sion

()

10 20 30 40 50 60 700Number of nodes



Perc

enta

ge fr

om to

tal c

hann

el ac

cess

atte

mpt

s (

)

20 30 40 50 60 7010Number of nodes

0

5

10

15

20

25

30



10 20 30 40 50 60 70Number of nodes


0

10

20

30

40

50

60

70

80

90

100

Num

ber o

f occ

urre

nces




20 30 40 50 60 7010Number of nodes

Stan

dard

dev

iatio

n of

the a

vera

ge b

acko

ff de

lay

2

3

4

5

6

7

8

u = 25

u = 5









11

11

11

11

11

11

q0

q0q0Q0

Q1


minus1 Ls minus 1 0



P


1 minus

P


1 minus


P

1 minus P

1 minus

0 minus1 1 0 0 1 0 1 1

m 11m 0 1


1 minus

minus2 0 1

minus1 Ls minus 1 1

minus2 Lc minus 1 1

minus1 0 1

P

1 minus P

1 minus

1 minus

0 minus1 1


P


minus1 0 n

minus1 Ls minus 1 n



P


pK(k | I = 0)

pK(k | I = 0)

pK(k | I = 0)

pK(k | I = 0)

pK(k | I = 1)

pK(k | I = 1)

pK(k | I = 1)

pK(k | I = m)

pK(k | I = m)

pK(k | I = m)

QL0minus1











rnum (119880119861 119904) = r (119880119861 119904) (119873 minus 1)119878 (3)




119911=1

( 119911sum119890=1

119888119903119900119911leV119911minus1119890


119911=1

( 119911sum119890=1

119888119903119900119911leV119911minus1119890





tknum (119878) = 2119878 (119878+1)sum119903119900=1

cnum (119903119900) (5)


knum (119896 119878) = (119878+1)sum119903119900=1

119896=bf119903119900(119878)

cnum (119903119900) (6)

where


119888119900=1


(7)



bstknum (119878) = 2119878 (8)



119896=bf(119878)1 (9)

where


119888119900=1


(10)


119868119863=1


119868119863=1

bsknum (119896 119894)bstknum (119894)



P (119894 119896 119895 | 119894 119896 + 1 119895) = 1 for 2119898119887 minus 1 ge 119896 ge 0 (12)




P (1198760 | 119898 0 119895) = 1199020 (120572 + (1 minus 120572) 120573) for 119895 lt 119899 (15)


P (1198760 | 119898 0 119899) = 1199020 (17)



119903=119896

119901119870 (119903 | 119868 = 119894) (19)1198871198940119895 = (120572 + (1 minus 120572) 120573) 119887119894minus10119895 (20)



119901119870 (119903 | 119868 = 119894) (22)


119901119870 (119903 | 119868 = 0) 119898sum119894=0

1198871198940119895minus1= 11988700119895 2119898119887minus1sum

119903=119896

119901119870 (119903 | 119868 = 0) (23)


119901119870 (119903 | 119868 = 119894) (24)





119887119894119896119895 = 119909119894119910119895119887000 2119898119887minus1sum119903=119896

119901119870 (119903 | 119868 = 119894) (27)


119899sum119895=0

2119898119887minus1sum119896=0

119898sum119894=0

119887119894119896119895 + 119898sum119894=0

119899sum119895=0

119887119894minus1119895+ 119899sum119895=0

(119871119904minus1sum119896=0

119887minus1119896119895 + 119871119888minus1sum119896=0

119887minus2119896119895) + 1198710minus1sum119897=0

119876119897 = 1 (28)



119898sum119894=0

(119909119894 2119898119887minus1sum119903=119896


(29)



119894=0

119899sum119895=0



(30)


119895=0

1 minus 1199101 minus 119910119899+1119910119895(119895 (119871119888 + 119864 [119879ℎ])+ 119898sum

119894=0

2119898119887minus1sum119903=0

119903119901119870 (119903 | 119868 = 119894) + 119879119878119862 2119898+1sum119890=1

119862119890120572120573 (119898 + 1)sdot (119873119890

120572 (119898 + 1) + 2119873119890120573 (119898 + 1)))]]

(31)



119894=0 119862120572120573 (119894) 119898sum119894=0

( 2119894sum119890=1

119862119890120572120573 (119894) 119894sum119897=0

2119898119887minus1sum119903=0

119903119901119870 (119903 | 119868 = 119897)) (33)



119894=0

2119898119887minus1sum119896=1

119899sum119895=0

119887119894119896119895 + 119864119904119888 119898sum119894=0

119899sum119895=0

(1198871198940119895 + 119887119894minus1119895)+ 119864119905 119899sum

119895=0

119871minus1sum119896=0

(119887minus1119896119895 + 119887minus2119896119895)+ 119864119894 119899sum

119895=0

(119887minus1119871119895 + 119887minus2119871119895)+ 119899sum119895=0

119871+119871119886119888119896+1sum119896=119871+1


119876119897(34)






0 10 20 30 40 50

P

O

T

SQ

R

E

A

N

G

L

J

K

I

D

U

F

M

W

V

X

P

O

T

SQQ

R

I

A

D

U

F

M

W

VV

X

E

N

G

L

JJ

K

B

C

H

0

10

20

30

40

50


(a)

0 10 20 30 40 50

1

45

2

6

3

1412

1520

919

8

16

17

22

21

1324

23

10

18 7

11

0

10

20

30

40

50


(b)












(36)











119895isinΦ119905119903 119895 =BS(1 minus 120591119895) (38)


120595ℎ(1 minus 120591119896)


| ⋃ℎisinΦℎ119888119905119903120595ℎ|119862119902sum

119898=1

( prod119894isin119889119898

119889119898=1198891198981 1198891198982 119889119898119902


120595ℎ119889119898


119899isin119889119898119889119898=1198891198981 1198891198982119889119898119902

(120572119899 + (1 minus 120572119899) 120573119899)))(39)






= 2119871 |Φℎ119905119903BS|sum119902=1

|Φℎ119905119903BS|119862119902sum119898=1

( prod119894isin119896119898

119896119898=1198961198981 1198961198982 119896119898119902



119899isin119896119898119896119898=1198961198981 1198961198982 119896119898119902

(120572119899 + (1 minus 120572119899) 120573119899)))(40)




119902=1

|Φ119905BS|119862119902sum119898=1

( prod119894isin119896119898

119896119898=1198961198981 1198961198982 119896119898119902



119899isin119896119898119896119898=1198961198981 1198961198982 119896119898119902


120595ℎ119905(1 minus 120591119896)

sdot | ⋃ℎisinΦ119905119888 120595ℎ119905|sum119902=1

| ⋃ℎisinΦ119905119888120595ℎ119905|119862119902sum

119898=1

( prod119894isin119889119898

119889119898=1198891198981 1198891198982119889119898119902


120595ℎ(119889119898cup119905)


119899isin119889119898119889119898=1198891198981 1198891198982 119889119898119902

(120572119899 + (1 minus 120572119899) 120573119899)))

(41)









P (1198611199041198971199001199051 cap 1198681198621198621198601) + P (1198681199041198971199001199051 cap 1198681198621198621198601) (43)


P (1198611199041198971199001199051 cap 1198681198621198621198601) + P (1198681199041198971199001199051 cap 1198681198621198621198601))sdot P (1198781199041198971199001199051) + 119875119887119890119905119886119860119862119870 (44)




(1 minus 120591119895))+ 119875119887119906119904119910119860119905119875119887119906119904119910119865119905 + 119875119887119906119904119910119860119905 + 119875119887119906119904119910119878119905 + 119875119894119889119897119890119905

(45)







IBSrceil) (46)






119877e-to-e = 119897prod119899=1

119877119899 (48)





119899=1

(119908119899 + 119863119899) (49)



119864e-to-e = 119897sum119899=1

119864119899 (50)


119894isinΦ119905119900119905119886119897

(1 minus 120591119894) 119875119904119906119888119888119890119904119904 = sum119894isinΦ119905119900119905119886119897

119875119878119879119894119875119887119906119904119910 (51)



119899isinΦ119905119900119905119886119897

sum119903isin119874119899

119877e-to-e (119899 119903)119863e-to-e (119899 119903) (52)



510

1520

25

12

34

= 3

= 4 = 5um

0

001

002

003

004

005

Relia

bilit

y


510

1520

25

12

34

= 3 = 4 = 5

um

5

10

15

20

25

30

Avg

del

ay (m

s)






510

1520

25

12

34

= 3 = 4

= 5

um

15

2

25

Pow

er co

nsum

ptio

n (m

W)







0

002

004

006

008

01

012

014

Relia

bilit

y







30 40 50 60 70 80

Prob

abili

ty o

f disc

ardi

ng p

acke

ts

Number of nodes

075

08

085

09

095

1

due t

o ch

anne

l acc

ess f

ailu

re







0875

0877

0879

0881

0883

0885

0887

0889

0891

Prob

abili

ty o

f uns

ucce

ssfu

l cha

nnel

acce

ss at

tem

pt





0

5

10

15

20

25

30

35

40

Avg

del

ay (m

s)









0

05

1

15

2

25

Ener

gy co

nsum

ptio

n (m

w)





0

005

01

015

02

025

03

Thro

ughp

ut






35 40 45 50 55 60 65 70 75 8030Number of nodes

12

13

14

15

16

17

18

19

Avg

del

ay (m

s)




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001

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m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2 m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 3

m = 3 m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 4

m = 4

m = 4m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4m = 4

m = 4

m = 4

m = 4







Φ16119888= 1 3 4 5 Φ16 4= 1 3 5 8 9 12 13 14 15 17 19 20 22 Φℎ16 4 = 0 2 21 Φℎ11988816 4 = 0 2 11986216 = 4 1205950 = 1 4 1205951 = 12 14 15 1205952 = 7 11 18 1205953 = 6 13 22 24 1205954 = 5 8 16 17 1205955 = 2 3 9 19 20

(53)










IEEE slotted CSMACA

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CAM 431-131-131CAM 431-430-131

CAM 631-430-131CAM 631-131-131










Appendix













where




bsknum (119896 119878) = 2119878sum119862119862119860119888119900119898119887=1


where

sumfn (119878 119862119862119860119888119900119898119887 119868119863)=


119872119894119899119861119865119904119906119898119879119890119903119898 =




1 if 119878 = 1119878 + 119878minus1sum119899=1




(A7)






119875119878119877ℎ119905 = (119871119886119888119896 + 119871) sum119899isinΦℎ119888119905119903


119875119878119879119896 + 119871119886119888119896 sum119899isinΦℎ119888119905119903

sum119896isin(120595119899capΦℎ119905119903)

119875119878119879119896 + sum119899isinΦℎ119888119905119903

sum119896isin(120595119899capΦ119905)

119875119878119879119896 minus (119871119886119888119896 + 119871) |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902




119875119878119879119896)minus 119871119886119888119896 |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


(( sum119896isin(120595119899capΦℎ119905119903)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911 119896notinΦ119905


119875119878119879119896))


minus |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


(( sum119896isin(120595119899capΦ119905)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911


119875119878119879119896))(B1)

119875119878119879119896 = 120591119896 prod119895isinΦ119896119899




119875119878119877119905 = 119871119886119888119896( sum119899isinΦ119905119888

sum119896isin120595119899119896 =119905

119875119878119879119896 minus |Φ119905119888 |sum119902=2

(minus1)119902 |Φ119905119888 |119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


( sum119896isin120595119899 119896 =119905


119875119878119879119896)) (B3)



119875119887119906119904119910119878119905 = sum119896isinΦ119905119896 =BS

119875119878119879119896 minus |119862|sum119902=2

(minus1)119902sdot |119862|119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982ℎ119898119902


( sum119896isin(120595119899capΦ119905)


119875119878119879119896)119875119887119906119904119910119865119905 = (1 minus prod

119895isinΦ119905119895 =BS(1 minus 120591119895))


(1 minus 120591119895)minus 119875119887119906119904119910119878119905 119875119887119906119904119910119860119905 = 119875119878119877119905119871119886119888119896

(B4)



119895isinΦ119905119895 =BS(1 minus 120591119895))



(1 minus 120591119895))119894minus1







Competing Interests


References










































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Node 2

Node 1





(bf (119895) + cca (119895)))sdotmod (119906 + 1) (1)











Transmitted Ack

0000192

00001920000128


1st CCA 2nd CCA

Destinationnode


Received data Pkt


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)

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the a

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acko

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6

7

8

u = 25

u = 5









11

11

11

11

11

11

q0

q0q0Q0

Q1


minus1 Ls minus 1 0



P


1 minus

P


1 minus


P

1 minus P

1 minus

0 minus1 1 0 0 1 0 1 1

m 11m 0 1


1 minus

minus2 0 1

minus1 Ls minus 1 1

minus2 Lc minus 1 1

minus1 0 1

P

1 minus P

1 minus

1 minus

0 minus1 1


P


minus1 0 n

minus1 Ls minus 1 n



P


pK(k | I = 0)

pK(k | I = 0)

pK(k | I = 0)

pK(k | I = 0)

pK(k | I = 1)

pK(k | I = 1)

pK(k | I = 1)

pK(k | I = m)

pK(k | I = m)

pK(k | I = m)

QL0minus1











rnum (119880119861 119904) = r (119880119861 119904) (119873 minus 1)119878 (3)




119911=1

( 119911sum119890=1

119888119903119900119911leV119911minus1119890


119911=1

( 119911sum119890=1

119888119903119900119911leV119911minus1119890





tknum (119878) = 2119878 (119878+1)sum119903119900=1

cnum (119903119900) (5)


knum (119896 119878) = (119878+1)sum119903119900=1

119896=bf119903119900(119878)

cnum (119903119900) (6)

where


119888119900=1


(7)



bstknum (119878) = 2119878 (8)



119896=bf(119878)1 (9)

where


119888119900=1


(10)


119868119863=1


119868119863=1

bsknum (119896 119894)bstknum (119894)



P (119894 119896 119895 | 119894 119896 + 1 119895) = 1 for 2119898119887 minus 1 ge 119896 ge 0 (12)




P (1198760 | 119898 0 119895) = 1199020 (120572 + (1 minus 120572) 120573) for 119895 lt 119899 (15)


P (1198760 | 119898 0 119899) = 1199020 (17)



119903=119896

119901119870 (119903 | 119868 = 119894) (19)1198871198940119895 = (120572 + (1 minus 120572) 120573) 119887119894minus10119895 (20)



119901119870 (119903 | 119868 = 119894) (22)


119901119870 (119903 | 119868 = 0) 119898sum119894=0

1198871198940119895minus1= 11988700119895 2119898119887minus1sum

119903=119896

119901119870 (119903 | 119868 = 0) (23)


119901119870 (119903 | 119868 = 119894) (24)





119887119894119896119895 = 119909119894119910119895119887000 2119898119887minus1sum119903=119896

119901119870 (119903 | 119868 = 119894) (27)


119899sum119895=0

2119898119887minus1sum119896=0

119898sum119894=0

119887119894119896119895 + 119898sum119894=0

119899sum119895=0

119887119894minus1119895+ 119899sum119895=0

(119871119904minus1sum119896=0

119887minus1119896119895 + 119871119888minus1sum119896=0

119887minus2119896119895) + 1198710minus1sum119897=0

119876119897 = 1 (28)



119898sum119894=0

(119909119894 2119898119887minus1sum119903=119896


(29)



119894=0

119899sum119895=0



(30)


119895=0

1 minus 1199101 minus 119910119899+1119910119895(119895 (119871119888 + 119864 [119879ℎ])+ 119898sum

119894=0

2119898119887minus1sum119903=0

119903119901119870 (119903 | 119868 = 119894) + 119879119878119862 2119898+1sum119890=1

119862119890120572120573 (119898 + 1)sdot (119873119890

120572 (119898 + 1) + 2119873119890120573 (119898 + 1)))]]

(31)



119894=0 119862120572120573 (119894) 119898sum119894=0

( 2119894sum119890=1

119862119890120572120573 (119894) 119894sum119897=0

2119898119887minus1sum119903=0

119903119901119870 (119903 | 119868 = 119897)) (33)



119894=0

2119898119887minus1sum119896=1

119899sum119895=0

119887119894119896119895 + 119864119904119888 119898sum119894=0

119899sum119895=0

(1198871198940119895 + 119887119894minus1119895)+ 119864119905 119899sum

119895=0

119871minus1sum119896=0

(119887minus1119896119895 + 119887minus2119896119895)+ 119864119894 119899sum

119895=0

(119887minus1119871119895 + 119887minus2119871119895)+ 119899sum119895=0

119871+119871119886119888119896+1sum119896=119871+1


119876119897(34)






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(36)











119895isinΦ119905119903 119895 =BS(1 minus 120591119895) (38)


120595ℎ(1 minus 120591119896)


| ⋃ℎisinΦℎ119888119905119903120595ℎ|119862119902sum

119898=1

( prod119894isin119889119898

119889119898=1198891198981 1198891198982 119889119898119902


120595ℎ119889119898


119899isin119889119898119889119898=1198891198981 1198891198982119889119898119902

(120572119899 + (1 minus 120572119899) 120573119899)))(39)






= 2119871 |Φℎ119905119903BS|sum119902=1

|Φℎ119905119903BS|119862119902sum119898=1

( prod119894isin119896119898

119896119898=1198961198981 1198961198982 119896119898119902



119899isin119896119898119896119898=1198961198981 1198961198982 119896119898119902

(120572119899 + (1 minus 120572119899) 120573119899)))(40)




119902=1

|Φ119905BS|119862119902sum119898=1

( prod119894isin119896119898

119896119898=1198961198981 1198961198982 119896119898119902



119899isin119896119898119896119898=1198961198981 1198961198982 119896119898119902


120595ℎ119905(1 minus 120591119896)

sdot | ⋃ℎisinΦ119905119888 120595ℎ119905|sum119902=1

| ⋃ℎisinΦ119905119888120595ℎ119905|119862119902sum

119898=1

( prod119894isin119889119898

119889119898=1198891198981 1198891198982119889119898119902


120595ℎ(119889119898cup119905)


119899isin119889119898119889119898=1198891198981 1198891198982 119889119898119902

(120572119899 + (1 minus 120572119899) 120573119899)))

(41)









P (1198611199041198971199001199051 cap 1198681198621198621198601) + P (1198681199041198971199001199051 cap 1198681198621198621198601) (43)


P (1198611199041198971199001199051 cap 1198681198621198621198601) + P (1198681199041198971199001199051 cap 1198681198621198621198601))sdot P (1198781199041198971199001199051) + 119875119887119890119905119886119860119862119870 (44)




(1 minus 120591119895))+ 119875119887119906119904119910119860119905119875119887119906119904119910119865119905 + 119875119887119906119904119910119860119905 + 119875119887119906119904119910119878119905 + 119875119894119889119897119890119905

(45)







IBSrceil) (46)






119877e-to-e = 119897prod119899=1

119877119899 (48)





119899=1

(119908119899 + 119863119899) (49)



119864e-to-e = 119897sum119899=1

119864119899 (50)


119894isinΦ119905119900119905119886119897

(1 minus 120591119894) 119875119904119906119888119888119890119904119904 = sum119894isinΦ119905119900119905119886119897

119875119878119879119894119875119887119906119904119910 (51)



119899isinΦ119905119900119905119886119897

sum119903isin119874119899

119877e-to-e (119899 119903)119863e-to-e (119899 119903) (52)



510

1520

25

12

34

= 3

= 4 = 5um

0

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= 3 = 4 = 5

um

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510

1520

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= 3 = 4

= 5

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0

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0879

0881

0883

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0891

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m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2 m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 3

m = 3 m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 4

m = 4

m = 4m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4m = 4

m = 4

m = 4

m = 4







Φ16119888= 1 3 4 5 Φ16 4= 1 3 5 8 9 12 13 14 15 17 19 20 22 Φℎ16 4 = 0 2 21 Φℎ11988816 4 = 0 2 11986216 = 4 1205950 = 1 4 1205951 = 12 14 15 1205952 = 7 11 18 1205953 = 6 13 22 24 1205954 = 5 8 16 17 1205955 = 2 3 9 19 20

(53)










IEEE slotted CSMACA

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CAM 431-131-131CAM 431-430-131

CAM 631-430-131CAM 631-131-131










Appendix













where




bsknum (119896 119878) = 2119878sum119862119862119860119888119900119898119887=1


where

sumfn (119878 119862119862119860119888119900119898119887 119868119863)=


119872119894119899119861119865119904119906119898119879119890119903119898 =




1 if 119878 = 1119878 + 119878minus1sum119899=1




(A7)






119875119878119877ℎ119905 = (119871119886119888119896 + 119871) sum119899isinΦℎ119888119905119903


119875119878119879119896 + 119871119886119888119896 sum119899isinΦℎ119888119905119903

sum119896isin(120595119899capΦℎ119905119903)

119875119878119879119896 + sum119899isinΦℎ119888119905119903

sum119896isin(120595119899capΦ119905)

119875119878119879119896 minus (119871119886119888119896 + 119871) |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902




119875119878119879119896)minus 119871119886119888119896 |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


(( sum119896isin(120595119899capΦℎ119905119903)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911 119896notinΦ119905


119875119878119879119896))


minus |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


(( sum119896isin(120595119899capΦ119905)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911


119875119878119879119896))(B1)

119875119878119879119896 = 120591119896 prod119895isinΦ119896119899




119875119878119877119905 = 119871119886119888119896( sum119899isinΦ119905119888

sum119896isin120595119899119896 =119905

119875119878119879119896 minus |Φ119905119888 |sum119902=2

(minus1)119902 |Φ119905119888 |119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


( sum119896isin120595119899 119896 =119905


119875119878119879119896)) (B3)



119875119887119906119904119910119878119905 = sum119896isinΦ119905119896 =BS

119875119878119879119896 minus |119862|sum119902=2

(minus1)119902sdot |119862|119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982ℎ119898119902


( sum119896isin(120595119899capΦ119905)


119875119878119879119896)119875119887119906119904119910119865119905 = (1 minus prod

119895isinΦ119905119895 =BS(1 minus 120591119895))


(1 minus 120591119895)minus 119875119887119906119904119910119878119905 119875119887119906119904119910119860119905 = 119875119878119877119905119871119886119888119896

(B4)



119895isinΦ119905119895 =BS(1 minus 120591119895))



(1 minus 120591119895))119894minus1







Competing Interests


References










































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Transmitted Ack

0000192

00001920000128


1st CCA 2nd CCA

Destinationnode


Received data Pkt


10 20 30 40 50 60 700Number of nodes

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10 20 30 40 50 60 700Number of nodes



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atte

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)

20 30 40 50 60 7010Number of nodes

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10 20 30 40 50 60 70Number of nodes


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20 30 40 50 60 7010Number of nodes

Stan

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acko

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2

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5

6

7

8

u = 25

u = 5









11

11

11

11

11

11

q0

q0q0Q0

Q1


minus1 Ls minus 1 0



P


1 minus

P


1 minus


P

1 minus P

1 minus

0 minus1 1 0 0 1 0 1 1

m 11m 0 1


1 minus

minus2 0 1

minus1 Ls minus 1 1

minus2 Lc minus 1 1

minus1 0 1

P

1 minus P

1 minus

1 minus

0 minus1 1


P


minus1 0 n

minus1 Ls minus 1 n



P


pK(k | I = 0)

pK(k | I = 0)

pK(k | I = 0)

pK(k | I = 0)

pK(k | I = 1)

pK(k | I = 1)

pK(k | I = 1)

pK(k | I = m)

pK(k | I = m)

pK(k | I = m)

QL0minus1











rnum (119880119861 119904) = r (119880119861 119904) (119873 minus 1)119878 (3)




119911=1

( 119911sum119890=1

119888119903119900119911leV119911minus1119890


119911=1

( 119911sum119890=1

119888119903119900119911leV119911minus1119890





tknum (119878) = 2119878 (119878+1)sum119903119900=1

cnum (119903119900) (5)


knum (119896 119878) = (119878+1)sum119903119900=1

119896=bf119903119900(119878)

cnum (119903119900) (6)

where


119888119900=1


(7)



bstknum (119878) = 2119878 (8)



119896=bf(119878)1 (9)

where


119888119900=1


(10)


119868119863=1


119868119863=1

bsknum (119896 119894)bstknum (119894)



P (119894 119896 119895 | 119894 119896 + 1 119895) = 1 for 2119898119887 minus 1 ge 119896 ge 0 (12)




P (1198760 | 119898 0 119895) = 1199020 (120572 + (1 minus 120572) 120573) for 119895 lt 119899 (15)


P (1198760 | 119898 0 119899) = 1199020 (17)



119903=119896

119901119870 (119903 | 119868 = 119894) (19)1198871198940119895 = (120572 + (1 minus 120572) 120573) 119887119894minus10119895 (20)



119901119870 (119903 | 119868 = 119894) (22)


119901119870 (119903 | 119868 = 0) 119898sum119894=0

1198871198940119895minus1= 11988700119895 2119898119887minus1sum

119903=119896

119901119870 (119903 | 119868 = 0) (23)


119901119870 (119903 | 119868 = 119894) (24)





119887119894119896119895 = 119909119894119910119895119887000 2119898119887minus1sum119903=119896

119901119870 (119903 | 119868 = 119894) (27)


119899sum119895=0

2119898119887minus1sum119896=0

119898sum119894=0

119887119894119896119895 + 119898sum119894=0

119899sum119895=0

119887119894minus1119895+ 119899sum119895=0

(119871119904minus1sum119896=0

119887minus1119896119895 + 119871119888minus1sum119896=0

119887minus2119896119895) + 1198710minus1sum119897=0

119876119897 = 1 (28)



119898sum119894=0

(119909119894 2119898119887minus1sum119903=119896


(29)



119894=0

119899sum119895=0



(30)


119895=0

1 minus 1199101 minus 119910119899+1119910119895(119895 (119871119888 + 119864 [119879ℎ])+ 119898sum

119894=0

2119898119887minus1sum119903=0

119903119901119870 (119903 | 119868 = 119894) + 119879119878119862 2119898+1sum119890=1

119862119890120572120573 (119898 + 1)sdot (119873119890

120572 (119898 + 1) + 2119873119890120573 (119898 + 1)))]]

(31)



119894=0 119862120572120573 (119894) 119898sum119894=0

( 2119894sum119890=1

119862119890120572120573 (119894) 119894sum119897=0

2119898119887minus1sum119903=0

119903119901119870 (119903 | 119868 = 119897)) (33)



119894=0

2119898119887minus1sum119896=1

119899sum119895=0

119887119894119896119895 + 119864119904119888 119898sum119894=0

119899sum119895=0

(1198871198940119895 + 119887119894minus1119895)+ 119864119905 119899sum

119895=0

119871minus1sum119896=0

(119887minus1119896119895 + 119887minus2119896119895)+ 119864119894 119899sum

119895=0

(119887minus1119871119895 + 119887minus2119871119895)+ 119899sum119895=0

119871+119871119886119888119896+1sum119896=119871+1


119876119897(34)






0 10 20 30 40 50

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(a)

0 10 20 30 40 50

1

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1412

1520

919

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11

0

10

20

30

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(b)












(36)











119895isinΦ119905119903 119895 =BS(1 minus 120591119895) (38)


120595ℎ(1 minus 120591119896)


| ⋃ℎisinΦℎ119888119905119903120595ℎ|119862119902sum

119898=1

( prod119894isin119889119898

119889119898=1198891198981 1198891198982 119889119898119902


120595ℎ119889119898


119899isin119889119898119889119898=1198891198981 1198891198982119889119898119902

(120572119899 + (1 minus 120572119899) 120573119899)))(39)






= 2119871 |Φℎ119905119903BS|sum119902=1

|Φℎ119905119903BS|119862119902sum119898=1

( prod119894isin119896119898

119896119898=1198961198981 1198961198982 119896119898119902



119899isin119896119898119896119898=1198961198981 1198961198982 119896119898119902

(120572119899 + (1 minus 120572119899) 120573119899)))(40)




119902=1

|Φ119905BS|119862119902sum119898=1

( prod119894isin119896119898

119896119898=1198961198981 1198961198982 119896119898119902



119899isin119896119898119896119898=1198961198981 1198961198982 119896119898119902


120595ℎ119905(1 minus 120591119896)

sdot | ⋃ℎisinΦ119905119888 120595ℎ119905|sum119902=1

| ⋃ℎisinΦ119905119888120595ℎ119905|119862119902sum

119898=1

( prod119894isin119889119898

119889119898=1198891198981 1198891198982119889119898119902


120595ℎ(119889119898cup119905)


119899isin119889119898119889119898=1198891198981 1198891198982 119889119898119902

(120572119899 + (1 minus 120572119899) 120573119899)))

(41)









P (1198611199041198971199001199051 cap 1198681198621198621198601) + P (1198681199041198971199001199051 cap 1198681198621198621198601) (43)


P (1198611199041198971199001199051 cap 1198681198621198621198601) + P (1198681199041198971199001199051 cap 1198681198621198621198601))sdot P (1198781199041198971199001199051) + 119875119887119890119905119886119860119862119870 (44)




(1 minus 120591119895))+ 119875119887119906119904119910119860119905119875119887119906119904119910119865119905 + 119875119887119906119904119910119860119905 + 119875119887119906119904119910119878119905 + 119875119894119889119897119890119905

(45)







IBSrceil) (46)






119877e-to-e = 119897prod119899=1

119877119899 (48)





119899=1

(119908119899 + 119863119899) (49)



119864e-to-e = 119897sum119899=1

119864119899 (50)


119894isinΦ119905119900119905119886119897

(1 minus 120591119894) 119875119904119906119888119888119890119904119904 = sum119894isinΦ119905119900119905119886119897

119875119878119879119894119875119887119906119904119910 (51)



119899isinΦ119905119900119905119886119897

sum119903isin119874119899

119877e-to-e (119899 119903)119863e-to-e (119899 119903) (52)



510

1520

25

12

34

= 3

= 4 = 5um

0

001

002

003

004

005

Relia

bilit

y


510

1520

25

12

34

= 3 = 4 = 5

um

5

10

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30

Avg

del

ay (m

s)






510

1520

25

12

34

= 3 = 4

= 5

um

15

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25

Pow

er co

nsum

ptio

n (m

W)







0

002

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006

008

01

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014

Relia

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30 40 50 60 70 80

Prob

abili

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ts

Number of nodes

075

08

085

09

095

1

due t

o ch

anne

l acc

ess f

ailu

re







0875

0877

0879

0881

0883

0885

0887

0889

0891

Prob

abili

ty o

f uns

ucce

ssfu

l cha

nnel

acce

ss at

tem

pt





0

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0

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35 40 45 50 55 60 65 70 75 8030Number of nodes

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Avg

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s)




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008

Relia

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35 40 45 50 55 60 65 70 75 8030Number of nodes







14

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2

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22

Ener

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nsum

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n (m

w)

35 40 45 50 55 60 65 70 75 8030Number of nodes




35 40 45 50 55 60 65 70 75 8030Number of nodes

0

005

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025

Thro

ughp

ut






















5 10 15 20 25 300u

05055

06065

07075

08085

Relia

bilit

y

5 10 15 20 25 300u

456789

1011121314

Avg

del

ay (m

s)

3638

442444648

552

Avg

ener

gy co

nsum

ptio

n (m

w)

5 10 15 20 25 300u

04045

05055

06065

07075

Relia

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y

5 10 15 20 25 300u

468

10121416

Avg

del

ay (m

s)

5 10 15 20 25 300u

332343638

442444648

Avg

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nsum

ptio

n (m

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5 10 15 20 25 300u

02025

03035

04045

05055

Relia

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y

5 10 15 20 25 300u

5

10

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20

Avg

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5 10 15 20 25 300u

2

25

3

35

Avg

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5 10 15 20 25 300u

01015

02025

03035

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Relia

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5 10 15 20 25 300u

468

1012141618202224

Avg

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5 10 15 20 25 300u

5 10 15 20 25 300u

1618

222242628

332

Avg

ener

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nsum

ptio

n (m

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0002004006008

01012014

Relia

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5 10 15 20 25 300u

5

10

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25

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Avg

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s)

5 10 15 20 25 300u

5 10 15 20 25 300u

112141618

222242628

3

Avg

ener

gy co

nsum

ptio

n (m

w)

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2 m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 3

m = 3 m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 4

m = 4

m = 4m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4m = 4

m = 4

m = 4

m = 4







Φ16119888= 1 3 4 5 Φ16 4= 1 3 5 8 9 12 13 14 15 17 19 20 22 Φℎ16 4 = 0 2 21 Φℎ11988816 4 = 0 2 11986216 = 4 1205950 = 1 4 1205951 = 12 14 15 1205952 = 7 11 18 1205953 = 6 13 22 24 1205954 = 5 8 16 17 1205955 = 2 3 9 19 20

(53)










IEEE slotted CSMACA

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to-e

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CAM 431-131-131CAM 431-430-131

CAM 631-430-131CAM 631-131-131







000E + 00

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400E + 01

500E + 01

600E + 01

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CAM 631-430-131CAM 631-131-131




01

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50

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IEEE slotted CSMACA

000E + 00

500E + 00

100E + 01

150E + 01

200E + 01

End-

to-e

nd p

ower

cons

umpt

ion

(mW

)

CAM 431-131-131CAM 431-430-131

CAM 631-430-131CAM 631-131-131










Appendix













where




bsknum (119896 119878) = 2119878sum119862119862119860119888119900119898119887=1


where

sumfn (119878 119862119862119860119888119900119898119887 119868119863)=


119872119894119899119861119865119904119906119898119879119890119903119898 =




1 if 119878 = 1119878 + 119878minus1sum119899=1




(A7)






119875119878119877ℎ119905 = (119871119886119888119896 + 119871) sum119899isinΦℎ119888119905119903


119875119878119879119896 + 119871119886119888119896 sum119899isinΦℎ119888119905119903

sum119896isin(120595119899capΦℎ119905119903)

119875119878119879119896 + sum119899isinΦℎ119888119905119903

sum119896isin(120595119899capΦ119905)

119875119878119879119896 minus (119871119886119888119896 + 119871) |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902




119875119878119879119896)minus 119871119886119888119896 |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


(( sum119896isin(120595119899capΦℎ119905119903)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911 119896notinΦ119905


119875119878119879119896))


minus |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


(( sum119896isin(120595119899capΦ119905)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911


119875119878119879119896))(B1)

119875119878119879119896 = 120591119896 prod119895isinΦ119896119899




119875119878119877119905 = 119871119886119888119896( sum119899isinΦ119905119888

sum119896isin120595119899119896 =119905

119875119878119879119896 minus |Φ119905119888 |sum119902=2

(minus1)119902 |Φ119905119888 |119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


( sum119896isin120595119899 119896 =119905


119875119878119879119896)) (B3)



119875119887119906119904119910119878119905 = sum119896isinΦ119905119896 =BS

119875119878119879119896 minus |119862|sum119902=2

(minus1)119902sdot |119862|119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982ℎ119898119902


( sum119896isin(120595119899capΦ119905)


119875119878119879119896)119875119887119906119904119910119865119905 = (1 minus prod

119895isinΦ119905119895 =BS(1 minus 120591119895))


(1 minus 120591119895)minus 119875119887119906119904119910119878119905 119875119887119906119904119910119860119905 = 119875119878119877119905119871119886119888119896

(B4)



119895isinΦ119905119895 =BS(1 minus 120591119895))



(1 minus 120591119895))119894minus1







Competing Interests


References










































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










10 20 30 40 50 60 70Number of nodes


0

10

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f occ

urre

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20 30 40 50 60 7010Number of nodes

Stan

dard

dev

iatio

n of

the a

vera

ge b

acko

ff de

lay

2

3

4

5

6

7

8

u = 25

u = 5









11

11

11

11

11

11

q0

q0q0Q0

Q1


minus1 Ls minus 1 0



P


1 minus

P


1 minus


P

1 minus P

1 minus

0 minus1 1 0 0 1 0 1 1

m 11m 0 1


1 minus

minus2 0 1

minus1 Ls minus 1 1

minus2 Lc minus 1 1

minus1 0 1

P

1 minus P

1 minus

1 minus

0 minus1 1


P


minus1 0 n

minus1 Ls minus 1 n



P


pK(k | I = 0)

pK(k | I = 0)

pK(k | I = 0)

pK(k | I = 0)

pK(k | I = 1)

pK(k | I = 1)

pK(k | I = 1)

pK(k | I = m)

pK(k | I = m)

pK(k | I = m)

QL0minus1











rnum (119880119861 119904) = r (119880119861 119904) (119873 minus 1)119878 (3)




119911=1

( 119911sum119890=1

119888119903119900119911leV119911minus1119890


119911=1

( 119911sum119890=1

119888119903119900119911leV119911minus1119890





tknum (119878) = 2119878 (119878+1)sum119903119900=1

cnum (119903119900) (5)


knum (119896 119878) = (119878+1)sum119903119900=1

119896=bf119903119900(119878)

cnum (119903119900) (6)

where


119888119900=1


(7)



bstknum (119878) = 2119878 (8)



119896=bf(119878)1 (9)

where


119888119900=1


(10)


119868119863=1


119868119863=1

bsknum (119896 119894)bstknum (119894)



P (119894 119896 119895 | 119894 119896 + 1 119895) = 1 for 2119898119887 minus 1 ge 119896 ge 0 (12)




P (1198760 | 119898 0 119895) = 1199020 (120572 + (1 minus 120572) 120573) for 119895 lt 119899 (15)


P (1198760 | 119898 0 119899) = 1199020 (17)



119903=119896

119901119870 (119903 | 119868 = 119894) (19)1198871198940119895 = (120572 + (1 minus 120572) 120573) 119887119894minus10119895 (20)



119901119870 (119903 | 119868 = 119894) (22)


119901119870 (119903 | 119868 = 0) 119898sum119894=0

1198871198940119895minus1= 11988700119895 2119898119887minus1sum

119903=119896

119901119870 (119903 | 119868 = 0) (23)


119901119870 (119903 | 119868 = 119894) (24)





119887119894119896119895 = 119909119894119910119895119887000 2119898119887minus1sum119903=119896

119901119870 (119903 | 119868 = 119894) (27)


119899sum119895=0

2119898119887minus1sum119896=0

119898sum119894=0

119887119894119896119895 + 119898sum119894=0

119899sum119895=0

119887119894minus1119895+ 119899sum119895=0

(119871119904minus1sum119896=0

119887minus1119896119895 + 119871119888minus1sum119896=0

119887minus2119896119895) + 1198710minus1sum119897=0

119876119897 = 1 (28)



119898sum119894=0

(119909119894 2119898119887minus1sum119903=119896


(29)



119894=0

119899sum119895=0



(30)


119895=0

1 minus 1199101 minus 119910119899+1119910119895(119895 (119871119888 + 119864 [119879ℎ])+ 119898sum

119894=0

2119898119887minus1sum119903=0

119903119901119870 (119903 | 119868 = 119894) + 119879119878119862 2119898+1sum119890=1

119862119890120572120573 (119898 + 1)sdot (119873119890

120572 (119898 + 1) + 2119873119890120573 (119898 + 1)))]]

(31)



119894=0 119862120572120573 (119894) 119898sum119894=0

( 2119894sum119890=1

119862119890120572120573 (119894) 119894sum119897=0

2119898119887minus1sum119903=0

119903119901119870 (119903 | 119868 = 119897)) (33)



119894=0

2119898119887minus1sum119896=1

119899sum119895=0

119887119894119896119895 + 119864119904119888 119898sum119894=0

119899sum119895=0

(1198871198940119895 + 119887119894minus1119895)+ 119864119905 119899sum

119895=0

119871minus1sum119896=0

(119887minus1119896119895 + 119887minus2119896119895)+ 119864119894 119899sum

119895=0

(119887minus1119871119895 + 119887minus2119871119895)+ 119899sum119895=0

119871+119871119886119888119896+1sum119896=119871+1


119876119897(34)






0 10 20 30 40 50

P

O

T

SQ

R

E

A

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G

L

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M

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X

P

O

T

SQQ

R

I

A

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U

F

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VV

X

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G

L

JJ

K

B

C

H

0

10

20

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40

50


(a)

0 10 20 30 40 50

1

45

2

6

3

1412

1520

919

8

16

17

22

21

1324

23

10

18 7

11

0

10

20

30

40

50


(b)












(36)











119895isinΦ119905119903 119895 =BS(1 minus 120591119895) (38)


120595ℎ(1 minus 120591119896)


| ⋃ℎisinΦℎ119888119905119903120595ℎ|119862119902sum

119898=1

( prod119894isin119889119898

119889119898=1198891198981 1198891198982 119889119898119902


120595ℎ119889119898


119899isin119889119898119889119898=1198891198981 1198891198982119889119898119902

(120572119899 + (1 minus 120572119899) 120573119899)))(39)






= 2119871 |Φℎ119905119903BS|sum119902=1

|Φℎ119905119903BS|119862119902sum119898=1

( prod119894isin119896119898

119896119898=1198961198981 1198961198982 119896119898119902



119899isin119896119898119896119898=1198961198981 1198961198982 119896119898119902

(120572119899 + (1 minus 120572119899) 120573119899)))(40)




119902=1

|Φ119905BS|119862119902sum119898=1

( prod119894isin119896119898

119896119898=1198961198981 1198961198982 119896119898119902



119899isin119896119898119896119898=1198961198981 1198961198982 119896119898119902


120595ℎ119905(1 minus 120591119896)

sdot | ⋃ℎisinΦ119905119888 120595ℎ119905|sum119902=1

| ⋃ℎisinΦ119905119888120595ℎ119905|119862119902sum

119898=1

( prod119894isin119889119898

119889119898=1198891198981 1198891198982119889119898119902


120595ℎ(119889119898cup119905)


119899isin119889119898119889119898=1198891198981 1198891198982 119889119898119902

(120572119899 + (1 minus 120572119899) 120573119899)))

(41)









P (1198611199041198971199001199051 cap 1198681198621198621198601) + P (1198681199041198971199001199051 cap 1198681198621198621198601) (43)


P (1198611199041198971199001199051 cap 1198681198621198621198601) + P (1198681199041198971199001199051 cap 1198681198621198621198601))sdot P (1198781199041198971199001199051) + 119875119887119890119905119886119860119862119870 (44)




(1 minus 120591119895))+ 119875119887119906119904119910119860119905119875119887119906119904119910119865119905 + 119875119887119906119904119910119860119905 + 119875119887119906119904119910119878119905 + 119875119894119889119897119890119905

(45)







IBSrceil) (46)






119877e-to-e = 119897prod119899=1

119877119899 (48)





119899=1

(119908119899 + 119863119899) (49)



119864e-to-e = 119897sum119899=1

119864119899 (50)


119894isinΦ119905119900119905119886119897

(1 minus 120591119894) 119875119904119906119888119888119890119904119904 = sum119894isinΦ119905119900119905119886119897

119875119878119879119894119875119887119906119904119910 (51)



119899isinΦ119905119900119905119886119897

sum119903isin119874119899

119877e-to-e (119899 119903)119863e-to-e (119899 119903) (52)



510

1520

25

12

34

= 3

= 4 = 5um

0

001

002

003

004

005

Relia

bilit

y


510

1520

25

12

34

= 3 = 4 = 5

um

5

10

15

20

25

30

Avg

del

ay (m

s)






510

1520

25

12

34

= 3 = 4

= 5

um

15

2

25

Pow

er co

nsum

ptio

n (m

W)







0

002

004

006

008

01

012

014

Relia

bilit

y







30 40 50 60 70 80

Prob

abili

ty o

f disc

ardi

ng p

acke

ts

Number of nodes

075

08

085

09

095

1

due t

o ch

anne

l acc

ess f

ailu

re







0875

0877

0879

0881

0883

0885

0887

0889

0891

Prob

abili

ty o

f uns

ucce

ssfu

l cha

nnel

acce

ss at

tem

pt





0

5

10

15

20

25

30

35

40

Avg

del

ay (m

s)









0

05

1

15

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Ener

gy co

nsum

ptio

n (m

w)





0

005

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015

02

025

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Thro

ughp

ut






35 40 45 50 55 60 65 70 75 8030Number of nodes

12

13

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Avg

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s)




0

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007

008

Relia

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y

35 40 45 50 55 60 65 70 75 8030Number of nodes







14

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Ener

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nsum

ptio

n (m

w)

35 40 45 50 55 60 65 70 75 8030Number of nodes




35 40 45 50 55 60 65 70 75 8030Number of nodes

0

005

01

015

02

025

Thro

ughp

ut






















5 10 15 20 25 300u

05055

06065

07075

08085

Relia

bilit

y

5 10 15 20 25 300u

456789

1011121314

Avg

del

ay (m

s)

3638

442444648

552

Avg

ener

gy co

nsum

ptio

n (m

w)

5 10 15 20 25 300u

04045

05055

06065

07075

Relia

bilit

y

5 10 15 20 25 300u

468

10121416

Avg

del

ay (m

s)

5 10 15 20 25 300u

332343638

442444648

Avg

ener

gy co

nsum

ptio

n (m

w)

5 10 15 20 25 300u

02025

03035

04045

05055

Relia

bilit

y

5 10 15 20 25 300u

5

10

15

20

Avg

del

ay (m

s)

5 10 15 20 25 300u

2

25

3

35

Avg

ener

gy co

nsum

ptio

n (m

w)

5 10 15 20 25 300u

01015

02025

03035

04

Relia

bilit

y

5 10 15 20 25 300u

468

1012141618202224

Avg

del

ay (m

s)

5 10 15 20 25 300u

5 10 15 20 25 300u

1618

222242628

332

Avg

ener

gy co

nsum

ptio

n (m

w)

0002004006008

01012014

Relia

bilit

y

5 10 15 20 25 300u

5

10

15

20

25

30

Avg

del

ay (m

s)

5 10 15 20 25 300u

5 10 15 20 25 300u

112141618

222242628

3

Avg

ener

gy co

nsum

ptio

n (m

w)

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2 m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 3

m = 3 m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 4

m = 4

m = 4m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4m = 4

m = 4

m = 4

m = 4







Φ16119888= 1 3 4 5 Φ16 4= 1 3 5 8 9 12 13 14 15 17 19 20 22 Φℎ16 4 = 0 2 21 Φℎ11988816 4 = 0 2 11986216 = 4 1205950 = 1 4 1205951 = 12 14 15 1205952 = 7 11 18 1205953 = 6 13 22 24 1205954 = 5 8 16 17 1205955 = 2 3 9 19 20

(53)










IEEE slotted CSMACA

0

01

02

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04

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06

07

08

End-

to-e

nd re

liabi

lity

CAM 431-131-131CAM 431-430-131

CAM 631-430-131CAM 631-131-131







000E + 00

100E + 01

200E + 01

300E + 01

400E + 01

500E + 01

600E + 01

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nd d

elay

(ms)


CAM 631-430-131CAM 631-131-131




01

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age n

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IEEE slotted CSMACA

000E + 00

500E + 00

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150E + 01

200E + 01

End-

to-e

nd p

ower

cons

umpt

ion

(mW

)

CAM 431-131-131CAM 431-430-131

CAM 631-430-131CAM 631-131-131










Appendix













where




bsknum (119896 119878) = 2119878sum119862119862119860119888119900119898119887=1


where

sumfn (119878 119862119862119860119888119900119898119887 119868119863)=


119872119894119899119861119865119904119906119898119879119890119903119898 =




1 if 119878 = 1119878 + 119878minus1sum119899=1




(A7)






119875119878119877ℎ119905 = (119871119886119888119896 + 119871) sum119899isinΦℎ119888119905119903


119875119878119879119896 + 119871119886119888119896 sum119899isinΦℎ119888119905119903

sum119896isin(120595119899capΦℎ119905119903)

119875119878119879119896 + sum119899isinΦℎ119888119905119903

sum119896isin(120595119899capΦ119905)

119875119878119879119896 minus (119871119886119888119896 + 119871) |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902




119875119878119879119896)minus 119871119886119888119896 |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


(( sum119896isin(120595119899capΦℎ119905119903)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911 119896notinΦ119905


119875119878119879119896))


minus |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


(( sum119896isin(120595119899capΦ119905)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911


119875119878119879119896))(B1)

119875119878119879119896 = 120591119896 prod119895isinΦ119896119899




119875119878119877119905 = 119871119886119888119896( sum119899isinΦ119905119888

sum119896isin120595119899119896 =119905

119875119878119879119896 minus |Φ119905119888 |sum119902=2

(minus1)119902 |Φ119905119888 |119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


( sum119896isin120595119899 119896 =119905


119875119878119879119896)) (B3)



119875119887119906119904119910119878119905 = sum119896isinΦ119905119896 =BS

119875119878119879119896 minus |119862|sum119902=2

(minus1)119902sdot |119862|119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982ℎ119898119902


( sum119896isin(120595119899capΦ119905)


119875119878119879119896)119875119887119906119904119910119865119905 = (1 minus prod

119895isinΦ119905119895 =BS(1 minus 120591119895))


(1 minus 120591119895)minus 119875119887119906119904119910119878119905 119875119887119906119904119910119860119905 = 119875119878119877119905119871119886119888119896

(B4)



119895isinΦ119905119895 =BS(1 minus 120591119895))



(1 minus 120591119895))119894minus1







Competing Interests


References










































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










11

11

11

11

11

11

q0

q0q0Q0

Q1


minus1 Ls minus 1 0



P


1 minus

P


1 minus


P

1 minus P

1 minus

0 minus1 1 0 0 1 0 1 1

m 11m 0 1


1 minus

minus2 0 1

minus1 Ls minus 1 1

minus2 Lc minus 1 1

minus1 0 1

P

1 minus P

1 minus

1 minus

0 minus1 1


P


minus1 0 n

minus1 Ls minus 1 n



P


pK(k | I = 0)

pK(k | I = 0)

pK(k | I = 0)

pK(k | I = 0)

pK(k | I = 1)

pK(k | I = 1)

pK(k | I = 1)

pK(k | I = m)

pK(k | I = m)

pK(k | I = m)

QL0minus1











rnum (119880119861 119904) = r (119880119861 119904) (119873 minus 1)119878 (3)




119911=1

( 119911sum119890=1

119888119903119900119911leV119911minus1119890


119911=1

( 119911sum119890=1

119888119903119900119911leV119911minus1119890





tknum (119878) = 2119878 (119878+1)sum119903119900=1

cnum (119903119900) (5)


knum (119896 119878) = (119878+1)sum119903119900=1

119896=bf119903119900(119878)

cnum (119903119900) (6)

where


119888119900=1


(7)



bstknum (119878) = 2119878 (8)



119896=bf(119878)1 (9)

where


119888119900=1


(10)


119868119863=1


119868119863=1

bsknum (119896 119894)bstknum (119894)



P (119894 119896 119895 | 119894 119896 + 1 119895) = 1 for 2119898119887 minus 1 ge 119896 ge 0 (12)




P (1198760 | 119898 0 119895) = 1199020 (120572 + (1 minus 120572) 120573) for 119895 lt 119899 (15)


P (1198760 | 119898 0 119899) = 1199020 (17)



119903=119896

119901119870 (119903 | 119868 = 119894) (19)1198871198940119895 = (120572 + (1 minus 120572) 120573) 119887119894minus10119895 (20)



119901119870 (119903 | 119868 = 119894) (22)


119901119870 (119903 | 119868 = 0) 119898sum119894=0

1198871198940119895minus1= 11988700119895 2119898119887minus1sum

119903=119896

119901119870 (119903 | 119868 = 0) (23)


119901119870 (119903 | 119868 = 119894) (24)





119887119894119896119895 = 119909119894119910119895119887000 2119898119887minus1sum119903=119896

119901119870 (119903 | 119868 = 119894) (27)


119899sum119895=0

2119898119887minus1sum119896=0

119898sum119894=0

119887119894119896119895 + 119898sum119894=0

119899sum119895=0

119887119894minus1119895+ 119899sum119895=0

(119871119904minus1sum119896=0

119887minus1119896119895 + 119871119888minus1sum119896=0

119887minus2119896119895) + 1198710minus1sum119897=0

119876119897 = 1 (28)



119898sum119894=0

(119909119894 2119898119887minus1sum119903=119896


(29)



119894=0

119899sum119895=0



(30)


119895=0

1 minus 1199101 minus 119910119899+1119910119895(119895 (119871119888 + 119864 [119879ℎ])+ 119898sum

119894=0

2119898119887minus1sum119903=0

119903119901119870 (119903 | 119868 = 119894) + 119879119878119862 2119898+1sum119890=1

119862119890120572120573 (119898 + 1)sdot (119873119890

120572 (119898 + 1) + 2119873119890120573 (119898 + 1)))]]

(31)



119894=0 119862120572120573 (119894) 119898sum119894=0

( 2119894sum119890=1

119862119890120572120573 (119894) 119894sum119897=0

2119898119887minus1sum119903=0

119903119901119870 (119903 | 119868 = 119897)) (33)



119894=0

2119898119887minus1sum119896=1

119899sum119895=0

119887119894119896119895 + 119864119904119888 119898sum119894=0

119899sum119895=0

(1198871198940119895 + 119887119894minus1119895)+ 119864119905 119899sum

119895=0

119871minus1sum119896=0

(119887minus1119896119895 + 119887minus2119896119895)+ 119864119894 119899sum

119895=0

(119887minus1119871119895 + 119887minus2119871119895)+ 119899sum119895=0

119871+119871119886119888119896+1sum119896=119871+1


119876119897(34)






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(36)











119895isinΦ119905119903 119895 =BS(1 minus 120591119895) (38)


120595ℎ(1 minus 120591119896)


| ⋃ℎisinΦℎ119888119905119903120595ℎ|119862119902sum

119898=1

( prod119894isin119889119898

119889119898=1198891198981 1198891198982 119889119898119902


120595ℎ119889119898


119899isin119889119898119889119898=1198891198981 1198891198982119889119898119902

(120572119899 + (1 minus 120572119899) 120573119899)))(39)






= 2119871 |Φℎ119905119903BS|sum119902=1

|Φℎ119905119903BS|119862119902sum119898=1

( prod119894isin119896119898

119896119898=1198961198981 1198961198982 119896119898119902



119899isin119896119898119896119898=1198961198981 1198961198982 119896119898119902

(120572119899 + (1 minus 120572119899) 120573119899)))(40)




119902=1

|Φ119905BS|119862119902sum119898=1

( prod119894isin119896119898

119896119898=1198961198981 1198961198982 119896119898119902



119899isin119896119898119896119898=1198961198981 1198961198982 119896119898119902


120595ℎ119905(1 minus 120591119896)

sdot | ⋃ℎisinΦ119905119888 120595ℎ119905|sum119902=1

| ⋃ℎisinΦ119905119888120595ℎ119905|119862119902sum

119898=1

( prod119894isin119889119898

119889119898=1198891198981 1198891198982119889119898119902


120595ℎ(119889119898cup119905)


119899isin119889119898119889119898=1198891198981 1198891198982 119889119898119902

(120572119899 + (1 minus 120572119899) 120573119899)))

(41)









P (1198611199041198971199001199051 cap 1198681198621198621198601) + P (1198681199041198971199001199051 cap 1198681198621198621198601) (43)


P (1198611199041198971199001199051 cap 1198681198621198621198601) + P (1198681199041198971199001199051 cap 1198681198621198621198601))sdot P (1198781199041198971199001199051) + 119875119887119890119905119886119860119862119870 (44)




(1 minus 120591119895))+ 119875119887119906119904119910119860119905119875119887119906119904119910119865119905 + 119875119887119906119904119910119860119905 + 119875119887119906119904119910119878119905 + 119875119894119889119897119890119905

(45)







IBSrceil) (46)






119877e-to-e = 119897prod119899=1

119877119899 (48)





119899=1

(119908119899 + 119863119899) (49)



119864e-to-e = 119897sum119899=1

119864119899 (50)


119894isinΦ119905119900119905119886119897

(1 minus 120591119894) 119875119904119906119888119888119890119904119904 = sum119894isinΦ119905119900119905119886119897

119875119878119879119894119875119887119906119904119910 (51)



119899isinΦ119905119900119905119886119897

sum119903isin119874119899

119877e-to-e (119899 119903)119863e-to-e (119899 119903) (52)



510

1520

25

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= 3

= 4 = 5um

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510

1520

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= 3 = 4 = 5

um

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510

1520

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12

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= 3 = 4

= 5

um

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0877

0879

0881

0883

0885

0887

0889

0891

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tem

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35 40 45 50 55 60 65 70 75 8030Number of nodes

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35 40 45 50 55 60 65 70 75 8030Number of nodes

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05055

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456789

1011121314

Avg

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Avg

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5 10 15 20 25 300u

04045

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06065

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Relia

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5 10 15 20 25 300u

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10121416

Avg

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5 10 15 20 25 300u

332343638

442444648

Avg

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n (m

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5 10 15 20 25 300u

02025

03035

04045

05055

Relia

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5 10 15 20 25 300u

5

10

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Avg

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5 10 15 20 25 300u

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Avg

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5 10 15 20 25 300u

01015

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5 10 15 20 25 300u

468

1012141618202224

Avg

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5 10 15 20 25 300u

1618

222242628

332

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0002004006008

01012014

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5 10 15 20 25 300u

5

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5 10 15 20 25 300u

112141618

222242628

3

Avg

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nsum

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w)

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2 m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 3

m = 3 m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 4

m = 4

m = 4m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4m = 4

m = 4

m = 4

m = 4







Φ16119888= 1 3 4 5 Φ16 4= 1 3 5 8 9 12 13 14 15 17 19 20 22 Φℎ16 4 = 0 2 21 Φℎ11988816 4 = 0 2 11986216 = 4 1205950 = 1 4 1205951 = 12 14 15 1205952 = 7 11 18 1205953 = 6 13 22 24 1205954 = 5 8 16 17 1205955 = 2 3 9 19 20

(53)










IEEE slotted CSMACA

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Appendix













where




bsknum (119896 119878) = 2119878sum119862119862119860119888119900119898119887=1


where

sumfn (119878 119862119862119860119888119900119898119887 119868119863)=


119872119894119899119861119865119904119906119898119879119890119903119898 =




1 if 119878 = 1119878 + 119878minus1sum119899=1




(A7)






119875119878119877ℎ119905 = (119871119886119888119896 + 119871) sum119899isinΦℎ119888119905119903


119875119878119879119896 + 119871119886119888119896 sum119899isinΦℎ119888119905119903

sum119896isin(120595119899capΦℎ119905119903)

119875119878119879119896 + sum119899isinΦℎ119888119905119903

sum119896isin(120595119899capΦ119905)

119875119878119879119896 minus (119871119886119888119896 + 119871) |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902




119875119878119879119896)minus 119871119886119888119896 |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


(( sum119896isin(120595119899capΦℎ119905119903)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911 119896notinΦ119905


119875119878119879119896))


minus |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


(( sum119896isin(120595119899capΦ119905)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911


119875119878119879119896))(B1)

119875119878119879119896 = 120591119896 prod119895isinΦ119896119899




119875119878119877119905 = 119871119886119888119896( sum119899isinΦ119905119888

sum119896isin120595119899119896 =119905

119875119878119879119896 minus |Φ119905119888 |sum119902=2

(minus1)119902 |Φ119905119888 |119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


( sum119896isin120595119899 119896 =119905


119875119878119879119896)) (B3)



119875119887119906119904119910119878119905 = sum119896isinΦ119905119896 =BS

119875119878119879119896 minus |119862|sum119902=2

(minus1)119902sdot |119862|119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982ℎ119898119902


( sum119896isin(120595119899capΦ119905)


119875119878119879119896)119875119887119906119904119910119865119905 = (1 minus prod

119895isinΦ119905119895 =BS(1 minus 120591119895))


(1 minus 120591119895)minus 119875119887119906119904119910119878119905 119875119887119906119904119910119860119905 = 119875119878119877119905119871119886119888119896

(B4)



119895isinΦ119905119895 =BS(1 minus 120591119895))



(1 minus 120591119895))119894minus1







Competing Interests


References










































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation


















rnum (119880119861 119904) = r (119880119861 119904) (119873 minus 1)119878 (3)




119911=1

( 119911sum119890=1

119888119903119900119911leV119911minus1119890


119911=1

( 119911sum119890=1

119888119903119900119911leV119911minus1119890





tknum (119878) = 2119878 (119878+1)sum119903119900=1

cnum (119903119900) (5)


knum (119896 119878) = (119878+1)sum119903119900=1

119896=bf119903119900(119878)

cnum (119903119900) (6)

where


119888119900=1


(7)



bstknum (119878) = 2119878 (8)



119896=bf(119878)1 (9)

where


119888119900=1


(10)


119868119863=1


119868119863=1

bsknum (119896 119894)bstknum (119894)



P (119894 119896 119895 | 119894 119896 + 1 119895) = 1 for 2119898119887 minus 1 ge 119896 ge 0 (12)




P (1198760 | 119898 0 119895) = 1199020 (120572 + (1 minus 120572) 120573) for 119895 lt 119899 (15)


P (1198760 | 119898 0 119899) = 1199020 (17)



119903=119896

119901119870 (119903 | 119868 = 119894) (19)1198871198940119895 = (120572 + (1 minus 120572) 120573) 119887119894minus10119895 (20)



119901119870 (119903 | 119868 = 119894) (22)


119901119870 (119903 | 119868 = 0) 119898sum119894=0

1198871198940119895minus1= 11988700119895 2119898119887minus1sum

119903=119896

119901119870 (119903 | 119868 = 0) (23)


119901119870 (119903 | 119868 = 119894) (24)





119887119894119896119895 = 119909119894119910119895119887000 2119898119887minus1sum119903=119896

119901119870 (119903 | 119868 = 119894) (27)


119899sum119895=0

2119898119887minus1sum119896=0

119898sum119894=0

119887119894119896119895 + 119898sum119894=0

119899sum119895=0

119887119894minus1119895+ 119899sum119895=0

(119871119904minus1sum119896=0

119887minus1119896119895 + 119871119888minus1sum119896=0

119887minus2119896119895) + 1198710minus1sum119897=0

119876119897 = 1 (28)



119898sum119894=0

(119909119894 2119898119887minus1sum119903=119896


(29)



119894=0

119899sum119895=0



(30)


119895=0

1 minus 1199101 minus 119910119899+1119910119895(119895 (119871119888 + 119864 [119879ℎ])+ 119898sum

119894=0

2119898119887minus1sum119903=0

119903119901119870 (119903 | 119868 = 119894) + 119879119878119862 2119898+1sum119890=1

119862119890120572120573 (119898 + 1)sdot (119873119890

120572 (119898 + 1) + 2119873119890120573 (119898 + 1)))]]

(31)



119894=0 119862120572120573 (119894) 119898sum119894=0

( 2119894sum119890=1

119862119890120572120573 (119894) 119894sum119897=0

2119898119887minus1sum119903=0

119903119901119870 (119903 | 119868 = 119897)) (33)



119894=0

2119898119887minus1sum119896=1

119899sum119895=0

119887119894119896119895 + 119864119904119888 119898sum119894=0

119899sum119895=0

(1198871198940119895 + 119887119894minus1119895)+ 119864119905 119899sum

119895=0

119871minus1sum119896=0

(119887minus1119896119895 + 119887minus2119896119895)+ 119864119894 119899sum

119895=0

(119887minus1119871119895 + 119887minus2119871119895)+ 119899sum119895=0

119871+119871119886119888119896+1sum119896=119871+1


119876119897(34)






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(36)











119895isinΦ119905119903 119895 =BS(1 minus 120591119895) (38)


120595ℎ(1 minus 120591119896)


| ⋃ℎisinΦℎ119888119905119903120595ℎ|119862119902sum

119898=1

( prod119894isin119889119898

119889119898=1198891198981 1198891198982 119889119898119902


120595ℎ119889119898


119899isin119889119898119889119898=1198891198981 1198891198982119889119898119902

(120572119899 + (1 minus 120572119899) 120573119899)))(39)






= 2119871 |Φℎ119905119903BS|sum119902=1

|Φℎ119905119903BS|119862119902sum119898=1

( prod119894isin119896119898

119896119898=1198961198981 1198961198982 119896119898119902



119899isin119896119898119896119898=1198961198981 1198961198982 119896119898119902

(120572119899 + (1 minus 120572119899) 120573119899)))(40)




119902=1

|Φ119905BS|119862119902sum119898=1

( prod119894isin119896119898

119896119898=1198961198981 1198961198982 119896119898119902



119899isin119896119898119896119898=1198961198981 1198961198982 119896119898119902


120595ℎ119905(1 minus 120591119896)

sdot | ⋃ℎisinΦ119905119888 120595ℎ119905|sum119902=1

| ⋃ℎisinΦ119905119888120595ℎ119905|119862119902sum

119898=1

( prod119894isin119889119898

119889119898=1198891198981 1198891198982119889119898119902


120595ℎ(119889119898cup119905)


119899isin119889119898119889119898=1198891198981 1198891198982 119889119898119902

(120572119899 + (1 minus 120572119899) 120573119899)))

(41)









P (1198611199041198971199001199051 cap 1198681198621198621198601) + P (1198681199041198971199001199051 cap 1198681198621198621198601) (43)


P (1198611199041198971199001199051 cap 1198681198621198621198601) + P (1198681199041198971199001199051 cap 1198681198621198621198601))sdot P (1198781199041198971199001199051) + 119875119887119890119905119886119860119862119870 (44)




(1 minus 120591119895))+ 119875119887119906119904119910119860119905119875119887119906119904119910119865119905 + 119875119887119906119904119910119860119905 + 119875119887119906119904119910119878119905 + 119875119894119889119897119890119905

(45)







IBSrceil) (46)






119877e-to-e = 119897prod119899=1

119877119899 (48)





119899=1

(119908119899 + 119863119899) (49)



119864e-to-e = 119897sum119899=1

119864119899 (50)


119894isinΦ119905119900119905119886119897

(1 minus 120591119894) 119875119904119906119888119888119890119904119904 = sum119894isinΦ119905119900119905119886119897

119875119878119879119894119875119887119906119904119910 (51)



119899isinΦ119905119900119905119886119897

sum119903isin119874119899

119877e-to-e (119899 119903)119863e-to-e (119899 119903) (52)



510

1520

25

12

34

= 3

= 4 = 5um

0

001

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003

004

005

Relia

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y


510

1520

25

12

34

= 3 = 4 = 5

um

5

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Avg

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510

1520

25

12

34

= 3 = 4

= 5

um

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Pow

er co

nsum

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n (m

W)







0

002

004

006

008

01

012

014

Relia

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30 40 50 60 70 80

Prob

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ardi

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ts

Number of nodes

075

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095

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o ch

anne

l acc

ess f

ailu

re







0875

0877

0879

0881

0883

0885

0887

0889

0891

Prob

abili

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f uns

ucce

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l cha

nnel

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ss at

tem

pt





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35 40 45 50 55 60 65 70 75 8030Number of nodes

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35 40 45 50 55 60 65 70 75 8030Number of nodes

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5 10 15 20 25 300u

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5 10 15 20 25 300u

01015

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1012141618202224

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5 10 15 20 25 300u

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Avg

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0002004006008

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Relia

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5 10 15 20 25 300u

5

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5 10 15 20 25 300u

112141618

222242628

3

Avg

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nsum

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n (m

w)

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2 m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 3

m = 3 m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 4

m = 4

m = 4m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4m = 4

m = 4

m = 4

m = 4







Φ16119888= 1 3 4 5 Φ16 4= 1 3 5 8 9 12 13 14 15 17 19 20 22 Φℎ16 4 = 0 2 21 Φℎ11988816 4 = 0 2 11986216 = 4 1205950 = 1 4 1205951 = 12 14 15 1205952 = 7 11 18 1205953 = 6 13 22 24 1205954 = 5 8 16 17 1205955 = 2 3 9 19 20

(53)










IEEE slotted CSMACA

0

01

02

03

04

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06

07

08

End-

to-e

nd re

liabi

lity

CAM 431-131-131CAM 431-430-131

CAM 631-430-131CAM 631-131-131







000E + 00

100E + 01

200E + 01

300E + 01

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500E + 01

600E + 01

End-

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(ms)


CAM 631-430-131CAM 631-131-131




01

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Aver

age n

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IEEE slotted CSMACA

000E + 00

500E + 00

100E + 01

150E + 01

200E + 01

End-

to-e

nd p

ower

cons

umpt

ion

(mW

)

CAM 431-131-131CAM 431-430-131

CAM 631-430-131CAM 631-131-131










Appendix













where




bsknum (119896 119878) = 2119878sum119862119862119860119888119900119898119887=1


where

sumfn (119878 119862119862119860119888119900119898119887 119868119863)=


119872119894119899119861119865119904119906119898119879119890119903119898 =




1 if 119878 = 1119878 + 119878minus1sum119899=1




(A7)






119875119878119877ℎ119905 = (119871119886119888119896 + 119871) sum119899isinΦℎ119888119905119903


119875119878119879119896 + 119871119886119888119896 sum119899isinΦℎ119888119905119903

sum119896isin(120595119899capΦℎ119905119903)

119875119878119879119896 + sum119899isinΦℎ119888119905119903

sum119896isin(120595119899capΦ119905)

119875119878119879119896 minus (119871119886119888119896 + 119871) |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902




119875119878119879119896)minus 119871119886119888119896 |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


(( sum119896isin(120595119899capΦℎ119905119903)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911 119896notinΦ119905


119875119878119879119896))


minus |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


(( sum119896isin(120595119899capΦ119905)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911


119875119878119879119896))(B1)

119875119878119879119896 = 120591119896 prod119895isinΦ119896119899




119875119878119877119905 = 119871119886119888119896( sum119899isinΦ119905119888

sum119896isin120595119899119896 =119905

119875119878119879119896 minus |Φ119905119888 |sum119902=2

(minus1)119902 |Φ119905119888 |119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


( sum119896isin120595119899 119896 =119905


119875119878119879119896)) (B3)



119875119887119906119904119910119878119905 = sum119896isinΦ119905119896 =BS

119875119878119879119896 minus |119862|sum119902=2

(minus1)119902sdot |119862|119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982ℎ119898119902


( sum119896isin(120595119899capΦ119905)


119875119878119879119896)119875119887119906119904119910119865119905 = (1 minus prod

119895isinΦ119905119895 =BS(1 minus 120591119895))


(1 minus 120591119895)minus 119875119887119906119904119910119878119905 119875119887119906119904119910119860119905 = 119875119878119877119905119871119886119888119896

(B4)



119895isinΦ119905119895 =BS(1 minus 120591119895))



(1 minus 120591119895))119894minus1







Competing Interests


References










































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











tknum (119878) = 2119878 (119878+1)sum119903119900=1

cnum (119903119900) (5)


knum (119896 119878) = (119878+1)sum119903119900=1

119896=bf119903119900(119878)

cnum (119903119900) (6)

where


119888119900=1


(7)



bstknum (119878) = 2119878 (8)



119896=bf(119878)1 (9)

where


119888119900=1


(10)


119868119863=1


119868119863=1

bsknum (119896 119894)bstknum (119894)



P (119894 119896 119895 | 119894 119896 + 1 119895) = 1 for 2119898119887 minus 1 ge 119896 ge 0 (12)




P (1198760 | 119898 0 119895) = 1199020 (120572 + (1 minus 120572) 120573) for 119895 lt 119899 (15)


P (1198760 | 119898 0 119899) = 1199020 (17)



119903=119896

119901119870 (119903 | 119868 = 119894) (19)1198871198940119895 = (120572 + (1 minus 120572) 120573) 119887119894minus10119895 (20)



119901119870 (119903 | 119868 = 119894) (22)


119901119870 (119903 | 119868 = 0) 119898sum119894=0

1198871198940119895minus1= 11988700119895 2119898119887minus1sum

119903=119896

119901119870 (119903 | 119868 = 0) (23)


119901119870 (119903 | 119868 = 119894) (24)





119887119894119896119895 = 119909119894119910119895119887000 2119898119887minus1sum119903=119896

119901119870 (119903 | 119868 = 119894) (27)


119899sum119895=0

2119898119887minus1sum119896=0

119898sum119894=0

119887119894119896119895 + 119898sum119894=0

119899sum119895=0

119887119894minus1119895+ 119899sum119895=0

(119871119904minus1sum119896=0

119887minus1119896119895 + 119871119888minus1sum119896=0

119887minus2119896119895) + 1198710minus1sum119897=0

119876119897 = 1 (28)



119898sum119894=0

(119909119894 2119898119887minus1sum119903=119896


(29)



119894=0

119899sum119895=0



(30)


119895=0

1 minus 1199101 minus 119910119899+1119910119895(119895 (119871119888 + 119864 [119879ℎ])+ 119898sum

119894=0

2119898119887minus1sum119903=0

119903119901119870 (119903 | 119868 = 119894) + 119879119878119862 2119898+1sum119890=1

119862119890120572120573 (119898 + 1)sdot (119873119890

120572 (119898 + 1) + 2119873119890120573 (119898 + 1)))]]

(31)



119894=0 119862120572120573 (119894) 119898sum119894=0

( 2119894sum119890=1

119862119890120572120573 (119894) 119894sum119897=0

2119898119887minus1sum119903=0

119903119901119870 (119903 | 119868 = 119897)) (33)



119894=0

2119898119887minus1sum119896=1

119899sum119895=0

119887119894119896119895 + 119864119904119888 119898sum119894=0

119899sum119895=0

(1198871198940119895 + 119887119894minus1119895)+ 119864119905 119899sum

119895=0

119871minus1sum119896=0

(119887minus1119896119895 + 119887minus2119896119895)+ 119864119894 119899sum

119895=0

(119887minus1119871119895 + 119887minus2119871119895)+ 119899sum119895=0

119871+119871119886119888119896+1sum119896=119871+1


119876119897(34)






0 10 20 30 40 50

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(a)

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18 7

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(b)












(36)











119895isinΦ119905119903 119895 =BS(1 minus 120591119895) (38)


120595ℎ(1 minus 120591119896)


| ⋃ℎisinΦℎ119888119905119903120595ℎ|119862119902sum

119898=1

( prod119894isin119889119898

119889119898=1198891198981 1198891198982 119889119898119902


120595ℎ119889119898


119899isin119889119898119889119898=1198891198981 1198891198982119889119898119902

(120572119899 + (1 minus 120572119899) 120573119899)))(39)






= 2119871 |Φℎ119905119903BS|sum119902=1

|Φℎ119905119903BS|119862119902sum119898=1

( prod119894isin119896119898

119896119898=1198961198981 1198961198982 119896119898119902



119899isin119896119898119896119898=1198961198981 1198961198982 119896119898119902

(120572119899 + (1 minus 120572119899) 120573119899)))(40)




119902=1

|Φ119905BS|119862119902sum119898=1

( prod119894isin119896119898

119896119898=1198961198981 1198961198982 119896119898119902



119899isin119896119898119896119898=1198961198981 1198961198982 119896119898119902


120595ℎ119905(1 minus 120591119896)

sdot | ⋃ℎisinΦ119905119888 120595ℎ119905|sum119902=1

| ⋃ℎisinΦ119905119888120595ℎ119905|119862119902sum

119898=1

( prod119894isin119889119898

119889119898=1198891198981 1198891198982119889119898119902


120595ℎ(119889119898cup119905)


119899isin119889119898119889119898=1198891198981 1198891198982 119889119898119902

(120572119899 + (1 minus 120572119899) 120573119899)))

(41)









P (1198611199041198971199001199051 cap 1198681198621198621198601) + P (1198681199041198971199001199051 cap 1198681198621198621198601) (43)


P (1198611199041198971199001199051 cap 1198681198621198621198601) + P (1198681199041198971199001199051 cap 1198681198621198621198601))sdot P (1198781199041198971199001199051) + 119875119887119890119905119886119860119862119870 (44)




(1 minus 120591119895))+ 119875119887119906119904119910119860119905119875119887119906119904119910119865119905 + 119875119887119906119904119910119860119905 + 119875119887119906119904119910119878119905 + 119875119894119889119897119890119905

(45)







IBSrceil) (46)






119877e-to-e = 119897prod119899=1

119877119899 (48)





119899=1

(119908119899 + 119863119899) (49)



119864e-to-e = 119897sum119899=1

119864119899 (50)


119894isinΦ119905119900119905119886119897

(1 minus 120591119894) 119875119904119906119888119888119890119904119904 = sum119894isinΦ119905119900119905119886119897

119875119878119879119894119875119887119906119904119910 (51)



119899isinΦ119905119900119905119886119897

sum119903isin119874119899

119877e-to-e (119899 119903)119863e-to-e (119899 119903) (52)



510

1520

25

12

34

= 3

= 4 = 5um

0

001

002

003

004

005

Relia

bilit

y


510

1520

25

12

34

= 3 = 4 = 5

um

5

10

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30

Avg

del

ay (m

s)






510

1520

25

12

34

= 3 = 4

= 5

um

15

2

25

Pow

er co

nsum

ptio

n (m

W)







0

002

004

006

008

01

012

014

Relia

bilit

y







30 40 50 60 70 80

Prob

abili

ty o

f disc

ardi

ng p

acke

ts

Number of nodes

075

08

085

09

095

1

due t

o ch

anne

l acc

ess f

ailu

re







0875

0877

0879

0881

0883

0885

0887

0889

0891

Prob

abili

ty o

f uns

ucce

ssfu

l cha

nnel

acce

ss at

tem

pt





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35 40 45 50 55 60 65 70 75 8030Number of nodes




35 40 45 50 55 60 65 70 75 8030Number of nodes

0

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5 10 15 20 25 300u

05055

06065

07075

08085

Relia

bilit

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5 10 15 20 25 300u

456789

1011121314

Avg

del

ay (m

s)

3638

442444648

552

Avg

ener

gy co

nsum

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n (m

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5 10 15 20 25 300u

04045

05055

06065

07075

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bilit

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5 10 15 20 25 300u

468

10121416

Avg

del

ay (m

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5 10 15 20 25 300u

332343638

442444648

Avg

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5 10 15 20 25 300u

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5 10 15 20 25 300u

112141618

222242628

3

Avg

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nsum

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n (m

w)

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2 m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 3

m = 3 m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 4

m = 4

m = 4m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4m = 4

m = 4

m = 4

m = 4







Φ16119888= 1 3 4 5 Φ16 4= 1 3 5 8 9 12 13 14 15 17 19 20 22 Φℎ16 4 = 0 2 21 Φℎ11988816 4 = 0 2 11986216 = 4 1205950 = 1 4 1205951 = 12 14 15 1205952 = 7 11 18 1205953 = 6 13 22 24 1205954 = 5 8 16 17 1205955 = 2 3 9 19 20

(53)










IEEE slotted CSMACA

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CAM 431-131-131CAM 431-430-131

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Appendix













where




bsknum (119896 119878) = 2119878sum119862119862119860119888119900119898119887=1


where

sumfn (119878 119862119862119860119888119900119898119887 119868119863)=


119872119894119899119861119865119904119906119898119879119890119903119898 =




1 if 119878 = 1119878 + 119878minus1sum119899=1




(A7)






119875119878119877ℎ119905 = (119871119886119888119896 + 119871) sum119899isinΦℎ119888119905119903


119875119878119879119896 + 119871119886119888119896 sum119899isinΦℎ119888119905119903

sum119896isin(120595119899capΦℎ119905119903)

119875119878119879119896 + sum119899isinΦℎ119888119905119903

sum119896isin(120595119899capΦ119905)

119875119878119879119896 minus (119871119886119888119896 + 119871) |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902




119875119878119879119896)minus 119871119886119888119896 |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


(( sum119896isin(120595119899capΦℎ119905119903)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911 119896notinΦ119905


119875119878119879119896))


minus |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


(( sum119896isin(120595119899capΦ119905)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911


119875119878119879119896))(B1)

119875119878119879119896 = 120591119896 prod119895isinΦ119896119899




119875119878119877119905 = 119871119886119888119896( sum119899isinΦ119905119888

sum119896isin120595119899119896 =119905

119875119878119879119896 minus |Φ119905119888 |sum119902=2

(minus1)119902 |Φ119905119888 |119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


( sum119896isin120595119899 119896 =119905


119875119878119879119896)) (B3)



119875119887119906119904119910119878119905 = sum119896isinΦ119905119896 =BS

119875119878119879119896 minus |119862|sum119902=2

(minus1)119902sdot |119862|119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982ℎ119898119902


( sum119896isin(120595119899capΦ119905)


119875119878119879119896)119875119887119906119904119910119865119905 = (1 minus prod

119895isinΦ119905119895 =BS(1 minus 120591119895))


(1 minus 120591119895)minus 119875119887119906119904119910119878119905 119875119887119906119904119910119860119905 = 119875119878119877119905119871119886119888119896

(B4)



119895isinΦ119905119895 =BS(1 minus 120591119895))



(1 minus 120591119895))119894minus1







Competing Interests


References










































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











P (1198760 | 119898 0 119895) = 1199020 (120572 + (1 minus 120572) 120573) for 119895 lt 119899 (15)


P (1198760 | 119898 0 119899) = 1199020 (17)



119903=119896

119901119870 (119903 | 119868 = 119894) (19)1198871198940119895 = (120572 + (1 minus 120572) 120573) 119887119894minus10119895 (20)



119901119870 (119903 | 119868 = 119894) (22)


119901119870 (119903 | 119868 = 0) 119898sum119894=0

1198871198940119895minus1= 11988700119895 2119898119887minus1sum

119903=119896

119901119870 (119903 | 119868 = 0) (23)


119901119870 (119903 | 119868 = 119894) (24)





119887119894119896119895 = 119909119894119910119895119887000 2119898119887minus1sum119903=119896

119901119870 (119903 | 119868 = 119894) (27)


119899sum119895=0

2119898119887minus1sum119896=0

119898sum119894=0

119887119894119896119895 + 119898sum119894=0

119899sum119895=0

119887119894minus1119895+ 119899sum119895=0

(119871119904minus1sum119896=0

119887minus1119896119895 + 119871119888minus1sum119896=0

119887minus2119896119895) + 1198710minus1sum119897=0

119876119897 = 1 (28)



119898sum119894=0

(119909119894 2119898119887minus1sum119903=119896


(29)



119894=0

119899sum119895=0



(30)


119895=0

1 minus 1199101 minus 119910119899+1119910119895(119895 (119871119888 + 119864 [119879ℎ])+ 119898sum

119894=0

2119898119887minus1sum119903=0

119903119901119870 (119903 | 119868 = 119894) + 119879119878119862 2119898+1sum119890=1

119862119890120572120573 (119898 + 1)sdot (119873119890

120572 (119898 + 1) + 2119873119890120573 (119898 + 1)))]]

(31)



119894=0 119862120572120573 (119894) 119898sum119894=0

( 2119894sum119890=1

119862119890120572120573 (119894) 119894sum119897=0

2119898119887minus1sum119903=0

119903119901119870 (119903 | 119868 = 119897)) (33)



119894=0

2119898119887minus1sum119896=1

119899sum119895=0

119887119894119896119895 + 119864119904119888 119898sum119894=0

119899sum119895=0

(1198871198940119895 + 119887119894minus1119895)+ 119864119905 119899sum

119895=0

119871minus1sum119896=0

(119887minus1119896119895 + 119887minus2119896119895)+ 119864119894 119899sum

119895=0

(119887minus1119871119895 + 119887minus2119871119895)+ 119899sum119895=0

119871+119871119886119888119896+1sum119896=119871+1


119876119897(34)






0 10 20 30 40 50

P

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SQ

R

E

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U

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M

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X

P

O

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SQQ

R

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K

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C

H

0

10

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(a)

0 10 20 30 40 50

1

45

2

6

3

1412

1520

919

8

16

17

22

21

1324

23

10

18 7

11

0

10

20

30

40

50


(b)












(36)











119895isinΦ119905119903 119895 =BS(1 minus 120591119895) (38)


120595ℎ(1 minus 120591119896)


| ⋃ℎisinΦℎ119888119905119903120595ℎ|119862119902sum

119898=1

( prod119894isin119889119898

119889119898=1198891198981 1198891198982 119889119898119902


120595ℎ119889119898


119899isin119889119898119889119898=1198891198981 1198891198982119889119898119902

(120572119899 + (1 minus 120572119899) 120573119899)))(39)






= 2119871 |Φℎ119905119903BS|sum119902=1

|Φℎ119905119903BS|119862119902sum119898=1

( prod119894isin119896119898

119896119898=1198961198981 1198961198982 119896119898119902



119899isin119896119898119896119898=1198961198981 1198961198982 119896119898119902

(120572119899 + (1 minus 120572119899) 120573119899)))(40)




119902=1

|Φ119905BS|119862119902sum119898=1

( prod119894isin119896119898

119896119898=1198961198981 1198961198982 119896119898119902



119899isin119896119898119896119898=1198961198981 1198961198982 119896119898119902


120595ℎ119905(1 minus 120591119896)

sdot | ⋃ℎisinΦ119905119888 120595ℎ119905|sum119902=1

| ⋃ℎisinΦ119905119888120595ℎ119905|119862119902sum

119898=1

( prod119894isin119889119898

119889119898=1198891198981 1198891198982119889119898119902


120595ℎ(119889119898cup119905)


119899isin119889119898119889119898=1198891198981 1198891198982 119889119898119902

(120572119899 + (1 minus 120572119899) 120573119899)))

(41)









P (1198611199041198971199001199051 cap 1198681198621198621198601) + P (1198681199041198971199001199051 cap 1198681198621198621198601) (43)


P (1198611199041198971199001199051 cap 1198681198621198621198601) + P (1198681199041198971199001199051 cap 1198681198621198621198601))sdot P (1198781199041198971199001199051) + 119875119887119890119905119886119860119862119870 (44)




(1 minus 120591119895))+ 119875119887119906119904119910119860119905119875119887119906119904119910119865119905 + 119875119887119906119904119910119860119905 + 119875119887119906119904119910119878119905 + 119875119894119889119897119890119905

(45)







IBSrceil) (46)






119877e-to-e = 119897prod119899=1

119877119899 (48)





119899=1

(119908119899 + 119863119899) (49)



119864e-to-e = 119897sum119899=1

119864119899 (50)


119894isinΦ119905119900119905119886119897

(1 minus 120591119894) 119875119904119906119888119888119890119904119904 = sum119894isinΦ119905119900119905119886119897

119875119878119879119894119875119887119906119904119910 (51)



119899isinΦ119905119900119905119886119897

sum119903isin119874119899

119877e-to-e (119899 119903)119863e-to-e (119899 119903) (52)



510

1520

25

12

34

= 3

= 4 = 5um

0

001

002

003

004

005

Relia

bilit

y


510

1520

25

12

34

= 3 = 4 = 5

um

5

10

15

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25

30

Avg

del

ay (m

s)






510

1520

25

12

34

= 3 = 4

= 5

um

15

2

25

Pow

er co

nsum

ptio

n (m

W)







0

002

004

006

008

01

012

014

Relia

bilit

y







30 40 50 60 70 80

Prob

abili

ty o

f disc

ardi

ng p

acke

ts

Number of nodes

075

08

085

09

095

1

due t

o ch

anne

l acc

ess f

ailu

re







0875

0877

0879

0881

0883

0885

0887

0889

0891

Prob

abili

ty o

f uns

ucce

ssfu

l cha

nnel

acce

ss at

tem

pt





0

5

10

15

20

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30

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40

Avg

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ay (m

s)









0

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1

15

2

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Ener

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nsum

ptio

n (m

w)





0

005

01

015

02

025

03

Thro

ughp

ut






35 40 45 50 55 60 65 70 75 8030Number of nodes

12

13

14

15

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17

18

19

Avg

del

ay (m

s)




0

001

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003

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005

006

007

008

Relia

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35 40 45 50 55 60 65 70 75 8030Number of nodes







14

15

16

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18

19

2

21

22

Ener

gy co

nsum

ptio

n (m

w)

35 40 45 50 55 60 65 70 75 8030Number of nodes




35 40 45 50 55 60 65 70 75 8030Number of nodes

0

005

01

015

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025

Thro

ughp

ut






















5 10 15 20 25 300u

05055

06065

07075

08085

Relia

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5 10 15 20 25 300u

456789

1011121314

Avg

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3638

442444648

552

Avg

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gy co

nsum

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n (m

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5 10 15 20 25 300u

04045

05055

06065

07075

Relia

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5 10 15 20 25 300u

468

10121416

Avg

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5 10 15 20 25 300u

332343638

442444648

Avg

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5 10 15 20 25 300u

02025

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5 10 15 20 25 300u

5

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5 10 15 20 25 300u

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3

35

Avg

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5 10 15 20 25 300u

01015

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5 10 15 20 25 300u

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1012141618202224

Avg

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5 10 15 20 25 300u

5 10 15 20 25 300u

1618

222242628

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Avg

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0002004006008

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5 10 15 20 25 300u

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5 10 15 20 25 300u

5 10 15 20 25 300u

112141618

222242628

3

Avg

ener

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nsum

ptio

n (m

w)

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2 m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 3

m = 3 m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 4

m = 4

m = 4m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4m = 4

m = 4

m = 4

m = 4







Φ16119888= 1 3 4 5 Φ16 4= 1 3 5 8 9 12 13 14 15 17 19 20 22 Φℎ16 4 = 0 2 21 Φℎ11988816 4 = 0 2 11986216 = 4 1205950 = 1 4 1205951 = 12 14 15 1205952 = 7 11 18 1205953 = 6 13 22 24 1205954 = 5 8 16 17 1205955 = 2 3 9 19 20

(53)










IEEE slotted CSMACA

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CAM 431-131-131CAM 431-430-131

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End-

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nd p

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cons

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(mW

)

CAM 431-131-131CAM 431-430-131

CAM 631-430-131CAM 631-131-131










Appendix













where




bsknum (119896 119878) = 2119878sum119862119862119860119888119900119898119887=1


where

sumfn (119878 119862119862119860119888119900119898119887 119868119863)=


119872119894119899119861119865119904119906119898119879119890119903119898 =




1 if 119878 = 1119878 + 119878minus1sum119899=1




(A7)






119875119878119877ℎ119905 = (119871119886119888119896 + 119871) sum119899isinΦℎ119888119905119903


119875119878119879119896 + 119871119886119888119896 sum119899isinΦℎ119888119905119903

sum119896isin(120595119899capΦℎ119905119903)

119875119878119879119896 + sum119899isinΦℎ119888119905119903

sum119896isin(120595119899capΦ119905)

119875119878119879119896 minus (119871119886119888119896 + 119871) |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902




119875119878119879119896)minus 119871119886119888119896 |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


(( sum119896isin(120595119899capΦℎ119905119903)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911 119896notinΦ119905


119875119878119879119896))


minus |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


(( sum119896isin(120595119899capΦ119905)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911


119875119878119879119896))(B1)

119875119878119879119896 = 120591119896 prod119895isinΦ119896119899




119875119878119877119905 = 119871119886119888119896( sum119899isinΦ119905119888

sum119896isin120595119899119896 =119905

119875119878119879119896 minus |Φ119905119888 |sum119902=2

(minus1)119902 |Φ119905119888 |119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


( sum119896isin120595119899 119896 =119905


119875119878119879119896)) (B3)



119875119887119906119904119910119878119905 = sum119896isinΦ119905119896 =BS

119875119878119879119896 minus |119862|sum119902=2

(minus1)119902sdot |119862|119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982ℎ119898119902


( sum119896isin(120595119899capΦ119905)


119875119878119879119896)119875119887119906119904119910119865119905 = (1 minus prod

119895isinΦ119905119895 =BS(1 minus 120591119895))


(1 minus 120591119895)minus 119875119887119906119904119910119878119905 119875119887119906119904119910119860119905 = 119875119878119877119905119871119886119888119896

(B4)



119895isinΦ119905119895 =BS(1 minus 120591119895))



(1 minus 120591119895))119894minus1







Competing Interests


References










































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(30)


119895=0

1 minus 1199101 minus 119910119899+1119910119895(119895 (119871119888 + 119864 [119879ℎ])+ 119898sum

119894=0

2119898119887minus1sum119903=0

119903119901119870 (119903 | 119868 = 119894) + 119879119878119862 2119898+1sum119890=1

119862119890120572120573 (119898 + 1)sdot (119873119890

120572 (119898 + 1) + 2119873119890120573 (119898 + 1)))]]

(31)



119894=0 119862120572120573 (119894) 119898sum119894=0

( 2119894sum119890=1

119862119890120572120573 (119894) 119894sum119897=0

2119898119887minus1sum119903=0

119903119901119870 (119903 | 119868 = 119897)) (33)



119894=0

2119898119887minus1sum119896=1

119899sum119895=0

119887119894119896119895 + 119864119904119888 119898sum119894=0

119899sum119895=0

(1198871198940119895 + 119887119894minus1119895)+ 119864119905 119899sum

119895=0

119871minus1sum119896=0

(119887minus1119896119895 + 119887minus2119896119895)+ 119864119894 119899sum

119895=0

(119887minus1119871119895 + 119887minus2119871119895)+ 119899sum119895=0

119871+119871119886119888119896+1sum119896=119871+1


119876119897(34)






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(b)












(36)











119895isinΦ119905119903 119895 =BS(1 minus 120591119895) (38)


120595ℎ(1 minus 120591119896)


| ⋃ℎisinΦℎ119888119905119903120595ℎ|119862119902sum

119898=1

( prod119894isin119889119898

119889119898=1198891198981 1198891198982 119889119898119902


120595ℎ119889119898


119899isin119889119898119889119898=1198891198981 1198891198982119889119898119902

(120572119899 + (1 minus 120572119899) 120573119899)))(39)






= 2119871 |Φℎ119905119903BS|sum119902=1

|Φℎ119905119903BS|119862119902sum119898=1

( prod119894isin119896119898

119896119898=1198961198981 1198961198982 119896119898119902



119899isin119896119898119896119898=1198961198981 1198961198982 119896119898119902

(120572119899 + (1 minus 120572119899) 120573119899)))(40)




119902=1

|Φ119905BS|119862119902sum119898=1

( prod119894isin119896119898

119896119898=1198961198981 1198961198982 119896119898119902



119899isin119896119898119896119898=1198961198981 1198961198982 119896119898119902


120595ℎ119905(1 minus 120591119896)

sdot | ⋃ℎisinΦ119905119888 120595ℎ119905|sum119902=1

| ⋃ℎisinΦ119905119888120595ℎ119905|119862119902sum

119898=1

( prod119894isin119889119898

119889119898=1198891198981 1198891198982119889119898119902


120595ℎ(119889119898cup119905)


119899isin119889119898119889119898=1198891198981 1198891198982 119889119898119902

(120572119899 + (1 minus 120572119899) 120573119899)))

(41)









P (1198611199041198971199001199051 cap 1198681198621198621198601) + P (1198681199041198971199001199051 cap 1198681198621198621198601) (43)


P (1198611199041198971199001199051 cap 1198681198621198621198601) + P (1198681199041198971199001199051 cap 1198681198621198621198601))sdot P (1198781199041198971199001199051) + 119875119887119890119905119886119860119862119870 (44)




(1 minus 120591119895))+ 119875119887119906119904119910119860119905119875119887119906119904119910119865119905 + 119875119887119906119904119910119860119905 + 119875119887119906119904119910119878119905 + 119875119894119889119897119890119905

(45)







IBSrceil) (46)






119877e-to-e = 119897prod119899=1

119877119899 (48)





119899=1

(119908119899 + 119863119899) (49)



119864e-to-e = 119897sum119899=1

119864119899 (50)


119894isinΦ119905119900119905119886119897

(1 minus 120591119894) 119875119904119906119888119888119890119904119904 = sum119894isinΦ119905119900119905119886119897

119875119878119879119894119875119887119906119904119910 (51)



119899isinΦ119905119900119905119886119897

sum119903isin119874119899

119877e-to-e (119899 119903)119863e-to-e (119899 119903) (52)



510

1520

25

12

34

= 3

= 4 = 5um

0

001

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Relia

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510

1520

25

12

34

= 3 = 4 = 5

um

5

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Avg

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s)






510

1520

25

12

34

= 3 = 4

= 5

um

15

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25

Pow

er co

nsum

ptio

n (m

W)







0

002

004

006

008

01

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014

Relia

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30 40 50 60 70 80

Prob

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ardi

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Number of nodes

075

08

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due t

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anne

l acc

ess f

ailu

re







0875

0877

0879

0881

0883

0885

0887

0889

0891

Prob

abili

ty o

f uns

ucce

ssfu

l cha

nnel

acce

ss at

tem

pt





0

5

10

15

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0

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1

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Ener

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0

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35 40 45 50 55 60 65 70 75 8030Number of nodes

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Avg

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35 40 45 50 55 60 65 70 75 8030Number of nodes







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35 40 45 50 55 60 65 70 75 8030Number of nodes




35 40 45 50 55 60 65 70 75 8030Number of nodes

0

005

01

015

02

025

Thro

ughp

ut






















5 10 15 20 25 300u

05055

06065

07075

08085

Relia

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y

5 10 15 20 25 300u

456789

1011121314

Avg

del

ay (m

s)

3638

442444648

552

Avg

ener

gy co

nsum

ptio

n (m

w)

5 10 15 20 25 300u

04045

05055

06065

07075

Relia

bilit

y

5 10 15 20 25 300u

468

10121416

Avg

del

ay (m

s)

5 10 15 20 25 300u

332343638

442444648

Avg

ener

gy co

nsum

ptio

n (m

w)

5 10 15 20 25 300u

02025

03035

04045

05055

Relia

bilit

y

5 10 15 20 25 300u

5

10

15

20

Avg

del

ay (m

s)

5 10 15 20 25 300u

2

25

3

35

Avg

ener

gy co

nsum

ptio

n (m

w)

5 10 15 20 25 300u

01015

02025

03035

04

Relia

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y

5 10 15 20 25 300u

468

1012141618202224

Avg

del

ay (m

s)

5 10 15 20 25 300u

5 10 15 20 25 300u

1618

222242628

332

Avg

ener

gy co

nsum

ptio

n (m

w)

0002004006008

01012014

Relia

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y

5 10 15 20 25 300u

5

10

15

20

25

30

Avg

del

ay (m

s)

5 10 15 20 25 300u

5 10 15 20 25 300u

112141618

222242628

3

Avg

ener

gy co

nsum

ptio

n (m

w)

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2 m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 3

m = 3 m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 4

m = 4

m = 4m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4m = 4

m = 4

m = 4

m = 4







Φ16119888= 1 3 4 5 Φ16 4= 1 3 5 8 9 12 13 14 15 17 19 20 22 Φℎ16 4 = 0 2 21 Φℎ11988816 4 = 0 2 11986216 = 4 1205950 = 1 4 1205951 = 12 14 15 1205952 = 7 11 18 1205953 = 6 13 22 24 1205954 = 5 8 16 17 1205955 = 2 3 9 19 20

(53)










IEEE slotted CSMACA

0

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End-

to-e

nd re

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lity

CAM 431-131-131CAM 431-430-131

CAM 631-430-131CAM 631-131-131







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CAM 631-430-131CAM 631-131-131




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CAM 431-131-131CAM 431-430-131

CAM 631-430-131CAM 631-131-131










Appendix













where




bsknum (119896 119878) = 2119878sum119862119862119860119888119900119898119887=1


where

sumfn (119878 119862119862119860119888119900119898119887 119868119863)=


119872119894119899119861119865119904119906119898119879119890119903119898 =




1 if 119878 = 1119878 + 119878minus1sum119899=1




(A7)






119875119878119877ℎ119905 = (119871119886119888119896 + 119871) sum119899isinΦℎ119888119905119903


119875119878119879119896 + 119871119886119888119896 sum119899isinΦℎ119888119905119903

sum119896isin(120595119899capΦℎ119905119903)

119875119878119879119896 + sum119899isinΦℎ119888119905119903

sum119896isin(120595119899capΦ119905)

119875119878119879119896 minus (119871119886119888119896 + 119871) |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902




119875119878119879119896)minus 119871119886119888119896 |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


(( sum119896isin(120595119899capΦℎ119905119903)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911 119896notinΦ119905


119875119878119879119896))


minus |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


(( sum119896isin(120595119899capΦ119905)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911


119875119878119879119896))(B1)

119875119878119879119896 = 120591119896 prod119895isinΦ119896119899




119875119878119877119905 = 119871119886119888119896( sum119899isinΦ119905119888

sum119896isin120595119899119896 =119905

119875119878119879119896 minus |Φ119905119888 |sum119902=2

(minus1)119902 |Φ119905119888 |119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


( sum119896isin120595119899 119896 =119905


119875119878119879119896)) (B3)



119875119887119906119904119910119878119905 = sum119896isinΦ119905119896 =BS

119875119878119879119896 minus |119862|sum119902=2

(minus1)119902sdot |119862|119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982ℎ119898119902


( sum119896isin(120595119899capΦ119905)


119875119878119879119896)119875119887119906119904119910119865119905 = (1 minus prod

119895isinΦ119905119895 =BS(1 minus 120591119895))


(1 minus 120591119895)minus 119875119887119906119904119910119878119905 119875119887119906119904119910119860119905 = 119875119878119877119905119871119886119888119896

(B4)



119895isinΦ119905119895 =BS(1 minus 120591119895))



(1 minus 120591119895))119894minus1







Competing Interests


References










































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 10 20 30 40 50

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(36)











119895isinΦ119905119903 119895 =BS(1 minus 120591119895) (38)


120595ℎ(1 minus 120591119896)


| ⋃ℎisinΦℎ119888119905119903120595ℎ|119862119902sum

119898=1

( prod119894isin119889119898

119889119898=1198891198981 1198891198982 119889119898119902


120595ℎ119889119898


119899isin119889119898119889119898=1198891198981 1198891198982119889119898119902

(120572119899 + (1 minus 120572119899) 120573119899)))(39)






= 2119871 |Φℎ119905119903BS|sum119902=1

|Φℎ119905119903BS|119862119902sum119898=1

( prod119894isin119896119898

119896119898=1198961198981 1198961198982 119896119898119902



119899isin119896119898119896119898=1198961198981 1198961198982 119896119898119902

(120572119899 + (1 minus 120572119899) 120573119899)))(40)




119902=1

|Φ119905BS|119862119902sum119898=1

( prod119894isin119896119898

119896119898=1198961198981 1198961198982 119896119898119902



119899isin119896119898119896119898=1198961198981 1198961198982 119896119898119902


120595ℎ119905(1 minus 120591119896)

sdot | ⋃ℎisinΦ119905119888 120595ℎ119905|sum119902=1

| ⋃ℎisinΦ119905119888120595ℎ119905|119862119902sum

119898=1

( prod119894isin119889119898

119889119898=1198891198981 1198891198982119889119898119902


120595ℎ(119889119898cup119905)


119899isin119889119898119889119898=1198891198981 1198891198982 119889119898119902

(120572119899 + (1 minus 120572119899) 120573119899)))

(41)









P (1198611199041198971199001199051 cap 1198681198621198621198601) + P (1198681199041198971199001199051 cap 1198681198621198621198601) (43)


P (1198611199041198971199001199051 cap 1198681198621198621198601) + P (1198681199041198971199001199051 cap 1198681198621198621198601))sdot P (1198781199041198971199001199051) + 119875119887119890119905119886119860119862119870 (44)




(1 minus 120591119895))+ 119875119887119906119904119910119860119905119875119887119906119904119910119865119905 + 119875119887119906119904119910119860119905 + 119875119887119906119904119910119878119905 + 119875119894119889119897119890119905

(45)







IBSrceil) (46)






119877e-to-e = 119897prod119899=1

119877119899 (48)





119899=1

(119908119899 + 119863119899) (49)



119864e-to-e = 119897sum119899=1

119864119899 (50)


119894isinΦ119905119900119905119886119897

(1 minus 120591119894) 119875119904119906119888119888119890119904119904 = sum119894isinΦ119905119900119905119886119897

119875119878119879119894119875119887119906119904119910 (51)



119899isinΦ119905119900119905119886119897

sum119903isin119874119899

119877e-to-e (119899 119903)119863e-to-e (119899 119903) (52)



510

1520

25

12

34

= 3

= 4 = 5um

0

001

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003

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005

Relia

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510

1520

25

12

34

= 3 = 4 = 5

um

5

10

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Avg

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s)






510

1520

25

12

34

= 3 = 4

= 5

um

15

2

25

Pow

er co

nsum

ptio

n (m

W)







0

002

004

006

008

01

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Relia

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Prob

abili

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f disc

ardi

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Number of nodes

075

08

085

09

095

1

due t

o ch

anne

l acc

ess f

ailu

re







0875

0877

0879

0881

0883

0885

0887

0889

0891

Prob

abili

ty o

f uns

ucce

ssfu

l cha

nnel

acce

ss at

tem

pt





0

5

10

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0

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35 40 45 50 55 60 65 70 75 8030Number of nodes

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35 40 45 50 55 60 65 70 75 8030Number of nodes







14

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35 40 45 50 55 60 65 70 75 8030Number of nodes




35 40 45 50 55 60 65 70 75 8030Number of nodes

0

005

01

015

02

025

Thro

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ut






















5 10 15 20 25 300u

05055

06065

07075

08085

Relia

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5 10 15 20 25 300u

456789

1011121314

Avg

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ay (m

s)

3638

442444648

552

Avg

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gy co

nsum

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n (m

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5 10 15 20 25 300u

04045

05055

06065

07075

Relia

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5 10 15 20 25 300u

468

10121416

Avg

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ay (m

s)

5 10 15 20 25 300u

332343638

442444648

Avg

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nsum

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n (m

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5 10 15 20 25 300u

02025

03035

04045

05055

Relia

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5 10 15 20 25 300u

5

10

15

20

Avg

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s)

5 10 15 20 25 300u

2

25

3

35

Avg

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n (m

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5 10 15 20 25 300u

01015

02025

03035

04

Relia

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5 10 15 20 25 300u

468

1012141618202224

Avg

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s)

5 10 15 20 25 300u

5 10 15 20 25 300u

1618

222242628

332

Avg

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gy co

nsum

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n (m

w)

0002004006008

01012014

Relia

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5 10 15 20 25 300u

5

10

15

20

25

30

Avg

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ay (m

s)

5 10 15 20 25 300u

5 10 15 20 25 300u

112141618

222242628

3

Avg

ener

gy co

nsum

ptio

n (m

w)

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2 m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 3

m = 3 m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 4

m = 4

m = 4m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4m = 4

m = 4

m = 4

m = 4







Φ16119888= 1 3 4 5 Φ16 4= 1 3 5 8 9 12 13 14 15 17 19 20 22 Φℎ16 4 = 0 2 21 Φℎ11988816 4 = 0 2 11986216 = 4 1205950 = 1 4 1205951 = 12 14 15 1205952 = 7 11 18 1205953 = 6 13 22 24 1205954 = 5 8 16 17 1205955 = 2 3 9 19 20

(53)










IEEE slotted CSMACA

0

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CAM 431-131-131CAM 431-430-131

CAM 631-430-131CAM 631-131-131







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600E + 01

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CAM 631-430-131CAM 631-131-131




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50

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IEEE slotted CSMACA

000E + 00

500E + 00

100E + 01

150E + 01

200E + 01

End-

to-e

nd p

ower

cons

umpt

ion

(mW

)

CAM 431-131-131CAM 431-430-131

CAM 631-430-131CAM 631-131-131










Appendix













where




bsknum (119896 119878) = 2119878sum119862119862119860119888119900119898119887=1


where

sumfn (119878 119862119862119860119888119900119898119887 119868119863)=


119872119894119899119861119865119904119906119898119879119890119903119898 =




1 if 119878 = 1119878 + 119878minus1sum119899=1




(A7)






119875119878119877ℎ119905 = (119871119886119888119896 + 119871) sum119899isinΦℎ119888119905119903


119875119878119879119896 + 119871119886119888119896 sum119899isinΦℎ119888119905119903

sum119896isin(120595119899capΦℎ119905119903)

119875119878119879119896 + sum119899isinΦℎ119888119905119903

sum119896isin(120595119899capΦ119905)

119875119878119879119896 minus (119871119886119888119896 + 119871) |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902




119875119878119879119896)minus 119871119886119888119896 |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


(( sum119896isin(120595119899capΦℎ119905119903)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911 119896notinΦ119905


119875119878119879119896))


minus |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


(( sum119896isin(120595119899capΦ119905)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911


119875119878119879119896))(B1)

119875119878119879119896 = 120591119896 prod119895isinΦ119896119899




119875119878119877119905 = 119871119886119888119896( sum119899isinΦ119905119888

sum119896isin120595119899119896 =119905

119875119878119879119896 minus |Φ119905119888 |sum119902=2

(minus1)119902 |Φ119905119888 |119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


( sum119896isin120595119899 119896 =119905


119875119878119879119896)) (B3)



119875119887119906119904119910119878119905 = sum119896isinΦ119905119896 =BS

119875119878119879119896 minus |119862|sum119902=2

(minus1)119902sdot |119862|119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982ℎ119898119902


( sum119896isin(120595119899capΦ119905)


119875119878119879119896)119875119887119906119904119910119865119905 = (1 minus prod

119895isinΦ119905119895 =BS(1 minus 120591119895))


(1 minus 120591119895)minus 119875119887119906119904119910119878119905 119875119887119906119904119910119860119905 = 119875119878119877119905119871119886119888119896

(B4)



119895isinΦ119905119895 =BS(1 minus 120591119895))



(1 minus 120591119895))119894minus1







Competing Interests


References










































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











(36)











119895isinΦ119905119903 119895 =BS(1 minus 120591119895) (38)


120595ℎ(1 minus 120591119896)


| ⋃ℎisinΦℎ119888119905119903120595ℎ|119862119902sum

119898=1

( prod119894isin119889119898

119889119898=1198891198981 1198891198982 119889119898119902


120595ℎ119889119898


119899isin119889119898119889119898=1198891198981 1198891198982119889119898119902

(120572119899 + (1 minus 120572119899) 120573119899)))(39)






= 2119871 |Φℎ119905119903BS|sum119902=1

|Φℎ119905119903BS|119862119902sum119898=1

( prod119894isin119896119898

119896119898=1198961198981 1198961198982 119896119898119902



119899isin119896119898119896119898=1198961198981 1198961198982 119896119898119902

(120572119899 + (1 minus 120572119899) 120573119899)))(40)




119902=1

|Φ119905BS|119862119902sum119898=1

( prod119894isin119896119898

119896119898=1198961198981 1198961198982 119896119898119902



119899isin119896119898119896119898=1198961198981 1198961198982 119896119898119902


120595ℎ119905(1 minus 120591119896)

sdot | ⋃ℎisinΦ119905119888 120595ℎ119905|sum119902=1

| ⋃ℎisinΦ119905119888120595ℎ119905|119862119902sum

119898=1

( prod119894isin119889119898

119889119898=1198891198981 1198891198982119889119898119902


120595ℎ(119889119898cup119905)


119899isin119889119898119889119898=1198891198981 1198891198982 119889119898119902

(120572119899 + (1 minus 120572119899) 120573119899)))

(41)









P (1198611199041198971199001199051 cap 1198681198621198621198601) + P (1198681199041198971199001199051 cap 1198681198621198621198601) (43)


P (1198611199041198971199001199051 cap 1198681198621198621198601) + P (1198681199041198971199001199051 cap 1198681198621198621198601))sdot P (1198781199041198971199001199051) + 119875119887119890119905119886119860119862119870 (44)




(1 minus 120591119895))+ 119875119887119906119904119910119860119905119875119887119906119904119910119865119905 + 119875119887119906119904119910119860119905 + 119875119887119906119904119910119878119905 + 119875119894119889119897119890119905

(45)







IBSrceil) (46)






119877e-to-e = 119897prod119899=1

119877119899 (48)





119899=1

(119908119899 + 119863119899) (49)



119864e-to-e = 119897sum119899=1

119864119899 (50)


119894isinΦ119905119900119905119886119897

(1 minus 120591119894) 119875119904119906119888119888119890119904119904 = sum119894isinΦ119905119900119905119886119897

119875119878119879119894119875119887119906119904119910 (51)



119899isinΦ119905119900119905119886119897

sum119903isin119874119899

119877e-to-e (119899 119903)119863e-to-e (119899 119903) (52)



510

1520

25

12

34

= 3

= 4 = 5um

0

001

002

003

004

005

Relia

bilit

y


510

1520

25

12

34

= 3 = 4 = 5

um

5

10

15

20

25

30

Avg

del

ay (m

s)






510

1520

25

12

34

= 3 = 4

= 5

um

15

2

25

Pow

er co

nsum

ptio

n (m

W)







0

002

004

006

008

01

012

014

Relia

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y







30 40 50 60 70 80

Prob

abili

ty o

f disc

ardi

ng p

acke

ts

Number of nodes

075

08

085

09

095

1

due t

o ch

anne

l acc

ess f

ailu

re







0875

0877

0879

0881

0883

0885

0887

0889

0891

Prob

abili

ty o

f uns

ucce

ssfu

l cha

nnel

acce

ss at

tem

pt





0

5

10

15

20

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30

35

40

Avg

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s)









0

05

1

15

2

25

Ener

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nsum

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n (m

w)





0

005

01

015

02

025

03

Thro

ughp

ut






35 40 45 50 55 60 65 70 75 8030Number of nodes

12

13

14

15

16

17

18

19

Avg

del

ay (m

s)




0

001

002

003

004

005

006

007

008

Relia

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y

35 40 45 50 55 60 65 70 75 8030Number of nodes







14

15

16

17

18

19

2

21

22

Ener

gy co

nsum

ptio

n (m

w)

35 40 45 50 55 60 65 70 75 8030Number of nodes




35 40 45 50 55 60 65 70 75 8030Number of nodes

0

005

01

015

02

025

Thro

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ut






















5 10 15 20 25 300u

05055

06065

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5 10 15 20 25 300u

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1011121314

Avg

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3638

442444648

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5 10 15 20 25 300u

04045

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5 10 15 20 25 300u

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10121416

Avg

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ay (m

s)

5 10 15 20 25 300u

332343638

442444648

Avg

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nsum

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5 10 15 20 25 300u

02025

03035

04045

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5 10 15 20 25 300u

5

10

15

20

Avg

del

ay (m

s)

5 10 15 20 25 300u

2

25

3

35

Avg

ener

gy co

nsum

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n (m

w)

5 10 15 20 25 300u

01015

02025

03035

04

Relia

bilit

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5 10 15 20 25 300u

468

1012141618202224

Avg

del

ay (m

s)

5 10 15 20 25 300u

5 10 15 20 25 300u

1618

222242628

332

Avg

ener

gy co

nsum

ptio

n (m

w)

0002004006008

01012014

Relia

bilit

y

5 10 15 20 25 300u

5

10

15

20

25

30

Avg

del

ay (m

s)

5 10 15 20 25 300u

5 10 15 20 25 300u

112141618

222242628

3

Avg

ener

gy co

nsum

ptio

n (m

w)

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2 m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 3

m = 3 m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 4

m = 4

m = 4m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4m = 4

m = 4

m = 4

m = 4







Φ16119888= 1 3 4 5 Φ16 4= 1 3 5 8 9 12 13 14 15 17 19 20 22 Φℎ16 4 = 0 2 21 Φℎ11988816 4 = 0 2 11986216 = 4 1205950 = 1 4 1205951 = 12 14 15 1205952 = 7 11 18 1205953 = 6 13 22 24 1205954 = 5 8 16 17 1205955 = 2 3 9 19 20

(53)










IEEE slotted CSMACA

0

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End-

to-e

nd re

liabi

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CAM 431-131-131CAM 431-430-131

CAM 631-430-131CAM 631-131-131







000E + 00

100E + 01

200E + 01

300E + 01

400E + 01

500E + 01

600E + 01

End-

to-e

nd d

elay

(ms)


CAM 631-430-131CAM 631-131-131




01

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Aver

age n

etw

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ughp

ut







50

100

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Net

wor

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odpu

t (bi

tms)



IEEE slotted CSMACA

000E + 00

500E + 00

100E + 01

150E + 01

200E + 01

End-

to-e

nd p

ower

cons

umpt

ion

(mW

)

CAM 431-131-131CAM 431-430-131

CAM 631-430-131CAM 631-131-131










Appendix













where




bsknum (119896 119878) = 2119878sum119862119862119860119888119900119898119887=1


where

sumfn (119878 119862119862119860119888119900119898119887 119868119863)=


119872119894119899119861119865119904119906119898119879119890119903119898 =




1 if 119878 = 1119878 + 119878minus1sum119899=1




(A7)






119875119878119877ℎ119905 = (119871119886119888119896 + 119871) sum119899isinΦℎ119888119905119903


119875119878119879119896 + 119871119886119888119896 sum119899isinΦℎ119888119905119903

sum119896isin(120595119899capΦℎ119905119903)

119875119878119879119896 + sum119899isinΦℎ119888119905119903

sum119896isin(120595119899capΦ119905)

119875119878119879119896 minus (119871119886119888119896 + 119871) |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902




119875119878119879119896)minus 119871119886119888119896 |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


(( sum119896isin(120595119899capΦℎ119905119903)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911 119896notinΦ119905


119875119878119879119896))


minus |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


(( sum119896isin(120595119899capΦ119905)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911


119875119878119879119896))(B1)

119875119878119879119896 = 120591119896 prod119895isinΦ119896119899




119875119878119877119905 = 119871119886119888119896( sum119899isinΦ119905119888

sum119896isin120595119899119896 =119905

119875119878119879119896 minus |Φ119905119888 |sum119902=2

(minus1)119902 |Φ119905119888 |119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


( sum119896isin120595119899 119896 =119905


119875119878119879119896)) (B3)



119875119887119906119904119910119878119905 = sum119896isinΦ119905119896 =BS

119875119878119879119896 minus |119862|sum119902=2

(minus1)119902sdot |119862|119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982ℎ119898119902


( sum119896isin(120595119899capΦ119905)


119875119878119879119896)119875119887119906119904119910119865119905 = (1 minus prod

119895isinΦ119905119895 =BS(1 minus 120591119895))


(1 minus 120591119895)minus 119875119887119906119904119910119878119905 119875119887119906119904119910119860119905 = 119875119878119877119905119871119886119888119896

(B4)



119895isinΦ119905119895 =BS(1 minus 120591119895))



(1 minus 120591119895))119894minus1







Competing Interests


References










































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119902=1

|Φ119905BS|119862119902sum119898=1

( prod119894isin119896119898

119896119898=1198961198981 1198961198982 119896119898119902



119899isin119896119898119896119898=1198961198981 1198961198982 119896119898119902


120595ℎ119905(1 minus 120591119896)

sdot | ⋃ℎisinΦ119905119888 120595ℎ119905|sum119902=1

| ⋃ℎisinΦ119905119888120595ℎ119905|119862119902sum

119898=1

( prod119894isin119889119898

119889119898=1198891198981 1198891198982119889119898119902


120595ℎ(119889119898cup119905)


119899isin119889119898119889119898=1198891198981 1198891198982 119889119898119902

(120572119899 + (1 minus 120572119899) 120573119899)))

(41)









P (1198611199041198971199001199051 cap 1198681198621198621198601) + P (1198681199041198971199001199051 cap 1198681198621198621198601) (43)


P (1198611199041198971199001199051 cap 1198681198621198621198601) + P (1198681199041198971199001199051 cap 1198681198621198621198601))sdot P (1198781199041198971199001199051) + 119875119887119890119905119886119860119862119870 (44)




(1 minus 120591119895))+ 119875119887119906119904119910119860119905119875119887119906119904119910119865119905 + 119875119887119906119904119910119860119905 + 119875119887119906119904119910119878119905 + 119875119894119889119897119890119905

(45)







IBSrceil) (46)






119877e-to-e = 119897prod119899=1

119877119899 (48)





119899=1

(119908119899 + 119863119899) (49)



119864e-to-e = 119897sum119899=1

119864119899 (50)


119894isinΦ119905119900119905119886119897

(1 minus 120591119894) 119875119904119906119888119888119890119904119904 = sum119894isinΦ119905119900119905119886119897

119875119878119879119894119875119887119906119904119910 (51)



119899isinΦ119905119900119905119886119897

sum119903isin119874119899

119877e-to-e (119899 119903)119863e-to-e (119899 119903) (52)



510

1520

25

12

34

= 3

= 4 = 5um

0

001

002

003

004

005

Relia

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510

1520

25

12

34

= 3 = 4 = 5

um

5

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Avg

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s)






510

1520

25

12

34

= 3 = 4

= 5

um

15

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25

Pow

er co

nsum

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n (m

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0

002

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006

008

01

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014

Relia

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30 40 50 60 70 80

Prob

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Number of nodes

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l acc

ess f

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re







0875

0877

0879

0881

0883

0885

0887

0889

0891

Prob

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f uns

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ss at

tem

pt





0

5

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35 40 45 50 55 60 65 70 75 8030Number of nodes

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35 40 45 50 55 60 65 70 75 8030Number of nodes







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Ener

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35 40 45 50 55 60 65 70 75 8030Number of nodes




35 40 45 50 55 60 65 70 75 8030Number of nodes

0

005

01

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Thro

ughp

ut






















5 10 15 20 25 300u

05055

06065

07075

08085

Relia

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5 10 15 20 25 300u

456789

1011121314

Avg

del

ay (m

s)

3638

442444648

552

Avg

ener

gy co

nsum

ptio

n (m

w)

5 10 15 20 25 300u

04045

05055

06065

07075

Relia

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5 10 15 20 25 300u

468

10121416

Avg

del

ay (m

s)

5 10 15 20 25 300u

332343638

442444648

Avg

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nsum

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n (m

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5 10 15 20 25 300u

02025

03035

04045

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5 10 15 20 25 300u

5

10

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5 10 15 20 25 300u

2

25

3

35

Avg

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nsum

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n (m

w)

5 10 15 20 25 300u

01015

02025

03035

04

Relia

bilit

y

5 10 15 20 25 300u

468

1012141618202224

Avg

del

ay (m

s)

5 10 15 20 25 300u

5 10 15 20 25 300u

1618

222242628

332

Avg

ener

gy co

nsum

ptio

n (m

w)

0002004006008

01012014

Relia

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5 10 15 20 25 300u

5

10

15

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Avg

del

ay (m

s)

5 10 15 20 25 300u

5 10 15 20 25 300u

112141618

222242628

3

Avg

ener

gy co

nsum

ptio

n (m

w)

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2 m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 3

m = 3 m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 4

m = 4

m = 4m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4m = 4

m = 4

m = 4

m = 4







Φ16119888= 1 3 4 5 Φ16 4= 1 3 5 8 9 12 13 14 15 17 19 20 22 Φℎ16 4 = 0 2 21 Φℎ11988816 4 = 0 2 11986216 = 4 1205950 = 1 4 1205951 = 12 14 15 1205952 = 7 11 18 1205953 = 6 13 22 24 1205954 = 5 8 16 17 1205955 = 2 3 9 19 20

(53)










IEEE slotted CSMACA

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CAM 431-131-131CAM 431-430-131

CAM 631-430-131CAM 631-131-131







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CAM 631-430-131CAM 631-131-131




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IEEE slotted CSMACA

000E + 00

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cons

umpt

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(mW

)

CAM 431-131-131CAM 431-430-131

CAM 631-430-131CAM 631-131-131










Appendix













where




bsknum (119896 119878) = 2119878sum119862119862119860119888119900119898119887=1


where

sumfn (119878 119862119862119860119888119900119898119887 119868119863)=


119872119894119899119861119865119904119906119898119879119890119903119898 =




1 if 119878 = 1119878 + 119878minus1sum119899=1




(A7)






119875119878119877ℎ119905 = (119871119886119888119896 + 119871) sum119899isinΦℎ119888119905119903


119875119878119879119896 + 119871119886119888119896 sum119899isinΦℎ119888119905119903

sum119896isin(120595119899capΦℎ119905119903)

119875119878119879119896 + sum119899isinΦℎ119888119905119903

sum119896isin(120595119899capΦ119905)

119875119878119879119896 minus (119871119886119888119896 + 119871) |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902




119875119878119879119896)minus 119871119886119888119896 |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


(( sum119896isin(120595119899capΦℎ119905119903)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911 119896notinΦ119905


119875119878119879119896))


minus |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


(( sum119896isin(120595119899capΦ119905)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911


119875119878119879119896))(B1)

119875119878119879119896 = 120591119896 prod119895isinΦ119896119899




119875119878119877119905 = 119871119886119888119896( sum119899isinΦ119905119888

sum119896isin120595119899119896 =119905

119875119878119879119896 minus |Φ119905119888 |sum119902=2

(minus1)119902 |Φ119905119888 |119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


( sum119896isin120595119899 119896 =119905


119875119878119879119896)) (B3)



119875119887119906119904119910119878119905 = sum119896isinΦ119905119896 =BS

119875119878119879119896 minus |119862|sum119902=2

(minus1)119902sdot |119862|119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982ℎ119898119902


( sum119896isin(120595119899capΦ119905)


119875119878119879119896)119875119887119906119904119910119865119905 = (1 minus prod

119895isinΦ119905119895 =BS(1 minus 120591119895))


(1 minus 120591119895)minus 119875119887119906119904119910119878119905 119875119887119906119904119910119860119905 = 119875119878119877119905119871119886119888119896

(B4)



119895isinΦ119905119895 =BS(1 minus 120591119895))



(1 minus 120591119895))119894minus1







Competing Interests


References










































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














IBSrceil) (46)






119877e-to-e = 119897prod119899=1

119877119899 (48)





119899=1

(119908119899 + 119863119899) (49)



119864e-to-e = 119897sum119899=1

119864119899 (50)


119894isinΦ119905119900119905119886119897

(1 minus 120591119894) 119875119904119906119888119888119890119904119904 = sum119894isinΦ119905119900119905119886119897

119875119878119879119894119875119887119906119904119910 (51)



119899isinΦ119905119900119905119886119897

sum119903isin119874119899

119877e-to-e (119899 119903)119863e-to-e (119899 119903) (52)



510

1520

25

12

34

= 3

= 4 = 5um

0

001

002

003

004

005

Relia

bilit

y


510

1520

25

12

34

= 3 = 4 = 5

um

5

10

15

20

25

30

Avg

del

ay (m

s)






510

1520

25

12

34

= 3 = 4

= 5

um

15

2

25

Pow

er co

nsum

ptio

n (m

W)







0

002

004

006

008

01

012

014

Relia

bilit

y







30 40 50 60 70 80

Prob

abili

ty o

f disc

ardi

ng p

acke

ts

Number of nodes

075

08

085

09

095

1

due t

o ch

anne

l acc

ess f

ailu

re







0875

0877

0879

0881

0883

0885

0887

0889

0891

Prob

abili

ty o

f uns

ucce

ssfu

l cha

nnel

acce

ss at

tem

pt





0

5

10

15

20

25

30

35

40

Avg

del

ay (m

s)









0

05

1

15

2

25

Ener

gy co

nsum

ptio

n (m

w)





0

005

01

015

02

025

03

Thro

ughp

ut






35 40 45 50 55 60 65 70 75 8030Number of nodes

12

13

14

15

16

17

18

19

Avg

del

ay (m

s)




0

001

002

003

004

005

006

007

008

Relia

bilit

y

35 40 45 50 55 60 65 70 75 8030Number of nodes







14

15

16

17

18

19

2

21

22

Ener

gy co

nsum

ptio

n (m

w)

35 40 45 50 55 60 65 70 75 8030Number of nodes




35 40 45 50 55 60 65 70 75 8030Number of nodes

0

005

01

015

02

025

Thro

ughp

ut






















5 10 15 20 25 300u

05055

06065

07075

08085

Relia

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5 10 15 20 25 300u

456789

1011121314

Avg

del

ay (m

s)

3638

442444648

552

Avg

ener

gy co

nsum

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n (m

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5 10 15 20 25 300u

04045

05055

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07075

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5 10 15 20 25 300u

468

10121416

Avg

del

ay (m

s)

5 10 15 20 25 300u

332343638

442444648

Avg

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gy co

nsum

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n (m

w)

5 10 15 20 25 300u

02025

03035

04045

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5 10 15 20 25 300u

5

10

15

20

Avg

del

ay (m

s)

5 10 15 20 25 300u

2

25

3

35

Avg

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nsum

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n (m

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5 10 15 20 25 300u

01015

02025

03035

04

Relia

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5 10 15 20 25 300u

468

1012141618202224

Avg

del

ay (m

s)

5 10 15 20 25 300u

5 10 15 20 25 300u

1618

222242628

332

Avg

ener

gy co

nsum

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n (m

w)

0002004006008

01012014

Relia

bilit

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5 10 15 20 25 300u

5

10

15

20

25

30

Avg

del

ay (m

s)

5 10 15 20 25 300u

5 10 15 20 25 300u

112141618

222242628

3

Avg

ener

gy co

nsum

ptio

n (m

w)

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2 m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 3

m = 3 m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 4

m = 4

m = 4m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4m = 4

m = 4

m = 4

m = 4







Φ16119888= 1 3 4 5 Φ16 4= 1 3 5 8 9 12 13 14 15 17 19 20 22 Φℎ16 4 = 0 2 21 Φℎ11988816 4 = 0 2 11986216 = 4 1205950 = 1 4 1205951 = 12 14 15 1205952 = 7 11 18 1205953 = 6 13 22 24 1205954 = 5 8 16 17 1205955 = 2 3 9 19 20

(53)










IEEE slotted CSMACA

0

01

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04

05

06

07

08

End-

to-e

nd re

liabi

lity

CAM 431-131-131CAM 431-430-131

CAM 631-430-131CAM 631-131-131







000E + 00

100E + 01

200E + 01

300E + 01

400E + 01

500E + 01

600E + 01

End-

to-e

nd d

elay

(ms)


CAM 631-430-131CAM 631-131-131




01

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Aver

age n

etw

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50

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odpu

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IEEE slotted CSMACA

000E + 00

500E + 00

100E + 01

150E + 01

200E + 01

End-

to-e

nd p

ower

cons

umpt

ion

(mW

)

CAM 431-131-131CAM 431-430-131

CAM 631-430-131CAM 631-131-131










Appendix













where




bsknum (119896 119878) = 2119878sum119862119862119860119888119900119898119887=1


where

sumfn (119878 119862119862119860119888119900119898119887 119868119863)=


119872119894119899119861119865119904119906119898119879119890119903119898 =




1 if 119878 = 1119878 + 119878minus1sum119899=1




(A7)






119875119878119877ℎ119905 = (119871119886119888119896 + 119871) sum119899isinΦℎ119888119905119903


119875119878119879119896 + 119871119886119888119896 sum119899isinΦℎ119888119905119903

sum119896isin(120595119899capΦℎ119905119903)

119875119878119879119896 + sum119899isinΦℎ119888119905119903

sum119896isin(120595119899capΦ119905)

119875119878119879119896 minus (119871119886119888119896 + 119871) |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902




119875119878119879119896)minus 119871119886119888119896 |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


(( sum119896isin(120595119899capΦℎ119905119903)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911 119896notinΦ119905


119875119878119879119896))


minus |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


(( sum119896isin(120595119899capΦ119905)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911


119875119878119879119896))(B1)

119875119878119879119896 = 120591119896 prod119895isinΦ119896119899




119875119878119877119905 = 119871119886119888119896( sum119899isinΦ119905119888

sum119896isin120595119899119896 =119905

119875119878119879119896 minus |Φ119905119888 |sum119902=2

(minus1)119902 |Φ119905119888 |119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


( sum119896isin120595119899 119896 =119905


119875119878119879119896)) (B3)



119875119887119906119904119910119878119905 = sum119896isinΦ119905119896 =BS

119875119878119879119896 minus |119862|sum119902=2

(minus1)119902sdot |119862|119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982ℎ119898119902


( sum119896isin(120595119899capΦ119905)


119875119878119879119896)119875119887119906119904119910119865119905 = (1 minus prod

119895isinΦ119905119895 =BS(1 minus 120591119895))


(1 minus 120591119895)minus 119875119887119906119904119910119878119905 119875119887119906119904119910119860119905 = 119875119878119877119905119871119886119888119896

(B4)



119895isinΦ119905119895 =BS(1 minus 120591119895))



(1 minus 120591119895))119894minus1







Competing Interests


References










































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119899=1

(119908119899 + 119863119899) (49)



119864e-to-e = 119897sum119899=1

119864119899 (50)


119894isinΦ119905119900119905119886119897

(1 minus 120591119894) 119875119904119906119888119888119890119904119904 = sum119894isinΦ119905119900119905119886119897

119875119878119879119894119875119887119906119904119910 (51)



119899isinΦ119905119900119905119886119897

sum119903isin119874119899

119877e-to-e (119899 119903)119863e-to-e (119899 119903) (52)



510

1520

25

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= 4 = 5um

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510

1520

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= 3 = 4 = 5

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510

1520

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= 3 = 4

= 5

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35 40 45 50 55 60 65 70 75 8030Number of nodes

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5 10 15 20 25 300u

1618

222242628

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0002004006008

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5

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5 10 15 20 25 300u

5 10 15 20 25 300u

112141618

222242628

3

Avg

ener

gy co

nsum

ptio

n (m

w)

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2 m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 3

m = 3 m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 4

m = 4

m = 4m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4m = 4

m = 4

m = 4

m = 4







Φ16119888= 1 3 4 5 Φ16 4= 1 3 5 8 9 12 13 14 15 17 19 20 22 Φℎ16 4 = 0 2 21 Φℎ11988816 4 = 0 2 11986216 = 4 1205950 = 1 4 1205951 = 12 14 15 1205952 = 7 11 18 1205953 = 6 13 22 24 1205954 = 5 8 16 17 1205955 = 2 3 9 19 20

(53)










IEEE slotted CSMACA

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000E + 00

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(mW

)

CAM 431-131-131CAM 431-430-131

CAM 631-430-131CAM 631-131-131










Appendix













where




bsknum (119896 119878) = 2119878sum119862119862119860119888119900119898119887=1


where

sumfn (119878 119862119862119860119888119900119898119887 119868119863)=


119872119894119899119861119865119904119906119898119879119890119903119898 =




1 if 119878 = 1119878 + 119878minus1sum119899=1




(A7)






119875119878119877ℎ119905 = (119871119886119888119896 + 119871) sum119899isinΦℎ119888119905119903


119875119878119879119896 + 119871119886119888119896 sum119899isinΦℎ119888119905119903

sum119896isin(120595119899capΦℎ119905119903)

119875119878119879119896 + sum119899isinΦℎ119888119905119903

sum119896isin(120595119899capΦ119905)

119875119878119879119896 minus (119871119886119888119896 + 119871) |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902




119875119878119879119896)minus 119871119886119888119896 |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


(( sum119896isin(120595119899capΦℎ119905119903)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911 119896notinΦ119905


119875119878119879119896))


minus |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


(( sum119896isin(120595119899capΦ119905)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911


119875119878119879119896))(B1)

119875119878119879119896 = 120591119896 prod119895isinΦ119896119899




119875119878119877119905 = 119871119886119888119896( sum119899isinΦ119905119888

sum119896isin120595119899119896 =119905

119875119878119879119896 minus |Φ119905119888 |sum119902=2

(minus1)119902 |Φ119905119888 |119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


( sum119896isin120595119899 119896 =119905


119875119878119879119896)) (B3)



119875119887119906119904119910119878119905 = sum119896isinΦ119905119896 =BS

119875119878119879119896 minus |119862|sum119902=2

(minus1)119902sdot |119862|119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982ℎ119898119902


( sum119896isin(120595119899capΦ119905)


119875119878119879119896)119875119887119906119904119910119865119905 = (1 minus prod

119895isinΦ119905119895 =BS(1 minus 120591119895))


(1 minus 120591119895)minus 119875119887119906119904119910119878119905 119875119887119906119904119910119860119905 = 119875119878119877119905119871119886119888119896

(B4)



119895isinΦ119905119895 =BS(1 minus 120591119895))



(1 minus 120591119895))119894minus1







Competing Interests


References










































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










510

1520

25

12

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= 3 = 4

= 5

um

15

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Pow

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nsum

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n (m

W)







0

002

004

006

008

01

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Relia

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abili

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f disc

ardi

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Number of nodes

075

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o ch

anne

l acc

ess f

ailu

re







0875

0877

0879

0881

0883

0885

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0889

0891

Prob

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f uns

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l cha

nnel

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ss at

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5

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5 10 15 20 25 300u

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5 10 15 20 25 300u

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5 10 15 20 25 300u

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1012141618202224

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5 10 15 20 25 300u

5 10 15 20 25 300u

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222242628

332

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0002004006008

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5 10 15 20 25 300u

5

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5 10 15 20 25 300u

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112141618

222242628

3

Avg

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gy co

nsum

ptio

n (m

w)

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2 m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 3

m = 3 m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 4

m = 4

m = 4m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4m = 4

m = 4

m = 4

m = 4







Φ16119888= 1 3 4 5 Φ16 4= 1 3 5 8 9 12 13 14 15 17 19 20 22 Φℎ16 4 = 0 2 21 Φℎ11988816 4 = 0 2 11986216 = 4 1205950 = 1 4 1205951 = 12 14 15 1205952 = 7 11 18 1205953 = 6 13 22 24 1205954 = 5 8 16 17 1205955 = 2 3 9 19 20

(53)










IEEE slotted CSMACA

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CAM 631-430-131CAM 631-131-131




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(mW

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CAM 431-131-131CAM 431-430-131

CAM 631-430-131CAM 631-131-131










Appendix













where




bsknum (119896 119878) = 2119878sum119862119862119860119888119900119898119887=1


where

sumfn (119878 119862119862119860119888119900119898119887 119868119863)=


119872119894119899119861119865119904119906119898119879119890119903119898 =




1 if 119878 = 1119878 + 119878minus1sum119899=1




(A7)






119875119878119877ℎ119905 = (119871119886119888119896 + 119871) sum119899isinΦℎ119888119905119903


119875119878119879119896 + 119871119886119888119896 sum119899isinΦℎ119888119905119903

sum119896isin(120595119899capΦℎ119905119903)

119875119878119879119896 + sum119899isinΦℎ119888119905119903

sum119896isin(120595119899capΦ119905)

119875119878119879119896 minus (119871119886119888119896 + 119871) |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902




119875119878119879119896)minus 119871119886119888119896 |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


(( sum119896isin(120595119899capΦℎ119905119903)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911 119896notinΦ119905


119875119878119879119896))


minus |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


(( sum119896isin(120595119899capΦ119905)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911


119875119878119879119896))(B1)

119875119878119879119896 = 120591119896 prod119895isinΦ119896119899




119875119878119877119905 = 119871119886119888119896( sum119899isinΦ119905119888

sum119896isin120595119899119896 =119905

119875119878119879119896 minus |Φ119905119888 |sum119902=2

(minus1)119902 |Φ119905119888 |119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


( sum119896isin120595119899 119896 =119905


119875119878119879119896)) (B3)



119875119887119906119904119910119878119905 = sum119896isinΦ119905119896 =BS

119875119878119879119896 minus |119862|sum119902=2

(minus1)119902sdot |119862|119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982ℎ119898119902


( sum119896isin(120595119899capΦ119905)


119875119878119879119896)119875119887119906119904119910119865119905 = (1 minus prod

119895isinΦ119905119895 =BS(1 minus 120591119895))


(1 minus 120591119895)minus 119875119887119906119904119910119878119905 119875119887119906119904119910119860119905 = 119875119878119877119905119871119886119888119896

(B4)



119895isinΦ119905119895 =BS(1 minus 120591119895))



(1 minus 120591119895))119894minus1







Competing Interests


References










































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










30 40 50 60 70 80

Prob

abili

ty o

f disc

ardi

ng p

acke

ts

Number of nodes

075

08

085

09

095

1

due t

o ch

anne

l acc

ess f

ailu

re







0875

0877

0879

0881

0883

0885

0887

0889

0891

Prob

abili

ty o

f uns

ucce

ssfu

l cha

nnel

acce

ss at

tem

pt





0

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35 40 45 50 55 60 65 70 75 8030Number of nodes




35 40 45 50 55 60 65 70 75 8030Number of nodes

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5 10 15 20 25 300u

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5 10 15 20 25 300u

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10121416

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442444648

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112141618

222242628

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Avg

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nsum

ptio

n (m

w)

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2 m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 3

m = 3 m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 4

m = 4

m = 4m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4m = 4

m = 4

m = 4

m = 4







Φ16119888= 1 3 4 5 Φ16 4= 1 3 5 8 9 12 13 14 15 17 19 20 22 Φℎ16 4 = 0 2 21 Φℎ11988816 4 = 0 2 11986216 = 4 1205950 = 1 4 1205951 = 12 14 15 1205952 = 7 11 18 1205953 = 6 13 22 24 1205954 = 5 8 16 17 1205955 = 2 3 9 19 20

(53)










IEEE slotted CSMACA

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CAM 431-131-131CAM 431-430-131

CAM 631-430-131CAM 631-131-131










Appendix













where




bsknum (119896 119878) = 2119878sum119862119862119860119888119900119898119887=1


where

sumfn (119878 119862119862119860119888119900119898119887 119868119863)=


119872119894119899119861119865119904119906119898119879119890119903119898 =




1 if 119878 = 1119878 + 119878minus1sum119899=1




(A7)






119875119878119877ℎ119905 = (119871119886119888119896 + 119871) sum119899isinΦℎ119888119905119903


119875119878119879119896 + 119871119886119888119896 sum119899isinΦℎ119888119905119903

sum119896isin(120595119899capΦℎ119905119903)

119875119878119879119896 + sum119899isinΦℎ119888119905119903

sum119896isin(120595119899capΦ119905)

119875119878119879119896 minus (119871119886119888119896 + 119871) |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902




119875119878119879119896)minus 119871119886119888119896 |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


(( sum119896isin(120595119899capΦℎ119905119903)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911 119896notinΦ119905


119875119878119879119896))


minus |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


(( sum119896isin(120595119899capΦ119905)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911


119875119878119879119896))(B1)

119875119878119879119896 = 120591119896 prod119895isinΦ119896119899




119875119878119877119905 = 119871119886119888119896( sum119899isinΦ119905119888

sum119896isin120595119899119896 =119905

119875119878119879119896 minus |Φ119905119888 |sum119902=2

(minus1)119902 |Φ119905119888 |119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


( sum119896isin120595119899 119896 =119905


119875119878119879119896)) (B3)



119875119887119906119904119910119878119905 = sum119896isinΦ119905119896 =BS

119875119878119879119896 minus |119862|sum119902=2

(minus1)119902sdot |119862|119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982ℎ119898119902


( sum119896isin(120595119899capΦ119905)


119875119878119879119896)119875119887119906119904119910119865119905 = (1 minus prod

119895isinΦ119905119895 =BS(1 minus 120591119895))


(1 minus 120591119895)minus 119875119887119906119904119910119878119905 119875119887119906119904119910119860119905 = 119875119878119877119905119871119886119888119896

(B4)



119895isinΦ119905119895 =BS(1 minus 120591119895))



(1 minus 120591119895))119894minus1







Competing Interests


References










































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











0

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35 40 45 50 55 60 65 70 75 8030Number of nodes

12

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18

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22

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35 40 45 50 55 60 65 70 75 8030Number of nodes




35 40 45 50 55 60 65 70 75 8030Number of nodes

0

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0002004006008

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3

Avg

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nsum

ptio

n (m

w)

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2 m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 3

m = 3 m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 4

m = 4

m = 4m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4m = 4

m = 4

m = 4

m = 4







Φ16119888= 1 3 4 5 Φ16 4= 1 3 5 8 9 12 13 14 15 17 19 20 22 Φℎ16 4 = 0 2 21 Φℎ11988816 4 = 0 2 11986216 = 4 1205950 = 1 4 1205951 = 12 14 15 1205952 = 7 11 18 1205953 = 6 13 22 24 1205954 = 5 8 16 17 1205955 = 2 3 9 19 20

(53)










IEEE slotted CSMACA

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CAM 431-131-131CAM 431-430-131

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(mW

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CAM 431-131-131CAM 431-430-131

CAM 631-430-131CAM 631-131-131










Appendix













where




bsknum (119896 119878) = 2119878sum119862119862119860119888119900119898119887=1


where

sumfn (119878 119862119862119860119888119900119898119887 119868119863)=


119872119894119899119861119865119904119906119898119879119890119903119898 =




1 if 119878 = 1119878 + 119878minus1sum119899=1




(A7)






119875119878119877ℎ119905 = (119871119886119888119896 + 119871) sum119899isinΦℎ119888119905119903


119875119878119879119896 + 119871119886119888119896 sum119899isinΦℎ119888119905119903

sum119896isin(120595119899capΦℎ119905119903)

119875119878119879119896 + sum119899isinΦℎ119888119905119903

sum119896isin(120595119899capΦ119905)

119875119878119879119896 minus (119871119886119888119896 + 119871) |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902




119875119878119879119896)minus 119871119886119888119896 |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


(( sum119896isin(120595119899capΦℎ119905119903)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911 119896notinΦ119905


119875119878119879119896))


minus |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


(( sum119896isin(120595119899capΦ119905)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911


119875119878119879119896))(B1)

119875119878119879119896 = 120591119896 prod119895isinΦ119896119899




119875119878119877119905 = 119871119886119888119896( sum119899isinΦ119905119888

sum119896isin120595119899119896 =119905

119875119878119879119896 minus |Φ119905119888 |sum119902=2

(minus1)119902 |Φ119905119888 |119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


( sum119896isin120595119899 119896 =119905


119875119878119879119896)) (B3)



119875119887119906119904119910119878119905 = sum119896isinΦ119905119896 =BS

119875119878119879119896 minus |119862|sum119902=2

(minus1)119902sdot |119862|119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982ℎ119898119902


( sum119896isin(120595119899capΦ119905)


119875119878119879119896)119875119887119906119904119910119865119905 = (1 minus prod

119895isinΦ119905119895 =BS(1 minus 120591119895))


(1 minus 120591119895)minus 119875119887119906119904119910119878119905 119875119887119906119904119910119860119905 = 119875119878119877119905119871119886119888119896

(B4)



119895isinΦ119905119895 =BS(1 minus 120591119895))



(1 minus 120591119895))119894minus1







Competing Interests


References










































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










14

15

16

17

18

19

2

21

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nsum

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n (m

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35 40 45 50 55 60 65 70 75 8030Number of nodes




35 40 45 50 55 60 65 70 75 8030Number of nodes

0

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Avg

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nsum

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n (m

w)

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2 m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 3

m = 3 m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 4

m = 4

m = 4m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4m = 4

m = 4

m = 4

m = 4







Φ16119888= 1 3 4 5 Φ16 4= 1 3 5 8 9 12 13 14 15 17 19 20 22 Φℎ16 4 = 0 2 21 Φℎ11988816 4 = 0 2 11986216 = 4 1205950 = 1 4 1205951 = 12 14 15 1205952 = 7 11 18 1205953 = 6 13 22 24 1205954 = 5 8 16 17 1205955 = 2 3 9 19 20

(53)










IEEE slotted CSMACA

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CAM 431-131-131CAM 431-430-131

CAM 631-430-131CAM 631-131-131







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CAM 631-430-131CAM 631-131-131




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000E + 00

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End-

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nd p

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cons

umpt

ion

(mW

)

CAM 431-131-131CAM 431-430-131

CAM 631-430-131CAM 631-131-131










Appendix













where




bsknum (119896 119878) = 2119878sum119862119862119860119888119900119898119887=1


where

sumfn (119878 119862119862119860119888119900119898119887 119868119863)=


119872119894119899119861119865119904119906119898119879119890119903119898 =




1 if 119878 = 1119878 + 119878minus1sum119899=1




(A7)






119875119878119877ℎ119905 = (119871119886119888119896 + 119871) sum119899isinΦℎ119888119905119903


119875119878119879119896 + 119871119886119888119896 sum119899isinΦℎ119888119905119903

sum119896isin(120595119899capΦℎ119905119903)

119875119878119879119896 + sum119899isinΦℎ119888119905119903

sum119896isin(120595119899capΦ119905)

119875119878119879119896 minus (119871119886119888119896 + 119871) |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902




119875119878119879119896)minus 119871119886119888119896 |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


(( sum119896isin(120595119899capΦℎ119905119903)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911 119896notinΦ119905


119875119878119879119896))


minus |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


(( sum119896isin(120595119899capΦ119905)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911


119875119878119879119896))(B1)

119875119878119879119896 = 120591119896 prod119895isinΦ119896119899




119875119878119877119905 = 119871119886119888119896( sum119899isinΦ119905119888

sum119896isin120595119899119896 =119905

119875119878119879119896 minus |Φ119905119888 |sum119902=2

(minus1)119902 |Φ119905119888 |119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


( sum119896isin120595119899 119896 =119905


119875119878119879119896)) (B3)



119875119887119906119904119910119878119905 = sum119896isinΦ119905119896 =BS

119875119878119879119896 minus |119862|sum119902=2

(minus1)119902sdot |119862|119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982ℎ119898119902


( sum119896isin(120595119899capΦ119905)


119875119878119879119896)119875119887119906119904119910119865119905 = (1 minus prod

119895isinΦ119905119895 =BS(1 minus 120591119895))


(1 minus 120591119895)minus 119875119887119906119904119910119878119905 119875119887119906119904119910119860119905 = 119875119878119877119905119871119886119888119896

(B4)



119895isinΦ119905119895 =BS(1 minus 120591119895))



(1 minus 120591119895))119894minus1







Competing Interests


References










































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation



















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m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 1

m = 1

m = 1

m = 1m = 1

m = 1

m = 1

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2 m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 2

m = 3

m = 3 m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 3

m = 4

m = 4

m = 4m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4

m = 4m = 4

m = 4

m = 4

m = 4







Φ16119888= 1 3 4 5 Φ16 4= 1 3 5 8 9 12 13 14 15 17 19 20 22 Φℎ16 4 = 0 2 21 Φℎ11988816 4 = 0 2 11986216 = 4 1205950 = 1 4 1205951 = 12 14 15 1205952 = 7 11 18 1205953 = 6 13 22 24 1205954 = 5 8 16 17 1205955 = 2 3 9 19 20

(53)










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CAM 431-131-131CAM 431-430-131

CAM 631-430-131CAM 631-131-131










Appendix













where




bsknum (119896 119878) = 2119878sum119862119862119860119888119900119898119887=1


where

sumfn (119878 119862119862119860119888119900119898119887 119868119863)=


119872119894119899119861119865119904119906119898119879119890119903119898 =




1 if 119878 = 1119878 + 119878minus1sum119899=1




(A7)






119875119878119877ℎ119905 = (119871119886119888119896 + 119871) sum119899isinΦℎ119888119905119903


119875119878119879119896 + 119871119886119888119896 sum119899isinΦℎ119888119905119903

sum119896isin(120595119899capΦℎ119905119903)

119875119878119879119896 + sum119899isinΦℎ119888119905119903

sum119896isin(120595119899capΦ119905)

119875119878119879119896 minus (119871119886119888119896 + 119871) |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902




119875119878119879119896)minus 119871119886119888119896 |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


(( sum119896isin(120595119899capΦℎ119905119903)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911 119896notinΦ119905


119875119878119879119896))


minus |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


(( sum119896isin(120595119899capΦ119905)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911


119875119878119879119896))(B1)

119875119878119879119896 = 120591119896 prod119895isinΦ119896119899




119875119878119877119905 = 119871119886119888119896( sum119899isinΦ119905119888

sum119896isin120595119899119896 =119905

119875119878119879119896 minus |Φ119905119888 |sum119902=2

(minus1)119902 |Φ119905119888 |119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


( sum119896isin120595119899 119896 =119905


119875119878119879119896)) (B3)



119875119887119906119904119910119878119905 = sum119896isinΦ119905119896 =BS

119875119878119879119896 minus |119862|sum119902=2

(minus1)119902sdot |119862|119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982ℎ119898119902


( sum119896isin(120595119899capΦ119905)


119875119878119879119896)119875119887119906119904119910119865119905 = (1 minus prod

119895isinΦ119905119895 =BS(1 minus 120591119895))


(1 minus 120591119895)minus 119875119887119906119904119910119878119905 119875119887119906119904119910119860119905 = 119875119878119877119905119871119886119888119896

(B4)



119895isinΦ119905119895 =BS(1 minus 120591119895))



(1 minus 120591119895))119894minus1







Competing Interests


References










































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













Φ16119888= 1 3 4 5 Φ16 4= 1 3 5 8 9 12 13 14 15 17 19 20 22 Φℎ16 4 = 0 2 21 Φℎ11988816 4 = 0 2 11986216 = 4 1205950 = 1 4 1205951 = 12 14 15 1205952 = 7 11 18 1205953 = 6 13 22 24 1205954 = 5 8 16 17 1205955 = 2 3 9 19 20

(53)










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Appendix













where




bsknum (119896 119878) = 2119878sum119862119862119860119888119900119898119887=1


where

sumfn (119878 119862119862119860119888119900119898119887 119868119863)=


119872119894119899119861119865119904119906119898119879119890119903119898 =




1 if 119878 = 1119878 + 119878minus1sum119899=1




(A7)






119875119878119877ℎ119905 = (119871119886119888119896 + 119871) sum119899isinΦℎ119888119905119903


119875119878119879119896 + 119871119886119888119896 sum119899isinΦℎ119888119905119903

sum119896isin(120595119899capΦℎ119905119903)

119875119878119879119896 + sum119899isinΦℎ119888119905119903

sum119896isin(120595119899capΦ119905)

119875119878119879119896 minus (119871119886119888119896 + 119871) |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902




119875119878119879119896)minus 119871119886119888119896 |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


(( sum119896isin(120595119899capΦℎ119905119903)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911 119896notinΦ119905


119875119878119879119896))


minus |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


(( sum119896isin(120595119899capΦ119905)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911


119875119878119879119896))(B1)

119875119878119879119896 = 120591119896 prod119895isinΦ119896119899




119875119878119877119905 = 119871119886119888119896( sum119899isinΦ119905119888

sum119896isin120595119899119896 =119905

119875119878119879119896 minus |Φ119905119888 |sum119902=2

(minus1)119902 |Φ119905119888 |119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


( sum119896isin120595119899 119896 =119905


119875119878119879119896)) (B3)



119875119887119906119904119910119878119905 = sum119896isinΦ119905119896 =BS

119875119878119879119896 minus |119862|sum119902=2

(minus1)119902sdot |119862|119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982ℎ119898119902


( sum119896isin(120595119899capΦ119905)


119875119878119879119896)119875119887119906119904119910119865119905 = (1 minus prod

119895isinΦ119905119895 =BS(1 minus 120591119895))


(1 minus 120591119895)minus 119875119887119906119904119910119878119905 119875119887119906119904119910119860119905 = 119875119878119877119905119871119886119888119896

(B4)



119895isinΦ119905119895 =BS(1 minus 120591119895))



(1 minus 120591119895))119894minus1







Competing Interests


References










































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation















IEEE slotted CSMACA

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Appendix













where




bsknum (119896 119878) = 2119878sum119862119862119860119888119900119898119887=1


where

sumfn (119878 119862119862119860119888119900119898119887 119868119863)=


119872119894119899119861119865119904119906119898119879119890119903119898 =




1 if 119878 = 1119878 + 119878minus1sum119899=1




(A7)






119875119878119877ℎ119905 = (119871119886119888119896 + 119871) sum119899isinΦℎ119888119905119903


119875119878119879119896 + 119871119886119888119896 sum119899isinΦℎ119888119905119903

sum119896isin(120595119899capΦℎ119905119903)

119875119878119879119896 + sum119899isinΦℎ119888119905119903

sum119896isin(120595119899capΦ119905)

119875119878119879119896 minus (119871119886119888119896 + 119871) |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902




119875119878119879119896)minus 119871119886119888119896 |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


(( sum119896isin(120595119899capΦℎ119905119903)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911 119896notinΦ119905


119875119878119879119896))


minus |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


(( sum119896isin(120595119899capΦ119905)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911


119875119878119879119896))(B1)

119875119878119879119896 = 120591119896 prod119895isinΦ119896119899




119875119878119877119905 = 119871119886119888119896( sum119899isinΦ119905119888

sum119896isin120595119899119896 =119905

119875119878119879119896 minus |Φ119905119888 |sum119902=2

(minus1)119902 |Φ119905119888 |119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


( sum119896isin120595119899 119896 =119905


119875119878119879119896)) (B3)



119875119887119906119904119910119878119905 = sum119896isinΦ119905119896 =BS

119875119878119879119896 minus |119862|sum119902=2

(minus1)119902sdot |119862|119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982ℎ119898119902


( sum119896isin(120595119899capΦ119905)


119875119878119879119896)119875119887119906119904119910119865119905 = (1 minus prod

119895isinΦ119905119895 =BS(1 minus 120591119895))


(1 minus 120591119895)minus 119875119887119906119904119910119878119905 119875119887119906119904119910119860119905 = 119875119878119877119905119871119886119888119896

(B4)



119895isinΦ119905119895 =BS(1 minus 120591119895))



(1 minus 120591119895))119894minus1







Competing Interests


References










































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











000E + 00

100E + 01

200E + 01

300E + 01

400E + 01

500E + 01

600E + 01

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to-e

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(ms)


CAM 631-430-131CAM 631-131-131




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CAM 431-131-131CAM 431-430-131

CAM 631-430-131CAM 631-131-131










Appendix













where




bsknum (119896 119878) = 2119878sum119862119862119860119888119900119898119887=1


where

sumfn (119878 119862119862119860119888119900119898119887 119868119863)=


119872119894119899119861119865119904119906119898119879119890119903119898 =




1 if 119878 = 1119878 + 119878minus1sum119899=1




(A7)






119875119878119877ℎ119905 = (119871119886119888119896 + 119871) sum119899isinΦℎ119888119905119903


119875119878119879119896 + 119871119886119888119896 sum119899isinΦℎ119888119905119903

sum119896isin(120595119899capΦℎ119905119903)

119875119878119879119896 + sum119899isinΦℎ119888119905119903

sum119896isin(120595119899capΦ119905)

119875119878119879119896 minus (119871119886119888119896 + 119871) |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902




119875119878119879119896)minus 119871119886119888119896 |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


(( sum119896isin(120595119899capΦℎ119905119903)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911 119896notinΦ119905


119875119878119879119896))


minus |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


(( sum119896isin(120595119899capΦ119905)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911


119875119878119879119896))(B1)

119875119878119879119896 = 120591119896 prod119895isinΦ119896119899




119875119878119877119905 = 119871119886119888119896( sum119899isinΦ119905119888

sum119896isin120595119899119896 =119905

119875119878119879119896 minus |Φ119905119888 |sum119902=2

(minus1)119902 |Φ119905119888 |119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


( sum119896isin120595119899 119896 =119905


119875119878119879119896)) (B3)



119875119887119906119904119910119878119905 = sum119896isinΦ119905119896 =BS

119875119878119879119896 minus |119862|sum119902=2

(minus1)119902sdot |119862|119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982ℎ119898119902


( sum119896isin(120595119899capΦ119905)


119875119878119879119896)119875119887119906119904119910119865119905 = (1 minus prod

119895isinΦ119905119895 =BS(1 minus 120591119895))


(1 minus 120591119895)minus 119875119887119906119904119910119878119905 119875119887119906119904119910119860119905 = 119875119878119877119905119871119886119888119896

(B4)



119895isinΦ119905119895 =BS(1 minus 120591119895))



(1 minus 120591119895))119894minus1







Competing Interests


References










































RoboticsJournal of





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VLSI Design



Shock and Vibration







Journal of



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Appendix













where




bsknum (119896 119878) = 2119878sum119862119862119860119888119900119898119887=1


where

sumfn (119878 119862119862119860119888119900119898119887 119868119863)=


119872119894119899119861119865119904119906119898119879119890119903119898 =




1 if 119878 = 1119878 + 119878minus1sum119899=1




(A7)






119875119878119877ℎ119905 = (119871119886119888119896 + 119871) sum119899isinΦℎ119888119905119903


119875119878119879119896 + 119871119886119888119896 sum119899isinΦℎ119888119905119903

sum119896isin(120595119899capΦℎ119905119903)

119875119878119879119896 + sum119899isinΦℎ119888119905119903

sum119896isin(120595119899capΦ119905)

119875119878119879119896 minus (119871119886119888119896 + 119871) |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902




119875119878119879119896)minus 119871119886119888119896 |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


(( sum119896isin(120595119899capΦℎ119905119903)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911 119896notinΦ119905


119875119878119879119896))


minus |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


(( sum119896isin(120595119899capΦ119905)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911


119875119878119879119896))(B1)

119875119878119879119896 = 120591119896 prod119895isinΦ119896119899




119875119878119877119905 = 119871119886119888119896( sum119899isinΦ119905119888

sum119896isin120595119899119896 =119905

119875119878119879119896 minus |Φ119905119888 |sum119902=2

(minus1)119902 |Φ119905119888 |119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


( sum119896isin120595119899 119896 =119905


119875119878119879119896)) (B3)



119875119887119906119904119910119878119905 = sum119896isinΦ119905119896 =BS

119875119878119879119896 minus |119862|sum119902=2

(minus1)119902sdot |119862|119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982ℎ119898119902


( sum119896isin(120595119899capΦ119905)


119875119878119879119896)119875119887119906119904119910119865119905 = (1 minus prod

119895isinΦ119905119895 =BS(1 minus 120591119895))


(1 minus 120591119895)minus 119875119887119906119904119910119878119905 119875119887119906119904119910119860119905 = 119875119878119877119905119871119886119888119896

(B4)



119895isinΦ119905119895 =BS(1 minus 120591119895))



(1 minus 120591119895))119894minus1







Competing Interests


References










































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










bsknum (119896 119878) = 2119878sum119862119862119860119888119900119898119887=1


where

sumfn (119878 119862119862119860119888119900119898119887 119868119863)=


119872119894119899119861119865119904119906119898119879119890119903119898 =




1 if 119878 = 1119878 + 119878minus1sum119899=1




(A7)






119875119878119877ℎ119905 = (119871119886119888119896 + 119871) sum119899isinΦℎ119888119905119903


119875119878119879119896 + 119871119886119888119896 sum119899isinΦℎ119888119905119903

sum119896isin(120595119899capΦℎ119905119903)

119875119878119879119896 + sum119899isinΦℎ119888119905119903

sum119896isin(120595119899capΦ119905)

119875119878119879119896 minus (119871119886119888119896 + 119871) |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902




119875119878119879119896)minus 119871119886119888119896 |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


(( sum119896isin(120595119899capΦℎ119905119903)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911 119896notinΦ119905


119875119878119879119896))


minus |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


(( sum119896isin(120595119899capΦ119905)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911


119875119878119879119896))(B1)

119875119878119879119896 = 120591119896 prod119895isinΦ119896119899




119875119878119877119905 = 119871119886119888119896( sum119899isinΦ119905119888

sum119896isin120595119899119896 =119905

119875119878119879119896 minus |Φ119905119888 |sum119902=2

(minus1)119902 |Φ119905119888 |119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


( sum119896isin120595119899 119896 =119905


119875119878119879119896)) (B3)



119875119887119906119904119910119878119905 = sum119896isinΦ119905119896 =BS

119875119878119879119896 minus |119862|sum119902=2

(minus1)119902sdot |119862|119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982ℎ119898119902


( sum119896isin(120595119899capΦ119905)


119875119878119879119896)119875119887119906119904119910119865119905 = (1 minus prod

119895isinΦ119905119895 =BS(1 minus 120591119895))


(1 minus 120591119895)minus 119875119887119906119904119910119878119905 119875119887119906119904119910119860119905 = 119875119878119877119905119871119886119888119896

(B4)



119895isinΦ119905119895 =BS(1 minus 120591119895))



(1 minus 120591119895))119894minus1







Competing Interests


References










































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











(A7)






119875119878119877ℎ119905 = (119871119886119888119896 + 119871) sum119899isinΦℎ119888119905119903


119875119878119879119896 + 119871119886119888119896 sum119899isinΦℎ119888119905119903

sum119896isin(120595119899capΦℎ119905119903)

119875119878119879119896 + sum119899isinΦℎ119888119905119903

sum119896isin(120595119899capΦ119905)

119875119878119879119896 minus (119871119886119888119896 + 119871) |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902




119875119878119879119896)minus 119871119886119888119896 |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


(( sum119896isin(120595119899capΦℎ119905119903)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911 119896notinΦ119905


119875119878119879119896))


minus |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


(( sum119896isin(120595119899capΦ119905)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911


119875119878119879119896))(B1)

119875119878119879119896 = 120591119896 prod119895isinΦ119896119899




119875119878119877119905 = 119871119886119888119896( sum119899isinΦ119905119888

sum119896isin120595119899119896 =119905

119875119878119879119896 minus |Φ119905119888 |sum119902=2

(minus1)119902 |Φ119905119888 |119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


( sum119896isin120595119899 119896 =119905


119875119878119879119896)) (B3)



119875119887119906119904119910119878119905 = sum119896isinΦ119905119896 =BS

119875119878119879119896 minus |119862|sum119902=2

(minus1)119902sdot |119862|119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982ℎ119898119902


( sum119896isin(120595119899capΦ119905)


119875119878119879119896)119875119887119906119904119910119865119905 = (1 minus prod

119895isinΦ119905119895 =BS(1 minus 120591119895))


(1 minus 120591119895)minus 119875119887119906119904119910119878119905 119875119887119906119904119910119860119905 = 119875119878119877119905119871119886119888119896

(B4)



119895isinΦ119905119895 =BS(1 minus 120591119895))



(1 minus 120591119895))119894minus1







Competing Interests


References










































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










minus |Φℎ119888119905119903|sum119902=2

(minus1)119902sdot |Φℎ119888119905119903|119862119902sum

119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


(( sum119896isin(120595119899capΦ119905)


119875119878119879119896) prod119911isin(ℎ119898119899)

( sum119896isin120595119911


119875119878119879119896))(B1)

119875119878119879119896 = 120591119896 prod119895isinΦ119896119899




119875119878119877119905 = 119871119886119888119896( sum119899isinΦ119905119888

sum119896isin120595119899119896 =119905

119875119878119879119896 minus |Φ119905119888 |sum119902=2

(minus1)119902 |Φ119905119888 |119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982 ℎ119898119902


( sum119896isin120595119899 119896 =119905


119875119878119879119896)) (B3)



119875119887119906119904119910119878119905 = sum119896isinΦ119905119896 =BS

119875119878119879119896 minus |119862|sum119902=2

(minus1)119902sdot |119862|119862119902sum119898=1


ℎ119898=ℎ1198981 ℎ1198982ℎ119898119902


( sum119896isin(120595119899capΦ119905)


119875119878119879119896)119875119887119906119904119910119865119905 = (1 minus prod

119895isinΦ119905119895 =BS(1 minus 120591119895))


(1 minus 120591119895)minus 119875119887119906119904119910119878119905 119875119887119906119904119910119860119905 = 119875119878119877119905119871119886119888119896

(B4)



119895isinΦ119905119895 =BS(1 minus 120591119895))



(1 minus 120591119895))119894minus1







Competing Interests


References










































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













Competing Interests


References










































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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