RESEARCH Open Access Delay-throughput analysis …...RESEARCH Open Access Delay-throughput analysis of multi-channel MAC protocols in ad hoc networks Jari Nieminen* and Riku Jäntti

RESEARCH Open Access

Delay-throughput analysis of multi-channel MACprotocols in ad hoc networksJari Nieminen* and Riku Jäntti

Abstract

Since delay and throughput are important Quality of Service parameters in many wireless applications, we studythe performance of different multi-channel Media Access Control (MAC) protocols in ad hoc networks byconsidering these measures in this paper. For this, we derive average access delays and throughputs in closed-form for different multi-channel MAC approaches in case of Poisson arrivals. Correctness of theoretical results isverified by simulations. Performance of the protocols is analyzed with respect to various critical operationparameters such as number of available channels, packet size and arrival rate. Presented results can be used toevaluate the performance of multi-channel MAC approaches in various scenarios and to study the impact of multi-channel communications on different wireless applications. More importantly, the derived theoretical results can beexploited in network design to ensure system stability.

I. IntroductionMulti-channel communications form the basis of variousfuture wireless systems such as cognitive radio, nextgeneration cellular and wireless sensor networks(WSNs). The reason for this is that the performance ofa wireless network can be improved by exploiting multi-ple frequency channels simultaneously to ensure robust-ness, minimize delay and/or enhance throughput. Ingeneral, performance of multi-channel networks is heav-ily dependent upon used Media Access Control (MAC)protocols and efficient medium access schemes are con-sidered as an essential part of any power-limited self-configurable wireless ad hoc network [1]. Furthermore,delay and throughput are important Quality of Service(QoS) parameters in many applications [2] and hence,the performance of multi-channel MAC schemes in adhoc networks should be investigated in detail withrespect to these measures.In the case of single-channel systems, the perfor-

mances of various MAC approaches have been investi-gated by considering both, throughput and delay.Carrier Sense Multiple Access (CSMA) for single chan-nel systems was first studied by Kleinrock and Tobagi in[3], where the authors deduced equations for delays andthroughputs of CSMA and ALOHA using the busy

period analysis. Later on delay distributions of slottedALOHA and CSMA systems were derived in [4] for dif-ferent retransmission methods. Operation of single-channel IEEE 802.11 systems was evaluated in [5] com-prehensively using a Markov chain model to model theimpact of backoff window sizes on the performance.Multi-channel MAC approaches have not been studiedas widely but a performance analysis of different multi-channel protocols in a single collision domain was pre-sented in [6] with respect to data rates by assumingsaturated traffic conditions. However, to the best ofauthors’ knowledge, delay-throughput characteristics ofmulti-channel MAC protocols have not been studied yetin case of Poisson arrivals and infinite number of users.Contention-based multi-channel MAC protocols

designed for ad hoc networks can be divided into threemain classes, namely split phase, periodic hopping anddedicated control channel. In split phase-based randomaccess approaches the operation is divided into twoparts. First, during contention periods nodes reserveresources on a common control channel and afterwards,data transmissions will take place during the data per-iod. On the other hand, the basic idea behind periodichopping approaches is to use channel hopping on everychannel to avoid availability and congestion problems ofthe common control channel. Moreover, dedicated con-trol channel schemes allocate one channel as a commoncontrol channel and carry out data transmissions on

* Correspondence: [email protected] of Communications and Networking, School of ElectricalEngineering, Aalto University, P.O. Box 13000, 00076 Aalto, Finland

Nieminen and Jäntti EURASIP Journal on Wireless Communications and Networking 2011, 2011:108http://jwcn.eurasipjournals.com/content/2011/1/108

© 2011 Nieminen and Jäntti; licensee Springer. This is an Open Access article distributed under the terms of the Creative CommonsAttribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction inany medium, provided the original work is properly cited.

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other channels. Each of these approaches has specificstrengths and weaknesses which will be discussed indetail.In this paper, we derive average access delays and

throughputs for different multi-channel MACapproaches in case of Poisson arrivals and analyze theperformance with respect to delay and throughput. Weuse a similar approach as in [4] but extend the analysisby taking into account the effect of multi-channel com-munications and deduce the closed-form solutions fordifferent multi-channel MAC schemes. Correctness oftheoretical derivations will be attested by simulations.Performance of the protocols is then analyzed withrespect to various critical operation parameters such asnumber of available channels, packet size and arrivalrate. Presented results can be used to analyze the perfor-mance and suitability of different multi-channel MACapproaches for prospective wireless applications and toguide system design.The rest of the paper is organized as follows. In Sec-

tion II, we specify used system models. Next, we intro-duce different multi-channel approaches in Section IIIand derive throughputs and expected delays in SectionIV for the different multi-channel protocols. Results andanalyses are presented in Section V. Section VI sum-marizes the paper.

II. System modelIn this paper, the focus is on MAC in multi-channel adhoc networks. Since optimal FDMA/TDMA schemesintroduce a lot of complexity and additional messaging,we restrict our study to random access schemes. Eachdevice is equipped with one half-duplex transceiver whichmakes protocols that require an additional receiver, suchas [7], impracticable. Throughputs and delays of differentcontention-based multi-channel MACs can be modeledsimilarly to single-channel CSMA systems with the excep-tion that now we have multiple channels to be exploited.We presume that a common control channel (CCC) ispredetermined for the protocols that require a CCC forfunctioning and it is always of good quality.If a packet transmission fails for some reason, retrans-

mission of the packet will be attempted until successfultransmission takes place, i.e. packets will not be dis-carded in any case. For the analysis, we divide theoperation into multiple discrete time slots and assumefixed packet sizes along with perfect time synchroniza-tion among the nodes. The length of a time slot τ isdefined to correspond to the maximum propagationdelay of resource request and acknowledgement mes-sages. Channel sensing time is equal to the maximumpropagation delay as well and we neglect channelswitching penalty for the sake of simplicity. We only

consider slotted systems with an infinite number ofusers.Packet arrivals are modeled as a Poisson process with

rate g packets per time slot which includes both, newand retransmitted, packet arrivals. In the case of retrans-missions, we consider large backoff windows, e.g. ω > 20such as in [4]. Thus, a station generates one packet in agiven time slot (t, t + τ) with probability

P[N(t + τ ) − N(t) = 1] = e−gτ (gτ ), (1)

where N(t) is the number of occured events up totime t. All new packets will try to access the channel inthe following time slot immediately after generation.Furthermore, we assume fixed packet sizes with trans-mission time T and define 2τ <T. Packet transmissiontime T also includes the acknowlegment message fromthe receiver. All the nodes in a network are awake con-stantly and have identical channel conditions.

III. Multi-Channel MAC protocols in ad hocnetworksResearch efforts in the field of access mechanisms forsingle-channel ad hoc networks have been extensive. Forexample, a multiplicity of single-channel MAC protocolshas been proposed for WSNs [8]. Moreover, variousmulti-channel MAC protocols have been designed fordifferent wireless systems as well. In this section, webriefly introduce operation principles of the most popu-lar multi-channel MAC approaches for which averageaccess delays and throughputs will be derived in SectionIV. We divide random access multi-channel MACs intothree main categories based on the nature of operations:split phase, periodic hopping and dedicated controlchannel. The categories include several protocolsdesigned for different purposes of use such as CognitiveRadio Network (CRN), WSN and Wireless Local AreaNetwork (WLAN). We will choose only one protocolfrom each category for a detailed study. In all of theconsidered cases resource reservations and negotiationsare based on the IEEE 802.11 RTS/CTS messageexchange. The main problem of multi-channel systemsis the multi-channel hidden node problem which occursif the channel usage of neighbor nodes is not knownand nodes choose to transmit on a busy channel.In split phase approaches the operation is divided into

two parts. First, during contention periods nodes reserveresources on the chosen common control channel andthen data transmissions will take place during data peri-ods. Split phase approach has been proposed in differentcontexts. For example, in WLANs Multi-channel MAC(MMAC) protocol [9] exploits this approach whereas incase of CRNs Cognitive MAC (C-MAC) [10] uses simi-lar frame structure. From these we choose MMAC,


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since it is designed for general ad hoc networks, for ourdelay-throughput analysis. Operation of MMAC is illu-strated in Figure 1a.Periodic hopping protocols hop on all the channels

according to a hopping pattern to avoid availability andcongestion problems of the common control channel.Nodes may obey a common hopping pattern or haveindividual hopping patterns. In multi-channel WLANsthe common hopping approach is used for example inChannel-Hopping Multiple Access (CHMA) which wasintroduced in [11]. In addition, in the context of CRNsat least SYN-MAC [12] uses this approach and similarapproach has been proposed for WSNs as well, calledY-MAC [13], which starts hopping only in the case ofcongestion. McMAC [14] and Slotted Seeded ChannelHopping (SSCH) [15] are examples of protocols whichemploy individual hopping patterns. Since the delay-throughput performance of various periodic hoppingprotocols is similar, we select SYN-MAC and evaluateits performance in this paper. Functioning of SYN-MACis depicted in Figure 1b.

Dedicated control channel approaches use one chan-nel only for distributing control information. The ideawas first presented in [16], where the basic operation ofIEEE 802.11 was extended for multiple channels simplyby allocating data transmissions to different channels.However, the multi-channel hidden node problem iscompletely ignored in the design. A protocol which con-siders the multi-channel hidden node problem in thisclass is CAM-MAC [17]. CAM-MAC requires all neigh-bors that hear a resource request message to verifyavailability of the proposed data channel. Consequently,channel reservations consume a lot of resources.A dedicated control channel approach which con-

sumes less resources than CAM-MAC while considersthe multi-channel hidden node problem is GenericMulti-channel MAC (G-McMAC) [18]. Thus, we chooseG-McMAC for the analysis from this class. The protocolis designed especially for multi-channel WSNs. G-McMAC is a hybrid CSMA/TDMA protocol in whichcontention and data periods are merged to minimizedelays. In general, the operation of the protocol is

(a) Split phase: Multi-channel MAC (MMAC)

(b) Periodic hopping: Synchronized MAC (SYN-MAC)

(c) Dedicated control channel: Generic Multi-channel MAC (G-McMAC)

Figure 1 Multi-channel MAC approaches. (a) Split phase: Multi-channel MAC (MMAC). (b) Periodic hopping: Synchronized MAC (SYN-MAC). (c)Dedicated control channel: Generic Multi-channel MAC (G-McMAC).


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divided into two segments: Beacon Period (BP) andContention plus Data Period (CDP). Activities of G-McMAC are illustrated in Figure 1c.Each beacon includes the following information: prefer-

able channel list, send time stamp, channel schedules,hierarchy level, beacon interval length. Gateway node(GW) of the WSN is on level 1 on the synchronizationhierarchy and starts the beaconing process by sendingthe first beacon. All the receivers synchronize to the timereference provided by the GW and set their level as 2.After this, the nodes on level 2 will broadcast beacons aswell and so forth. After a node has received beaconsfrom all its neighbors, it can start the data negotiationprocess. If a node has a packet to send it first senses thewanted data channel to acquire the latest channel infor-mation and after this the node will send a ResourceRequest (RsREQ) message to the intended receiver whichincludes the desired data channel and transmission time,if the channel is free. The proposed frequency-time blockwill be chosen by utilizing the receiver’s and transmitter’spreferable channel lists and schedules. After receiving aRsREQ message, the intended receiver will sense thedesired data channel and respond with a ResourceAcknowledgment (RsACK) message on the commoncontrol channel if the proposed channel is available.Afterwards, the nodes will carry out the data transmis-sion on the chosen channel at the agreed time.

IV. Throughputs and expected delaysSince, we assume that packet arrivals follow Poissonprocess performance evaluation of random accessschemes can be carried out by exploiting the busy per-iod analysis [19], where the average busy time B andaverage idle time I are used for determining the charac-teristics of various schemes. In the appendices, wederive the following probabilities for different multi-channel protocols using the busy period analysis: Ps isthe probability of successful transmission, Pc is theprobability of collision and Pb is the probability that thechannel is sensed busy. In this section, we derive closed-form solutions for average access delays and through-puts of various multi-channel MAC schemes individu-ally by exploiting derived probabilities. Theoreticalresults are confirmed by simulations. Examined proto-cols are G-McMAC, MMAC and SYN-MAC. In thecase of G-McMAC and SYN-MAC, we derive the theo-retical results rigorously. On the other hand, sinceMMAC uses finite contention windows, only approxi-mations can be found in case of MMAC which are thenjustified by simulation results.We specify throughput S as follows

S = gTPs, (2)

where T is the packet size in discrete time slots τ.Next, we define average access delay. Average accessdelay is the sum of the initial access delay and the delaybecause of i unsuccessful transmissions. We denote theinitial access delay with D0 and the delay of ith retrans-mission with Di. In general form, the total access delayin case of R retransmissions is

D =R∑i=0

Di. (3)

Added to this, different retransmission policies inducedifferent delays. By denoting the ith backoff delay asuniformly distributed random variable Wi ~ U(1, 2i-1ω),where ω is the original backoff window in slots, we getthe following expected delay for the ith backoff in caseof Binary Exponential Backoff (BEB)

E[Wbebi ] =

1 + 2i−1ω

2. (4)

and, respectively, in case of Uniform Backoff (UB) wehave Wi ~ U(1, ω) and

E[Wub] =1 + ω

2. (5)

A. Generic multi-channel MAC (G-McMAC)First, we derive equations for the throughput and aver-age access delay of G-McMAC [18]. We exclude thebeacon period from this analysis since beaconing maybe used by other protocols as well, such as MMAC, orperiodic beaconing may be required for time synchroni-zation, routing, etc. For example, many routing proto-cols use broadcast messages to distribute routinginformation [20] and hence, require a beacon period inpractice to avoid transmission of a routing packet manytimes. Moreover, it is presumed that beacon periods arecarried out rarely such that the impact of the period isnegligible to the packet arrival process.In G-McMAC, if a node generates a packet, it first

senses the desired data channel to make sure that it isidle. After this, if the channel is sensed busy, a randombackoff will be induced. On the other hand, if thedesired channel is free the RTS/CTS message exchangewill be carried out on the CCC. The receiver will sensethe wanted data channel before replying. Finally, if themessage exchange was performed successfully, nodescan start the data transmission on the chosen data chan-nel. Figure 2 illustrates the operation of G-McMAC dur-ing CDPs in detail.Average access delay of G-McMAC depends on two

issues. First, the contention process on the CCC andpossible collisions induce some delay. Second, if all data


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channels are occupied an extra delay will be added aswell. We deduce the delay of the contention processfirst and the impact of occupied channels will be takeninto account while deriving the probability of successfultransmission in Appendix A.Now, if the CCC is sensed busy, the latency time for

the first unsuccessful transmission is

D1 = (W1 + 1) · τ . (6)

Respectively, if the channel is sensed idle, the trans-mitter waits for 4τ to conclude whether there was a col-lision or not. In case of a collision, the delay time forthe second unsuccessful transmission is

D2 = (W2 + 4) · τ . (7)

Consequently, by denoting the number of retransmis-sion because of the channel is sensed busy by K, thetotal delay time can be calculated as follows

D = D0 +K∑i=1

(W1 + 1) · τ +R∑

j=K+1

(W2 + 4) · τ

= D0 + τ

R∑i=1

Wi + Kτ + 4(R − K) · τ ,

(8)

where D0 ~ U (5τ, 6τ) is the initial transmission delayin case of successful transmission and 0 ≤ K ≤ R. Hence,R - K is the amount of retransmission due to packet col-lisions during contention. The joint distribution of Rand K is

P{R = r,K = k} =(rk

)PkbP

r−kc Ps, 0 ≤ k ≤ r, (9)

and the used probabilities for G-McMAC are derivedin Appendix A. Now, the expected delay conditioned onR = r and K = k for G-McMAC can be formulated as

E[D|R = r,K = k] = E[D0] + τ

r∑i=1

E[Wi]

+ kτ + 4(r − k) · τ

=τ

2(ω2r + 9r − 6k + 11 − ω).

(10)

Moreover, to derive the average access delay we needto remove the conditioning on R and K. Therefore, theaverage access delay is given by

D =∞∑r=0

r∑k=0

E[D—R = r, K = k] · P{R = r, K = k}

=τ

2

(ωPs

1 − 2(1 − Ps)+

9Ps

− 6PbPs

+ 2 − ω

),

Ps > 0.5,

(11)

where Ps > 0.5 is required to have a finite averagedelay. In addition, availability of channels causes addi-tional delay as well. We model the impact of multi-channel communications using a Markov model andthus, the probability that all the data channels are occu-pied (Pocc) can be calculated using the Erlang B formula[21]. As a result, the throughput of G-McMAC is

S = gT · e−gτ

4 − 3e−gτ· (1 − Pocc), (12)

where

Pocc =

GN−1

(N − 1)!∑N−1

i=0Gi

i!

, (13)

and G = gT. Since the control channel is not used fordata transmissions, only N - 1 channels are available fordata transmissions. Figure 3 shows that the theoretical

Figure 2 Operation of G-McMAC during a CDP.


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and simulated results match up well for different num-ber of channels with respect to delay.

B. Multi-channel MAC (MMAC)Next, we study split phase approaches using MMAC [9]as an example. Operation of MMAC is divided into twoparts which form a cycle. MMAC is designed for IEEE802.11 networks and it exploits Ad hoc Traffic Indica-tion Message (ATIM) windows of IEEE 802.11 PowerSaving Mechanism (PSM) which are originally used onlyfor power management. In MMAC ATIM windows areextended and channel reservations conducted duringATIM windows on the CCC. Data transmissions takeplace on all available channels afterwards. We denotethe length of the ATIM window by Tatim and the lengthof the data interval by T, both in time slots. Thus, thetotal length of one cycle is Tc = Tatim + T. Lengths ofthese intervals are predetermined and fixed and hence,the intervals determine the average access delay as well.We set Tatim = 0.2 · Tc and T = 0.8 · Tc since thesevalues were used in the initial simulation model in [9].

Furthermore, it is assumed that packets fit perfectly tothe chosen cycle structure. Figure 4 depicts the opera-tion of MMAC during ATIM windows.In the case of MMAC, a node has to wait until the end

of an ATIM window even though the initial transmissionwould be successful before transmitting data. Conse-quently, on average the initial transmission delay is

E[D0] =Tatim2

· TatimTc

+(TD2

+ Tatim

)· TD

Tc. (14)

Moreover, if a node has not been able to reserveresources before the end of an ATIM window, it has towait for the next data interval and an additional delay ofTc is added. Hence, the overall delay is

D = D0 +M · Tc, (15)

where M denotes the number of additional cycles. Ifthe delay due to CSMA operations during an ATIMwindow is larger than the length of the ATIM windowor all of the channels are occupied before a node canreserve resources, a packet will be delayed. By denotingthe latency of a packet during an ATIM window with L,this blocking probability can be represented as

Pblock = P{L > Tatim} + P{L ≤ Tatim} · P{Occupied}. (16)Since all resource reservations will be made during

ATIM windows, the packet arrival rate has to be scaledsuch that all packets are generated during an ATIMwindow in one cycle for theoretical analysis. Hence, intheory we have the following packet arrival rate for thecontention phase

ga = g · TcTatim

. (17)

First, we find out the probability that a node can notreserve resources during an ATIM window due to theshortage of data channels. We approximate this by com-paring the number of channel reservations to the num-ber of channels. This is done by scaling the difference

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

5

10

15

20

25

30

35

Arrival rate (g)

Ave

rage

Acc

ess

Del

ay

TheoryN=10SimN=10TheoryN=16SimN=16

Figure 3 Theoretical and simulated results for average accessdelay of G-McMAC (T = 100, ω = 32).

Figure 4 Negotiation during an ATIM window.


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between the amount of successful negotiations and thenumber of channels with the amount of successfulnegotiations. All of the used probabilities are derived inAppendix B. The amount of successful data negotiationsduring an ATIM window is on average

E[packets] = PsgaTatim. (18)

In the beginning of each ATIM window all the chan-nels are free and hence, the previously used Markovmodel can not be exploited. In consequence, we approx-imate the probability that a packet is blocked because ofchannel shortage as follows

Pcb1ock ≈ max

{0,

PsgaTatim − NPsgaTatim

}. (19)

Second, in the case of small ATIM windows, the per-formance will be bounded by the fact that only a certainamount of data channels can be reserved in time beforethe end of an ATIM window. Now, if a node senses thatthe control channel is busy during contention, it willbackoff according to BEB. Same happens in case of colli-sions as well. During an ATIM window the latency of asuccessful RTS/CTS message exchange is 3τ. Since ω =32, the performance is dominated by P{R = 0} and P{R= 1} while the total delay is L ≤ 35. Furthermore, while35 <Tatim ≤ 2ω, P{R ≤ 2} dominates. Finally, if Tatim >2ω the effect of Pd

b1ock becomes negligible since multipleretransmissions may take place and it is very unlikelythat a packet is delayed due to the end of an ATIM win-dow. We set the probability of a retransmission as Pr =Pc + Pb and approximate the probability of block due tothe end of a contention window as follows

Pdb1ockc ≈

⎧⎨⎩1 − (Ps + Pr · Ps · Tatim

ω), Tatim ≤ 35,

1 − (Ps + (P2r + Pr) · Ps), 35 < Tatim ≤ 2ω,

0, otherwise.

Figure 5 depicts theoretical and simulated results fordifferent packet sizes. When the packet size is 100, the

blocking probability is determined by Pdb1ock and with

the packet size of 1,000, the blocking probability isdetermined by Pc

b1ock. With moderate packet sizes, theblocking probability is determined by both probabilitiesand hence, the simulated and theoretical results do notmatch perfectly. Nevertheless, according to our resultsthese approximations do not significantly under- oroverestimate the performance of MMAC in any caseand hence, the use of these approximates is justifiablefor adequate analysis.Finally, effect of additional cycles can be formulated as

Dblock = (Pdb1ock + Pc

b1ock − Pdb1ock · Pc

b1ock)Tc, (20)

and thus, the average access delay of MMAC is givenby

D = E[D0] + Dblock. (21)

and the throughput is

S = gaT · e−gτ

(3 − 2 e−gaτ )· (1 − Pblock). (22)

C. Synchronized MAC (SYN-MAC)We use SYN-MAC [12] as an example of common hop-ping approaches and the same delay-throughput analysisapplies to parallel rendezvous schemes as well. SYN-MAC exploits periodic hopping and resource reserva-tions can be done only for the current channel to avoidthe multi-channel hidden node problem. Therefore, theperformance of SYN-MAC can be estimated similarly tosingle-channel systems by reducing the arrival rate ofpackets due to the utilization of multiple channelssimultaneously. General operation of SYN-MAC on asingle channel is demonstrated in Figure 6. For analysispurposes, we assume that all generated packets have towait until the next resource reservation interval beforecompeting for resources and data transmissions startprecisely at the end of contention windows.

Figure 5 Theoretical and simulated results for the probability of block as a function of arrival rate. (a) T = 100 (Pdblock dominates). (b) T =

1, 000(Pcblock dominates).


Page 7 of 15

Resource reservation interval is divided into multiplesmall time slots (τ) and to avoid collisions, each trans-mitter chooses a random backoff value from a givenfixed window ω. In other words, SYN-MAC exploitsUB. Length of the contention period is Ts = ωτ and weset Ts = 10 since this should give good results in generalaccording to [12]. Consequently, to validate the assump-tion of Poisson arrivals, retransmitted packets aredelayed over several contention windows randomly insimulations. Moreover, we denote the total length of acycle by Tc = T + Ts.Arrival rates have to be scaled correspond to the

operation of SYN-MAC. Naturally, the arrival rate isinversely proportional to the number of channels N.Moreover, packets generated during the packet trans-mission time T will stack up. Hence, in case of SYN-MAC we scale arrival rates as follows

gs = g · ω + T

T/ω· 1N

= g · (ω + T)ωT · N . (23)

Now, in case of SYN-MAC the latency of a successfultransmission is simply

E[D0] = Ts +Ts2, (24)

on average. Contrary to other approaches, the inducedlatencies because of collisions or if a channel is sensedbusy are equal in SYN-MAC. If resource request mes-sages collide or the channel is sensed busy, a delay of Ts

will be added always. Thus, the delay due to R retrans-missions is simply

Dr =R∑i=1

Ts = Ts · R, (25)

and the amount of retransmissions on average is givenby

E[R] =Pb + Pc

Ps. (26)

Finally, we can find out the average access delay asfollows

D = E[D0] + Ts · E[R]

= E[D0] + Ts

(1 − PsPs

)

= Ts

(2 + PsPs

), Ps > 0,

(27)

and the throughput is

S = gsT · (Ts/T)e−gsτ

1 + (Ts/T) − e−gsτ. (28)

The probabilities for SYN-MAC are derived in Appen-dix C. Again, we compare our theoretical results withsimulation results and the outcome is illustrated in Fig-ure 7. With large packets (T ≥ (N - 1)Ts) theoretical andsimulated results are identical when Ps ≥ 0.5. But then,with smaller packets (T < (N - 1)Ts) results are slightlydifferent since a data transmission on one channel willbe over before nodes hop onto that particular channelagain and thus, packet size does not have any impact onthe performance in that case. Nevertheless, since theprobabilities of successful transmission and that thechannel is sensed busy match without using Equation(23) and retransmissions, we conclude that the theoreti-cal results for SYN-MAC are correct.

V. Results and analysisIn this section, we analyze the performance of differentmulti-channel MAC approaches with respect tothroughput and average access delay using previouslydeduced analytical results which were confirmed bysimulations. First, we focus on delay analysis and

Figure 6 Operation of SYN-MAC on a single channel.


Page 8 of 15

consider the impact of arrival rate, number of channelsand packet sizes on the expected delays. Second, weevaluate the performance of the protocols in terms oftotal throughput with respect to the same critical systemparameters. Finally, we consider stability of the differentapproaches since it is of significant importance tounderstand what is the maximum traffic load that aMAC protocol can handle.

A. Delay analysisIt is extremely important to understand delay character-istics of the used MAC protocols to assure sufficientQoS and system stability. Hence, in this subsection weanalyze the performance of different multi-channelMAC protocols with respect to average access delay.First, we consider the effect of packet size and presentthe results for average access delay as a function ofpacket size in Figure 8. In general, G-McMAC offerssignificantly lower delays than other approaches withsmall packets regardless of the number of channels andthe impact of packet size starts to be visible just beforeapproaching the stability point, which is T = 300 whileN = 10 and g = 0.04 for G-McMAC, even though theimpact of packet size on the delay is small in general.Stability point of G-McMAC, and other protocols aswell, moves to the left on x-axis if the arrival rate isincreased and right if the arrival rate is decreased.Moreover, SYN-MAC offers relatively constant delays

with different packet sizes and approaches G-McMACwhen we get closer to the stability point of G-McMAC.However, with small packets the difference is remark-able and SYN-MAC introduces over twice as largedelays as G-McMAC. Furthermore, performance ofMMAC is significantly worse already with small packetsizes and access delay increases linearly when the packet

size grows. As the packet size is increased, delay ofMMAC grows constantly and the difference comparedwith other protocols enhances. In this case, the numberof channels does not have any impact on the delay ofMMAC since Tatim ≤ 2ω. As the results imply, delay ofMMAC is heavily affected by the chosen packet sizewhereas G-McMAC and SYN-MAC offer relatively con-stant delays with different packet sizes. To summarize,G-McMAC achieves the best performance in generalwhile SYN-MAC performs better with large packet sizessince it does not suffer from stability problems asquickly.Different multi-channel approaches are not equally

affected by the arrival rate as can be seen in Figure 9,where expected delays are depicted as a function of arri-val rate. G-McMAC performs remarkably well while

0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.0514

15

16

17

18

19

20

21

22

23

24

Arrival rate (g)

Ave

rage

Acc

ess

Del

ay

TheoryN=4SimN=4TheoryN=10SimN=10TheoryN=16SimN=16

Figure 7 Theoretical and simulated results for average accessdelay in case of SYN-MAC (T = 200, ω = 10).

50 100 150 200 2500

20

40

60

80

100

120

140

160

180

200

220

Packet Size (T)

Ave

rage

Acc

ess

Del

ay

MMACN=10MMACN=16SYN MACN=10SYN MACN=16G McMACN=10G McMACN=16

Figure 8 Average access delays as a function of packet size (g= 0.04).

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.080

20

40

60

80

100

120

140

160

180

200

Arrival Rate (g)

Ave

rage

Acc

ess

Del

ay

MMACT=200MMACT=100SYN MACT=200SYN MACT=100G McMACT=200G McMACT=100

Figure 9 Average access delays as a function of arrival rate (N= 16).


Page 9 of 15

arrival rates are small. However, as the arrival rate isincreased, the difference in delay between G-McMACand SYN-MAC diminishes when approaching to the sta-bility point of G-McMAC. Nevertheless, G-McMACachieves lower access delays regardless of the arrivalrate given that a finite delay can be found for G-McMAC. However, the performance of MMAC is sig-nificantly worse already with low arrival rates since onlya small number of successful negotiations can be carriedout during the very short contention period and conse-quently, MMAC can not fully utilize the capacity of themulti-channel system. G-McMAC outperforms otherprotocols again while SYN-MAC achieves lower averageaccess delays than MMAC.As stated previously, the third critical parameter is the

amount of available channels. According to our resultsshown in Figure 10, the performance of MMAC seems tobe constant regardless of the number of channels whenthe packet size is small. This is because of the fact thatwhen packet size is 100 the length of the contention per-iod is 25 and hence, only a small amount of successfulnegotiations can be performed and MMAC does notexploit all the available channels. In other words, the per-formance is bounded by the length of ATIM windowsrather than the number of channels. Moreover, eventhough the performance of SYN-MAC depends on thenumber of channels, the delay becomes close to constantquickly as the number of channels is increased. Neverthe-less, SYN-MAC outperforms MMAC always. Finally, G-McMAC gives the lowest delays regardless of the numberof channels and the performance saturates quickly withthese parameters. However, it should be noted that G-McMAC does not achieve finite average access delays if g= 0.04 and N ≤ 6 while T = 100 or N ≤ 8 while T = 200.

The results infer that G-McMAC outperforms other pro-tocols in terms of delay in all of the cases while it is stable.

B. Throughput analysisNext, we study the impact of critical parameters on thethroughput of different multi-channel MAC approaches.We begin with the effect of arrival rate and Figure 11shows the protocols’ throughputs as a function of packetarrival rate for two different packet sizes. In the case ofsmall arrival rates G-McMAC outperforms other proto-cols clearly. However, the achieved gain depends on thechosen packet size and arrival rate. With these para-meters, MMAC provides the smallest throughputsregardless of the arrival rate. On the other hand, SYN-MAC will surpass G-McMAC in terms of throughput inall of the cases eventually when approaching the stabilitypoint of G-McMAC. For example, SYN-MAC will givebetter throughput than G-McMAC if T = 200, N = 16and g ≥ 0.13. As a conclusion, G-McMAC achieves bet-ter throughput than SYN-MAC especially when we havesmall or moderate arrival rates. The main reasons forthis are that G-McMAC neither utilizes fixed contentionperiods such as SYN-MAC nor exploits periodic hop-ping patterns. Nevertheless, SYN-MAC will offer thehighest throughputs in case of high arrival rates andsmall packets.Naturally, throughput of multi-channel systems is

dependent upon the number of available channels. Fig-ure 12 demonstrates how the number of channels affectsdifferent multi-channel MAC approaches with a lowpacket arrival rate g = 0.04. With these parameters, G-McMAC offers the highest throughput regardless of theamount of channels and once again, MMAC gives con-stant throughput due to the short ATIM window. How-ever, now MMAC can offer higher throughputs than

8 9 10 11 12 13 14 15 160

20

40

60

80

100

120

140

160

Number of Channels (N)

Ave

rage

Acc

ess

Del

ay

MMACT=200

MMACT=100

SYN MACT=200

SYN MACT=100

G McMACT=200

G McMACT=100

Figure 10 Average access delays as a function of number ofchannels (g = 0.04).

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.20

2

4

6

8

10

12

Arrival Rate (g)

Thro

ughp

ut (S

)

G McMACT=200G McMACT=100SYN MACT=200SYN MACT=100MMACT=200MMACT=100

Figure 11 Throughputs as a function of arrival rate (N = 16).


Page 10 of 15

SYN-MAC if the amount of available channels is smalland T = 200. The reason behind this is the cyclic hop-ping pattern of SYN-MAC which may cause silent peri-ods during the operation. Nevertheless, SYN-MAC willachieve higher throughput than MMAC if the numberof available channels is large. In case of small arrivalrates SYN-MAC will also achieve as good performanceas G-McMAC in terms of throughput if the number ofchannels is increased enough, even though averageaccess delays of SYN-MAC are significantly higher asdiscussed previously.On the other hand, with high arrival rates the situa-

tion is different as shown in Figure 13. In this case, thethroughputs of SYN-MAC and G-McMAC grow linearlyas the number of available channels is increased whileMMAC gives constant throughput regardless of theamount of channels. However, now SYN-MAC

outperforms G-McMAC especially when the number ofchannels is large. The results imply that with these para-meters the negotiation process of G-McMAC restrictsthe performance of the protocol since similar through-puts are achieved with different packet sizes. That is tosay, with high packet arrival rates the common controlchannel will be occupied all the time which causes theperformance to saturate. Since the negotiation processof SYN-MAC is shorter and carried out on each channelin turn, the performance continues to improve and thecapacity of multi-channel systems can be fully exploitedin case of high arrival rates and small packets.We also studied the impact of different packet sizes

on the throughputs and the results are presented in Fig-ures 14 and 15 for g = 0.04 and g = 0.2, respectively. Ingeneral, the throughput of MMAC grows as a functionof packet size due to the assumption of fixed and opti-mal packet sizes. Regardless of this fact SYN-MAC andG-McMAC outperform MMAC in case of small packetsand small or moderate arrival rates. On the other hand,MMAC will eventually surpass other protocols since theperformances of G-McMAC and SYN-MAC saturate atsome point as the packet size is increased. Furthermore,G-McMAC gives better throughput than SYN-MACwith low packet arrival rates whereas SYN-MACachieves similar performance with higher arrival rates.We can also see the impact of Pc

b1ock in Figure 15 sincethe performance of MMAC is constant when N = 10while it continues to improve when N = 16. Neverthe-less, it should be noted that in practice it may not bepossible to predetermine optimal cycle structures forMMAC since packet sizes may be variable. This wouldnaturally deteriorate the performance of MMAC. More-over, average access delays of MMAC are many timesworse than that of G-McMAC and the difference grows

8 9 10 11 12 13 14 15 162

2.5

3

3.5

4

4.5

5

5.5

6

6.5

7


Thro

ughp

ut (S

)

G McMACT=200

G McMACT=100

SYN MACT=200

SYN MACT=100

MMACT=200

MMACT=100

Figure 12 Throughputs as a function of channels (g = 0.04).

8 9 10 11 12 13 14 15 160

5

10

15


Thro

ughp

ut (S

)

G McMACT=200G McMACT=100SYN MACT=200SYN MACT=100MMACT=200MMACT=100

Figure 13 Throughputs as a function of channels (g = 0.2).

100 200 300 400 500 600 700 800 900 10000

5

10

15

20

25

Packet Size (T)

Thro

ughp

ut (S

)


Figure 14 Throughputs as a function of packet size (g = 0.04).


Page 11 of 15

as the packet size is increased, which makes MMACunsuitable for delay-sensitive applications.We conclude that G-McMAC achieves highest

throughputs in case of small or moderate packet arrivalrates while packets are small. On the other hand, SYN-MAC outperforms other approaches in case of smallpackets and high packet arrival rates. Finally, MMACprovides the best performance with respect to through-put when the packets are large. However, MMAC causesvery high latencies in general. Our delay analysisundoubtedly shows that G-McMAC outperforms otherprotocols clearly in terms of delay.

C. System stabilityWhen embarking on any wireless communication design,it is essential to understand the operation region of theused MAC protocol to ensure system stability. Figure 16

illustrates delay-throughput curves of MMAC, SYN-MAC and G-McMAC. Evidently, MMAC performs theworst since it induces high latencies and becomesunstable when the throughput is low. After this point,the throughput of MMAC starts to decrease while delaycontinues to grow. On the other hand, we can see thatG-McMAC clearly outperforms SYN-MAC by offeringlower delays in general. However, G-McMAC becomesunstable before SYN-MAC and in fact after the stabilitypoint of G-McMAC the throughput of SYN-MAC stillcontinues to improve. Based on this observation, we con-clude that to minimize access delay, G-McMAC shouldbe used. Whereas, if it is important to maximize through-put at the expense of access delays, SYN-MAC should beexploited.

VI. ConclusionsIn this paper, the performance of multi-channel MACprotocols in ad hoc networks was studied with respectto two important QoS parameters, delay and through-put. We deduced average access delays and throughputsfor different multi-channel MAC approaches in closed-form by considering Poisson arrivals. Theoretical resultswere verified by simulations for each of the consideredprotocols. Throughput and delay analyses were given interms of critical system parameters such as number ofavailable channels, arrival rate and packet sizes. We con-clude that Generic Multi-channel MAC (G-McMAC)consistently outperforms other protocols with respect todelay. G-McMAC also achieves higher throughputs insome cases compared with other approaches, whereas,in some cases other approaches will achieve betterthroughput. Moreover, the low stability point of G-McMAC may be a problem for some applications andin those cases other approaches should be used. Pre-sented results can be exploited to study the performanceand suitability of different multi-channel MACapproaches for different wireless applications and toguide system design.

APPENDIX A: Probabilities for G-MCMACPerformance evaluation of random access schemes hasbeen traditionally carried out by exploiting busy periodanalysis in which the average busy time B and averageidle time I are used for determining the characteristicsof various schemes. In this appendix we consider G-McMAC and derive the following probabilities using thebusy period analysis [19]: Ps is the probability of suc-cessful transmission, Pc is the probability of collisionand Pb is the probability that the control channel issensed busy. We model multi-channel communicationswith a Markov chain. States represent the number ofoccupied data channels such that we have N - 1 data

500 600 700 800 900 10000

5

10

15

20

25

30

35

Packet Size (T)

Thro

ughp

ut (S

)


Figure 15 Throughputs as a function of packet size (g = 0.2).

0 2 4 6 8 10 120

50

100

150

200

250

Throughput

Ave

rage

Acc

ess

Del

ay

MMACT=200

MMACT=100

SYN MACT=200

SYN MACT=100

G McMACT=200

G McMACT=100

Figure 16 Delay as a function of throughput (N = 16).


Page 12 of 15

channels in total. Hence, the probability that all thechannels are occupied can be found using the Erlang Bformula [21] and is given by

Pocc =

GN−1

(N − 1)!∑N−1

i=0Gi

i!

, (A� 1)

where G = gT. To find out the probabilities, we needto derive the average idle and busy periods. For a start,the average idle period consists of k - 1 times no arrivalsand at least one arrival in the last slot. Hence, the aver-age idle time I is

I =τ

1 − e−gτ. (A� 2)

Next, we derive the average busy period which isdefined as follows. The length of the busy period con-sists of k transmission periods if there is at least onearrival in the last k - 1 slots and no arrival in the lastslot. Moreover, in the case of G-McMAC each busy per-iod lasts 3τ + τ. Consequently, we find out the averagebusy period of G-McMAC as follows

B =4τ

e−gτ. (A� 3)

In one cycle, the number of possible time slots forsuccessful transmission is I/τ given that there is apacket arrival. Consequently, by taking into accountthe probability that all the channels are occupied wehave

Ps = P{success}

=I/τ

(I + B)/τ· (1 − Pocc)

=e−gτ

4 − 3e−gτ· (1 − Pocc).

(A� 4)

Similarly, the amount of busy slots, i.e. channel issensed busy and packet transmission delayed, isB · 2/(3τ ). Now, we can derive the probability that thechannel is sensed busy as follows

Pb = P{busy}

=B · 2/(3τ )

(I + B)/τ+ Ps · Pocc

=3(1 − e−gτ )4 − 3e−gτ

+ Ps · Pocc.

(A� 5)

In the case of G-McMAC, the amount of collidedpackets is B/4τ. Hence, we can formulate the probabilityfor packet collisions as

Pc = P{collision}

=B/3τ

(I + B)/τ

=1 − e−gτ

4 − 3e−gτ.

(A� 6)

And clearly,

Ps + Pb + Pc =e−gτ

4 − 3e−gτ− Ps · Pocc

+3(1 − e−gτ )4 − 3e−gτ

+ Ps · Pocc

+1 − e−gτ

4 − 3e−gτ

= 1,

(A� 7)

as expected. We verified theoretical derivations of Poccby simulations and the results are presented in Figure17. As we can see, theoretical results correspond tosimulation results well.

APPENDIX B: Probabilities for MMACIn this appendix, the probabilities for MMAC duringinfinite ATIM windows will be deduced. Naturally, theaverage idle time of MMAC is equal to the average timeof G-McMAC given in Equation (A-2). In the case ofATIM windows, the negotiation process consists of onesensing and RTS/CTS message exchange with our nota-tion. Therefore, the length of the busy period is 2τ + τ,and the average busy period is

B =3τ

e−gτ. (B� 1)

0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05

0.05

0.1

0.15

0.2

0.25

Arrival rate (g)

Pro

babi

lity

of o

ccup

ancy

TheoryT=100

SimT=100

TheoryT=150

SimT=150

TheoryT=200

SimT=200

Figure 17 Theoretical and simulated results for Pocc (N = 10, ω= 32).


Page 13 of 15

Furthermore, the probability of successful transmis-sion can now be derived as follows

Ps =e−gτ

(3 − 2e−gτ ). (B� 2)

In this case the amount of busy slots is B · 2/(3τ ) andthe probability that the channel is sensed busy is givenby

Pb =2(1 − e−gτ )(3 − 2e−gτ )

. (B� 3)

Finally, collisions occur if the channel is sensed idlebut more than one packet arrived during the last timeslot. Now the amount of collided packets is B/3τ andthus, we can formulate the following probability forpacket collisions

Pc =1 − e−gτ

(3 − 2e−gτ ). (B� 4)

Simulation results shown in Figure 18 attest the cor-rectness of the theoretical results.

APPENDIX C: Probabilities for SYN-MACFinally, in this appendix we give the correspondingprobabilities for SYN-MAC. Since SYN-MAC is mod-eled as a single channel system with reduced arrival ratethe average idle time of SYN-MAC is equal to the aver-age time of G-McMAC given in Equation (A-2) by sub-stituting τ with Ts. Moreover, in this case the length ofa busy period is T + Ts, where Ts = ωτ, and thus, theaverage busy period of SYN-MAC is given by

B =T + Ts

e−gsyn−mac. (C� 1)

Furthermore, in one cycle the number of possible timeslots for successful transmission is I/Ts given that thereis a packet arrival. Consequently, we have

Ps =(Ts/T)e−gτ

1 + (Ts/T) − e−gτ. (C� 2)

Similarly, the amount of busy slots isB · ((T + Ts)/Ts − 1)/(T + Ts). As previously, we can nowderive the probability that the channel is sensed busy asfollows

Pb =1 − e−gτ

1 + (Ts/T) − e−gτ. (C� 3)

In the case of SYN-MAC, the amount of collidedpackets is B/(T + Ts). Hence, we can formulate the prob-ability for packet collisions as

Pc =(Ts/T)(1 − e−gτ )1 + (Ts/T) − e−gτ

. (C� 4)

Once again, we verified theoretical derivations bysimulations and the results are presented in Figure 19.

AcknowledgementsThis research work is supported by TEKES (Finnish Funding Agency forTechnology and Innovation) as part of the Wireless Sensor and ActuatorNetworks for Measurement and Control (WiSA-II) program.

Competing interestsThe authors declare that they have no competing interests.

Received: 28 January 2011 Accepted: 22 September 2011Published: 22 September 2011

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0 0.05 0.1 0.15 0.20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Arrival rate (g)

Pro

babi

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Ps,theory

Ps,sim

Pb,theory

Pb,sim

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ucce

ssfu

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nsm

issi

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doi:10.1186/1687-1499-2011-108Cite this article as: Nieminen and Jäntti: Delay-throughput analysis ofmulti-channel MAC protocols in ad hoc networks. EURASIP Journal onWireless Communications and Networking 2011 2011:108.

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RESEARCH Open Access Delay-throughput analysis …...RESEARCH Open Access Delay-throughput analysis of multi-channel MAC protocols in ad hoc networks Jari Nieminen* and Riku Jäntti