Efcient and Reliable Broadcast in Inter-Vehicle

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Efficient and Reliable Broadcast inInter-Vehicle Communications

Networks: A Cross Layer Approach

Yuanguo Bi, Lin X. Cai, Xuemin(Sherman) Shen, Hai ZhaoDate Submitted: 7 November 2009Date Published: 16 November 2009

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Subject Classification Vehicular Technology

Keywords Inter-vehicle communications; Cross layer design;Relayingmetric; Broadcast protocol;

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Copyright Copyright © Date Submitted: 7 November 2009 Yuanguo Bi etal. This is an open access article distributed under the CreativeCommons Attribution 2.5 Canada License , which permitsunrestricted use, distribution, and reproduction in any medium,provided the original work is properly cited.



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Effi cient and Reliable Broadcast in Inter-VehicleCommunications Networks: A Cross Layer Approach

Yuanguo Bi †,‡, Lin X. Cai ‡, Student Member, IEEE

Xuemin (Sherman) Shen ‡, Fellow, IEEE , and Hai Zhao †

Department of Computer Science and Technology †,

Northeastern University, Shenyang, 110004, China

[email protected], [email protected]

Department of Electrical and Computer Engineering ‡,

University of Waterloo, Waterloo, ON N2L 3G1, Canada

{ygbi, lcai, xshen }@bbcr.uwaterloo.ca

Correspondence: Professor Xuemin (Sherman) ShenDepartment of Electrical and Computer Engineering

University of Waterloo

Waterloo, Ontario, Canada N2L 3G1

Phone: + 1 (519) 888-4567 ext. 32691

Fax: + 1 (519) 746-3077

Email: [email protected]

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Efficient and Reliable Broadcast in Inter-Vehicle

Communications Networks: A Cross Layer Approach

Abstract

Broadcast transmission is an e ff ective way to disseminate safety-related information for cooperative

driving in inter-vehicle communications (IVC). However, it is fraught with fundamental challenges such

as message redundancy, link unreliability, hidden terminal, and broadcast storm, which greatly degrade

the network performance. In this paper, we introduce a cross layer approach to design an e fficient

and reliable broadcast protocol for emergency message dissemination in inter-vehicle communication

systems. We rst propose a novel composite relaying metric for relay selection, by jointly considering

geographical locations, physical layer channel conditions, and moving velocities of vehicles. Based on

the relaying metric, a distributed relay selection scheme is proposed to assure a unique relay is selected

to reliably forward the emergency message in the desired propagation direction. We further apply IEEE

802.11e EDCA MAC to guarantee QoS provisioning to safety related services. In addition, an analytical

model is developed to study the performance of the proposed CLBP in terms of relay selection delay

and emergency message access delay. NS-2 simulation results are given to validate the analysis. It

is shown that CLBP can not only minimize the broadcast message redundancy, but also quickly and

reliably deliver emergency messages in IVC.

Index Terms

Inter-vehicle communications, Cross layer design, Relaying metric, Broadcast protocol

I. I

Cooperative driving can improve safety and e fficiency by enabling vehicles to exchange

emergency messages to each other in the neighborhood. In vehicular ad hoc network (VANET),

vehicles transmit tra ffic and safety related information including tra ffic congestion avoidance

message, accident warning, and accident report, etc., which assists drivers to make proper

decisions to avoid vehicle collisions and congestions. Compared to vehicle-to-infrastructure

communications, inter-vehicle communications is more exible for deployment with low cost [2],




2

and research on IVC systems has attracted great attention from academia, industry, and govern-

ments recently. The U.S. Federal Communications Commission (FCC) has approved 75 MHz

(5 .850

−5.925 GHz) bandwidth for Dedicated Short-Range Communications (DSRC) systems

in support of Intelligent Transportation Systems (ITS) applications [3]. Industry manufacturers

have launched several projects to study cooperative driving in an IVC, such as Advanced

Driver Assistance Systems (ADASE2) [4], Crash Avoidance Metrics Partnership (CAMP) [5],

CarTALK2000 [6], FleetNet [7], Partners for Advanced Transit and Highways (PATH) [8], etc.

Broadcast transmission is a frequently used approach to advertise information in VANET.

Nevertheless, e ff ectively broadcasting emergency messages to other vehicles in an IVC system

is extremely challenging especially due to the high mobility and hostile wireless environment.

First, as no acknowledgment (ACK) mechanism is applied for broadcast messages in the medium

access control (MAC) layer, message loss due to packet collisions or poor channel conditions

cannot be easily detected. Since life critical emergency messages have to be delivered to other

vehicles as fast and reliable as possible [9], the traditional broadcasting scheme without an ACK

mechanism is not suitable for emergency message delivery in an IVC system. Second, due to

the limited transmission range, message relaying from intermediate nodes 1 is required to reach

remote vehicles. However, without an e ff ective broadcast control mechanism, multiple copies of

the broadcast messages may be delivered among nodes, which could result in broadcast storm

problem [10] and degrade the network resource utilization. Some research works propose to

reduce message redundancy and prevent broadcast storm by selecting a subset of neighboring

nodes to forward the broadcast message. However, it is a non-trivial task to determine a proper

subset of nodes that can guarantee the message reliability and achieve e fficient resource utilization

simultaneously.

To address the aforementioned issues, several broadcasting protocols have been proposed in the

1 the terms “node” and “vehicle” are used interchangeably throughout the paper.




3

literature. Some protocols use network layer broadcast control algorithms to reduce the message

redundancy [12]–[16], but they cannot guarantee the MAC layer reliability. Other protocols aim at

improving the the transmission reliability by repeatedly broadcasting messages [17] or selecting

the farthest node to relay messages [18]–[20]. However, repeated broadcast cannot completely

guarantee the transmission reliability but degrade the resource utilization. The farthest node may

suff er from high packet error rate (PER) and is not an ideal relay candidate, especially in high

speed vehicle networks. In this paper, we propose a cross layer broadcast protocol (CLBP) for

emergency message dissemination in a multihop IVC system, aiming to improve the transmission

reliability and minimize the message redundancy. Considering the particular characteristics of

VANETs, we design a novel relaying metric which is composed of geographical locations, phys-

ical layer channel conditions, and moving velocities of vehicles. Based on the metric, we apply

a revised request-to-send / clear-to-send (RTS / CTS) scheme to select an appropriate relaying node

distributedly. In specic, after receiving the broadcast RTS (BRTS), each relay candidate starts

its backo ff timer to reply a broadcast CTS (BCTS) based on the calculated relaying metric in a

distributed manner. After a successful BRTS / BCTS handshake, one node is successfully selected

as the next hop relay to forward the broadcast message in the desired propagation direction.

Furthermore, to support di ff erent services with various quality of service (QoS) requirements in

the IVC system, we adopt the priority based enhanced distributed coordination access (EDCA)

of IEEE 802.11e MAC to support safety services. The emergency messages are served with the

highest priority and thus the minimum channel access delay can be achieved.

The main contributions of this paper are three-fold. First, we design a novel metric for selecting

a proper relaying node to forward the emergency message. Second, based on the derived metric,

we propose a cross layer approach to e fficiently broadcast emergency messages in the desired

propagation direction. MAC layer service di ff erentiation is applied for emergency messages.

Third, we analytically study the network performance in terms of the packet error rate (PER) of

the emergency message, relay selection delay, and emergency message access delay. Analytical




4

and simulation results with NS-2 demonstrate that the proposed cross layer approach can quickly

and reliably deliver emergency messages while minimizing the broadcast message redundancy.

The remainder of this paper is organized as follows. We briey review the related work

in Sec. II. The proposed CLBP is described in Sec. III. An analytical model is developed to

study the performance of CLBP in Sec. IV. The simulation results are given to demonstrate the

efficiency of CLBP in Sec. V, followed by conclusions in Sec. VI.

II. R W

Broadcast protocols in mobile ad hoc networks (MANET) can be classied into four cate-

gories [11]: i) simple ooding [12], [13], in which a node rebroadcasts a new message until it

reaches all connected nodes in the network; ii) probability based methods [14], in which protocols

can be further divided into two sub-classes: (a) a node rebroadcasts a message according to a

predened probability, and this scheme becomes simple ooding one if the probability is set

to 1; and (b) a node decides whether to rebroadcast a message based on the number of the

received copies during a certain interval; iii) area based method [14], in which a node that

can cover more additional area is selected to forward the received message; and iv) neighborknowledge method [15], [16], in which a node makes a forwarding decision according to the

knowledge of its one-hop or two-hop neighbors. All these aforementioned broadcast protocols

aim to reduce the number of redundant messages at the network layer, without considering

the MAC layer hidden terminal problem, collisions, and link reliability, etc. It is well known

that broadcast transmission is not reliable due to the lack of ACK scheme in the MAC layer.

However, some emergency messages are life critical, the delivery of which should be guaranteed.

Therefore, previous works on network layer broadcast protocol design can not be directly applied

to IVC. Recently, some protocols have been proposed for emergency message delivery in IVC.

In [25], a distributed MAC scheme for emergency message dissemination is presented. A node

reserves the data channel for emergency message broadcast by sending a pulse signal through




5

the control channel. A MAC designed for emergency message broadcasting is studied in [17],

where a node broadcasts emergency messages for several times to increase the transmission

reliability. However, repeatedly broadcasting messages cannot guarantee the successful reception

of broadcast messages but may increase the contention level in a distributed vehicle network and

waste the scarce wireless network resources. A black burst based ad hoc multi-hop broadcast

(AMB) protocol is proposed for emergency message dissemination in [18]. A neighboring node

sends channel jamming signal (black-burst) with the time duration proportional to its distance.

Thus, the farthest neighboring node sending the longest jamming signal wins the contention and

becomes the next hop relaying node. Nevertheless, the largest jamming duration used by the

relay candidate causes a long delay for emergency messages. In the position based multi-hop

broadcast protocol (PMBP) [19], the farthest neighboring node waits the shortest time duration

to reply the broadcast node. However, the farthest node usually su ff ers from a large path loss

and a high packet error rate (PER) which may cause MAC layer retransmissions and thus a

longer link delay. In [20], each node maintains a list of neighboring nodes and always selects

the farthest neighboring node as the next hop relay. However, network topology of IVC changes

dynamically due to the high mobility of vehicles, to e ff ectively update the list of neighbors is

not a trivial task.

In order to reduce link delay and improve throughput, many channel condition based relaying

and routing metrics have been proposed in cooperative relaying schemes and routing protocols.

In [21], the expected transmission count (ETX) is proposed to measure the expected number of

transmissions that a node attempts until a packet is successfully delivered to the next relaying

node. The routing scheme based on ETX assures that the selected path achieves the minimum link

delay. Similar routing metrics such as expected transmission time (ETT) and weighted cumulative

ETT (WCETT) [22] also consider channel conditions and link reliability in the metric design.

In [23], the enhanced interior gateway routing protocol (EIGRP) adopts a composite metric,

which uses weight factors to decide the impacts of minimum link bandwidth, tra ffic load, link




6

delay, and reliability on path selection. The cooperative MAC (CoopMAC) is proposed in [24],

in which each node maintains a table of relays that can improve the link throughput, and selects

the relay with a better channel condition and higher data rate. All these schemes select paths or

relays based on channel conditions. However, they do not consider the specic characteristics

of VANET, i.e., high mobility. In this paper, we propose to jointly consider the geographical

locations, the channel conditions, and the relative velocities of vehicles to make a relay decision

in IVC.

III. P C L B P

Consider a highway with M lanes. Half of the lanes are for vehicles driving to one direction,

while the other half for vehicles driving to the opposite direction. A vehicle’s velocity is randomly

distributed among a discrete set V = {V i | V i−1 < V i, i∈

(1 , P ]}, and the velocity is directional

since vehicles may move to two di ff erent directions. Each vehicle is equipped with a half-

duplex transceiver and a Globe Positioning System (GPS) by which it can acquire its position

information, moving velocity, and moving direction. The transmission range of a vehicle Rt is

divided into a number of blocks, and the length of each block is φ which should be at leastthe minimum safety distance for two adjacent moving vehicles. Therefore, there are Q = Rt /φ

blocks within Rt , and their distances to the broadcast vehicle are represented as {Bi | Bi = i·φ, i∈

[1 , Q]}. We use carrier sense multiple access with collision avoidance (CSMA / CA) based 802.11e

MAC for channel access and service di ff erentiation among multiple nodes. To provide reliable

transmissions of broadcast messages, broadcast request to send (BRTS) / broadcast clear to send

(BCTS) frames are exchanged before emergency messages. In addition, in the proposed CLBP,

one relaying node is selected to forward the emergency message in the desired propagation

direction, based on a novel relaying metric designed for the IVC system.




7

A. BRTS/ BCTS handshake

The structure of a broadcast RTS (BRTS) frame is shown in Fig. 1. Compared to the traditional

RTS frame, ve elds are added in BRTS: em inf o , t direction , t velocity , r x, r y. The eld

em inf o takes the information of the source node which initially transmits the emergency

message, and it contains: i) the source node address init addr ; ii) the position information of the

source node init x , and init y ; iii) the sequence number of the emergency message em seq ; and

iv) the weight factors α 1, α 2, α 3 that are used for relaying metric calculation and relaying node

selection. t direction is the message propagation direction, t velocity is the moving velocity of

the current broadcast node, and r x and r y indicate the position of the broadcast node.

duration em_info t_yt_x fcst_addrr_addr

init_addr init_yinit_x em_seq

t_direction

1 2 3

frame_control t_velocity

Fig. 1. Format of BRTS.

When a node has an emergency message for transmission, it rst broadcasts BRTS based on

the CSMA / CA mechanism and starts a timer, t brts r = t brts + t d i f s + t bcts , where t brts and t bcts are the

transmission times of BRTS and BCTS, respectively, and t d i f s is the time duration of a DIFS.

If there is no BCTS response within t brts r , the node contends for channel access to rebroadcast

BRTS immediately until BCTS is successfully received. The broadcast node sets its duration

eld in BRTS such that any node that hears the BRTS but is not eligible for replying BCTS

will set its NAV and defer its own transmissions accordingly.

After receiving BRTS, a node decides whether it is eligible for replying BCTS based on

direction information or the position information of the received BRTS. If init addr in the

received BRTS is the same as the address of the current broadcast node, it implies that this is

the rst hop emergency message dissemination, and the node will decide whether to reply BCTS




8

based on propagation direction t direction . Otherwise, if its own position is between the original

source node and the current broadcast node, it will not reply BCTS since there is no distance

gain along the propagation direction. In this case, the node updates its NAV according to the

duration eld in the received BRTS. Otherwise, it starts a backo ff timer for replying BCTS and

keep sensing the channel in the mean time. As shown in Fig. 2, A is the source node that initiates

an emergency message, B is the current broadcast node. Node C will not reply BCTS since it

locates between A and B, while D is eligible for relaying the message and starts a backo ff timer

upon receiving BRTS. This guarantees that the emergency message will be e fficiently forwarded

along the desired propagation direction.

t R

A

B

C

D

A block

Fig. 2. Relaying node selection.

Each eligible relaying node which locates at ( x, y) and moves at velocity v will start a timer

for replying BCTS according to the following metrics: i) the distance from the current broadcast

node to itself; ii) the received SNR and PER which can be estimated from the received BRTS;




9

and iii) the velocity di ff erence from the current broadcast node. Based on the three metrics, the

relay candidate evaluates the composite relaying metric F used for relay selection, which is

given by

F = α 1 ·(1 −d

BQ) + α 2 ·

eE max

+ α 3 ·v

2V P, (1)

where

d = (x −r x)2 + (y −r y)2

φ ·φ,

and

v=

| −→v −−−−−−−−−→t velocity |,d is the transmission distance, e is the PER of the emergency message that is calculated based

on the measured SNR, v is the relative velocity, BQ is the distance of the farthest block in

the transmission range, E max is maximum tolerable PER dened in [26], V P is the maximum

velocity, α 1 , α 2 , α 3 (α 1 0, α 2 0, α 3 0) are weight factors and usually congured by users.

For instance, if a user wants the messages to be delivered over a fewer number of hops or with

a reduced PER, he can set a larger α 1 or α 2 accordingly. Moreover, if the topology is relatively

steady, a small α 3 can be set.

The main objective of the proposed CLBP is to deliver the emergency message to other

vehicles as fast and reliable as possible. d is a metric to determine the number of hops, i.e.,

the message will be forwarded over a fewer number of hops with a larger d . In addition,

MAC layer delay of the message highly depends on the PER e. A higher PER may result in

retransmissions that lead to a longer link delay. Finally, a small relative speed v is usually

desirable in high speed vehicle networks to guarantee the channel between two moving nodes

is relatively stationary. The proof in [27] veries that if two routing metrics are bounded, their

additive composite metric is also bounded. As d ∈

[B1 , BQ], v∈

[0 , 2 ·V P ], and e∈

[0 , 1],

the composite metric F is consequently bounded. The maximum and minimum values of F are






11

BRTS / BCTS frames, it will update its NAV accordingly.

It is possible that multiple relay candidates may choose the same mini-slot to reply BCTS,

which causes collisions. When a collision occurs, the relay candidates that have started their

backo ff timers but have not replied BCTS will sense the channel busy, and they will stop their

own timers accordingly. If a relay candidate which has replied BCTS receives a rebroadcast

BRTS, it will enter the backo ff stage again and divide 0 into W n segments, each of which is

1 = 0/ W n , i.e., the relay candidate will wait i (i∈

[1 , W n]) mini-slots to reply BCTS again if

F min + (F − F min )/ 0 · 0 + (i −1) 1 F , (4)

F < F min + (F − F min )/ 0 · 0 + i · 1 . (5)

The procedure continues until retransmissions due to BCTS collisions reach r max times, which

implies some nodes have very close F values. Then from the r max round, the relay candidates

that were collided in the last round will randomly select a mini-slot to reply BCTS until a relay is

successfully selected. In CLBP, the relaying metric consists of three variables and it is less likely

that two nodes have exactly the same

F . Therefore, the proposed collision resolution scheme

is very efficient for selecting a unique relaying node. The psuedo code of the relay selection

process is presented in Algorithm 1.

B. Emergency message broadcast

After a successful BRTS / BCTS handshake, the current broadcast node that successfully re-

ceives BCTS will broadcast the emergency message after one SIFS interval. The selected relay

will acknowledge the reception of the emergency message if the transmission is successful.

To avoid message redundancy, each node in the system maintains a list to keep records of all

received emergency messages. Each entry in the list records the address of the source node and

the sequence number of the emergency message, and entries with out-of-date messages will be

deleted. A node which receives an emergency message will check the list and drop this message




12

Algorithm 1 Relay Selection Algorithm1: A node j received BRTS.2: if t addr = init addr then3: if j receives BRTS at the rst time then4: Check t direction .5: if j is in the propagation direction then

6: Go to line 24.7: else8: Set the NAV.9: end if

10: else11: Go to line 27.12: end if 13: else14: if j receives BRTS at the rst time then15: if j has distance gain in the propagation direction then16: Go to line 24.17: else18: Set the NAV.19: end if 20: else21: Go to line 27;22: end if 23: end if 24: Compute F min , F max , 0 , distance, relative velocity, and PER.25: Map F of j to mini-slots.26: Start the backo ff timer, and go to line 34.27: if 0 < t retry < r max then28: Compute t retry = 0 / (W n)t retry , map F of j to mini-slots.29: Start the backo ff timer, and go to line 34.30: else31: Randomly select a mini-slot from W n .32: Start the backo ff timer, and go to line 34.33: end if 34: while the backo ff timer 0 do35: if j receives BCTS replying the same BRTS then36: Stop the timer and set the NAV.37: break.38: end if 39: end while40: if the backo ff timer = 0 then41: Reply BCTS, and t retry ++ .42: end if 43: return.

if it has already been recorded. Otherwise, it will receive the message and update the list. After

successfully replying an ACK, the selected relay becomes the next relaying node and repeats

BRTS / BCTS handshake again at the MAC layer.




13

C. Priority

To provide safety related services with satisfactory delay guarantee in IVC system, we use

priority based IEEE802.11e enhanced distributed channel access (EDCA) for service di ff erenti-

ation. We include the safety services and divide all services into ve classes. Di ff erent classes

of services have di ff erent priorities to access the channel based on the access categories (AC)

as shown in Table I. The setting of arbitration inter-frame space (AIFS) and contention window

(CW) are the same as those specied in IEEE 802.11e [26],

AIFS [AC ] = t s i f s + AIFSN [AC ] ·σ, (6)

CW [AC ] = min(( CW [AC ] + 1)PF [AC ], CWmax [AC ]), (7)

where σ is a time slot, PF is the persistence factor which is set to 1 for safety services and 2 for

other services. In other words, a node always selects a backo ff counter from the minimum CW

for emergency message delivery while it doubles its CW after each collision for other services.

In this way, emergency messages have the highest service priority.

TABLE IP

AC CWmin CWmax AIFSN PF0 CW MIN CW MAX 7 21 CW MIN CW MAX 3 22 (CW MIN + 1) / 2-1 CW MIN 2 23 (CW MIN + 1) / 4-1 (CW MIN + 1) / 2-1 2 24 (CW MIN + 1) / 4-1 (CW MIN + 1) / 4-1 2 1

IV. PERFORMANCE ANALYSIS

In this section, we develop an analytical model to analyze the performance of the proposed

CLBP. To make the proposed scheme tractable, we make the following assumptions: i) nodes

are randomly distributed, and the node density is λ per Rt ; ii) all nodes are saturated, i.e., the




14

nodes always have data packets in their bu ff ers for transmissions, and data packets of the same

access category AC[i] have the same transmission probability p i and collision probability q i that

can be obtained by Eqs. (1), (2), (3), (4), and (7) in [30]; iii) all data packets of the same access

category AC[i] have the same payload size D i that is larger than rts threshold ; iv) PERs of

BRTS, BCTS, and ACK are negligible due to small packet size; and v) the retransmission time

due to BCTS collisions is no larger than r max .

In our proposed protocol, a node starts a timer (in terms of mini-slots) and contends to send

BCTS based on the composite relaying metric F in Eq. (1). d and v can be evaluated from the

received BRTS, and PER e is dependent on the channel conditions. To the best of our knowledge,

there is no consensus on fading and shadowing models for VANET so far [31]. In our analytical

model, we adopt the Friis free-space model [32] to determine the received signal power. Over

an additive white Gaussian noise (AWGN) channel, the bit error rate (BER) of the emergency

message with BPSK modulation is Q 2ε bN 0

= Q 2P r r b N 0

[33], where Q(x) = 1√ 2π ∞x e−t 2 / 2dt ,

ε b is the received energy per bit, N 0 is noise power spectral density, P r is the received power,

r b is the basic rate. Since e = 1 − 1 −Q 2P r r b N 0

L

= 1 − 1 −Q I d

L[34], Eq. (1) can be

rewritten as

F = α 1 ·(1 −d

BQ) +

α 2

E max · 1 − 1 −QI d

L

+ α 3 ·v

2V P(8)

where I = 2P t G t G r (c/ f c)2

r b N 0 (4π)2 , P t is the transmitted power, G t and G r are the transmitter and receiver

antenna gains, respectively, c is the speed of light, and f c is the carrier frequency. F is a function

of d , and v, given the parameters α 1, α 2, α 3, BQ , V P , P t , G t , G r , c, f c , r b , N 0, L. The derivations

of F min , F max are given in Appendix A. Therefore, the selection of mini-slots is dependent on

the distance and the relative velocity to the broadcast node.

Emergency message access delay T is dened as the time interval from an emergency

message arriving at the head of the queue until it is successfully acknowledged, which includes: i)

an AIFS; ii) T b consisting of the backo ff time, the backo ff frozen time due to other transmissions,




15

retransmission time due to BRTS collisions, and a successful BRTS transmission time; iii) T c

consisting of retransmission time caused by BCTS collisions, a successful BCTS transmission

time, and iv) T d the sum of delay due to retransmissions caused by the emergency message

errors, a successful emergency message transmission and its acknowledgement. Thus, we have

T = AIFS [4] + T b + T c + T d . (9)

Relay selection delay T rs is dened as the time duration from a broadcast node attempting

to transmit BRTS until a relay is successfully selected, and we have T rs = AIFS [4] + T b + T c .

Denote w as the average time that a backo ff timer of a broadcast node reaches 0, and we have

T b =∞

m= 0

qm4 (1 −q4) [(w + t brts ) + m(w + t brts r )] , (10)

where qm4 (1 −q4) is the probability that the broadcast node successfully delivers BRTS at backo ff

stage m, and (w + t brts ) + m(w + t brts r ) is the corresponding delay. Denote w|j ( j∈

[0 , CW [4]]) as

the value of w given that the j’th time slot is selected. Since the broadcast node selects a time

slot uniformly from [0 , CW [4]], we have

w =CW [4]

j= 0

(w|j) ·1

CW [4] + 1, (11)

where

w|j =jk = 1 Y k , j

∈[1 , CW [4]]

0, j = 0,(12)

and Y k is the mean of Y k which denotes time delay in the k ’th slot of CW[4]. Y k can be one

idle time slot, or the frozen time due to a successful data transmission or collisions. Let E ks ,

E kc , and E ki denote the events that a node transmits a message successfully in slot k , a collision




16

occurs in slot k , and no node transmits in slot k , respectively, we have

pr (E ki) =4

i= 0

(1 −p i)ni·xi,k

pr (E ks ) =4

i= 0

xi,k ·n i

1 ·p i ·(1 −p i)ni−1 ·i

∈[0 ,4] , i i

(1 −pi

)ni

pr (E kc) = 1 −pr (E ik ) −pr (E ks ), (13)

where

xi,k =1, i f AI FS [i] AIFS [4] + k ,

0, otherwise ,(14)

n i is the number of contending neighboring nodes belonging to AC[i], and xi,k denotes whether

neighboring nodes of AC[i] will contend for channel access with the broadcast node in the k ’th

slot of CW[4]. As shown in Fig. 3, CW[4] is divided into three sub-windows cw0 , cw1, cw2. If

the broadcast node selects time slot 0, it only contends with neighboring nodes of AC[3], AC[2],

and x3,0 = 1, x2,0 = 1, x1,0 = 0, x0,0 = 0. Similarly, if the node chooses a time slot k from cw1, it

must contend with neighboring nodes of AC[3], AC[2], AC[1], and x3,k = 1, x2,k = 1, x1,k = 1,

x0,k = 0.

AIFS[4]

AIFS[3]

AIFS[2]

AIFS[1]

AIFS[0]

…...

…...

…...

…...

0cw 1cw 2cw

CW[4]

Fig. 3. Contention windows.

We denote S as the average frozen time the broadcast node experiences for one successful

packet transmission, and S i as one successful transmission time of AC[i]. For AC[i] ( i∈

[0 , 3]),




17

S i = 3 · t s i f s + t rt s + t cts + D i/ r d + t ack + AIFS [4], while for safety services, S 4 approximately

equals to 2 · t s i f s + t d i f s + t brts + t bcts + L/ r b + t ack + AIFS [4]. Since the successful transmission

probability of AC[i] is n i1

·p i

·(1

−p i)ni−1

·m∈

[0 ,4] ,m i (1

−pm)nm , we obtain S = 4

i= 0ni1

·p i

·(1 −p i)n i−1 · m∈

[0 ,4] ,m i (1 −pm)nm ·S i. Let C represent the average frozen time the broadcast

node experiences owing to one packet collision, and C approximately equals to t rts + AIFS [4].

Finally, we have

Y k = σ ·pr (E ki) + S · pr (E ks ) + C ·pr (E kc). (15)

With Eqs. (11), (12), (13), and (15), T b can be obtained.

T c , which denotes the time interval from the successful reception of BRTS to the successful

reception of BCTS, is a variable and depends on how long the broadcast node can successfully

receive BCTS from its relay candidates. In CLBP, a relay candidate starts its backo ff timer to

reply BCTS after receiving BRTS from the broadcast node. In order to capture the activities of

the backo ff timer of a relay candidate, the backo ff process is illustrated in a three dimension

diagram with the state space ( m, n, l), as shown in Fig. 4, where m (m∈

[0 , r max )) is the backo ff

stage, n (n∈

[1 , W n]) is the initial value of the backo ff timer, and l (l∈

[0 , W n]) is the number

of mini-slots elapsed since the start of the timer.

The state transitions of a backo ff timer are given in Appendix B-A, and therefore we have

T c = S 0 ·t 0 +r max

m= 1

m−1

j= 0

C m ·S m ·t m, (16)

where S m, C m, t m are successful transmission probability of BCTS, collision probability of BCTS,

and the average time taken for a relay candidate successfully replying a BCTS at backo ff stage

m, respectively, the derivations of which are given in Appendix B-B. Finally, T d which denotes

the time spent on emergency message transmission, can be represented as

T d =∞

m= 0

em ·(1 −e) · t s i f s + L/ r b + t s i f s + t ack + m ·(T b + T c + t s i f s + L/ r b + t s i f s + t ack ) , (17)




18

0, ,0

0,2,0

nW 0, ,1

0, -1,0nW

0, ,2

0, -1,1nW

0, -2,0nW

0, , -2

0,3,1

nW

. . .

0,1,0

0, , -1

0,3,2

nW

. . .

0,2,1

0,1,1

0,3,3. . .

0,2,2

0,0,0

0, ,

, ,0

,2,0

nW , ,1nW

, -1,0nW

, ,2nW

, -1,1nW

, -2,0nW

, , -2

,3,1

nW

. . .

,1,0

,3,2. . .

,2,1

,1,1

,3,3

nW

. . .

,2,2

, ,

maxr

maxr

maxr

maxr

maxr

maxr

maxr

maxr

maxr

maxr

maxr

maxr

maxr

maxr

maxr

maxr

nW nW nW nW nW

nW , , -1nW maxr

nW nW

nW

Fig. 4. State transitions of the backo ff timer.

where em · (1 −e) is the successful transmission probability of the emergency message after

m retransmissions, and t s i f s + L/ r b + t s i f s + t ack + m · (T b + T c + t s i f s + L/ r b + t s i f s + t ack ) is the

corresponding time taken in the retransmission process.

V. SIMULATION RESULTS

In this section, we evaluate the performance of the proposed CLBP, in terms of the packet error

rate (PER), relay selection delay, and the emergency message access delay, via NS-2 simulations.

Vehicles are randomly distributed over a two-lane highway, and one is selected as the broadcast

node. The velocity of a vehicle takes a value among {20 , 25 , 30 , 35 , 40 , 45 , 50}m / s. In the default

setting, ve data ows are set up with the rate 100 packets / s. Other simulation parameters are

listed in TABLE II.




19

TABLE II

P

Parameter Value Parameter Valuet s i f s 10 µs PLCP&preamble 192 µsσ 20 µs RTS 20byte

E max 8% CTS 14byter b 1M BRTS 37byter d 2M BCTS 17byteRt 250m L 1024byteφ 25m Data packet 512 byte

CW MIN 31 CW MAX 1023f c 2.4G P t 15dBm

G t 1 G r 1B1 25m BQ 250mV 1 20m / s V P 50m / sρ 1 µs t swith 1 µs

α 1 1 α 2 1

α 3 1 r max 7

A. PER of the emergency message

We rst compare the PER performance of CLBP with that of AMB proposed in [18] under

various N 0. For a smaller N 0, both CLBP and AMB achieve a low PER. When N 0 increases, the

PER of AMB increases while that of CLBP does not change much. In CLBP, the broadcast node

jointly considers the distance, channel condition, and the relative velocity to select the next hop

relaying node. Under an ideal channel condition, the farthest relay candidate has the lowest F ,and is selected as the relaying node; while under a poor channel condition, the received SNR at

the farthest relay candidate decreases and accordingly the achieved PER increases, in which case

a closer relay candidate with a lower PER may be selected with CLBP. As show in Fig. 6, the

PER of CLBP decreases slightly when N 0 increases from −174 .6 dBw / Hz to −173 .88 dBw / Hz .

Therefore, CLBP assures the PER performance of the emergency message and thus is more

suitable for IVC system with variant channel conditions.




20

- 1 7 6 . 0 - 1 7 5 . 5 - 1 7 5 . 0 - 1 7 4 . 5 - 1 7 4 . 0 - 1 7 3 . 5

- 0 . 0 1

0 . 0 0

0 . 0 1

0 . 0 2

0 . 0 3

0 . 0 4

0 . 0 5

0 . 0 6

P

E

R

N 0 ( d B w / H z )

A M B ( )

C L B P ( )

Fig. 5. PER of the emergency message.

B. Relay selection delay

Relay selection delay is dened as the interval from the time the broadcast node attempts

to deliver BRTS to the time it successfully receives BCTS. In Fig. 7(a), we compare the relay

selection delays of CLBP and AMB. By applying service di ff erentiation in CLBP, the emergency

messages are served with the highest priority. Therefore, AMB which adopts basic CSMA / CA

achieves longer access delay compared with CLBP. In addition, the node sending the longest

channel jamming signal becomes the relaying node in AMB, while a node waiting the shortest

time to reply a BCTS becomes the relaying node in CLBP. As shown in Fig. 7(a), the relay

selection delay of CLBP is much shorter than that of AMB. However, both relay selection delays

of CLBP and AMB increase with the increase of node density due to retransmissions caused by

collisions.

C. Emergency message access delay

Finally, we show the emergency message access delay under various node densities and

background noise levels in Fig. 7(a)-7(d). It can be seen that the emergency message access




21

5 1 0 1 5 2 0

1

2

3

4

5

R

e

l

a

y

s

e

l

e

c

t

i

o

n

d

e

l

a

y

(

m

s

)

( N 0 = - 1 7 5 . 8 1 d B w / H z )

A M B

C L B P

Fig. 6. Relay selection delay.

delays of AMB are higher than those of CLBP, and their di ff erences increase with the node

densities and background noise levels. This is because, rst, CLBP gives the highest priority for

safety services by adjusting AIFSN, PF, CWmin, and CWmax, which results in a smaller access

delay, whereas in AMB, emergency messages have to contend with other services with the same

priority. Second, in CLBP, the selected relaying node waits the minimum number of mini-slots

to reply BCTS, while in AMB, the selected relaying node sends the longest black burst signal

to win the opportunity to reply clear-to-broadcast (CTB). Third, under a poor channel condition,

the broadcast node in CLBP chooses an appropriate node with a reasonable PER performance

to relay the emergency message. In AMB, the broadcast node always selects the farthest relay

candidate, which incurs retransmissions with a high PER.

VI. C

In this paper, we have developed a composite relaying metric to select an appropriate re-

laying node, considering the special characteristics of vehicle networks. Based on the relaying

metric, we have proposed a cross layer broadcast protocol to e fficiently disseminate emergency






23

A A

D F min , F max , 0

Consider continuous function z(x, y) = α 1

·(1

−x

BQ) + α 2

E max

·1

−1

−Q I

x

L+ α 3

·

y2V P

, where

x∈

[B1 , BQ], y∈

[0 , 2V P ], and its partial di ff erential coe fficient z x(x) and z y(y) can be expressed

as

z x(x) = −α 1

BQ+

α 2 ·L ·I · 1 −Q I x

L−1

√ 2π ·E max ·x2 ·eI 2 / 2x2(A.1)

z y(y) =α 3

2V P. (A.2)

Thus, z is a monotonic increasing function of x if z x(x) > 0, and a monotonic decreasing

function of variable x if z x(x) < 0, where x∈

[B1 , BQ]. Let X ∗

= {xi | z x(xi) = 0, z x(xi) > 0, xi∈[B1 , BQ]}, and X ∗= {xi |z x(xi) = 0, z x(xi) < 0, xi∈

[B1 , BQ]}. Let Z ∗

= z( xiφ ·φ, V 1) | xi∈

X ∗

z( xiφ

and Z ∗= z( xiφ ·φ, V 1) | xi∈

X ∗

z( xiφ ·φ, V 1) | xi∈

X ∗. Similarly, z is a monotonic increasing function of y since z y = α 32V P

0.

Therefore, the minimum value F min and maximum value F max of the discrete function F can be

expressed as

F min =

z(BQ , V 1), z x(x) 0, x∈

[B1 , BQ]

min (Z ∗), Z

∗ ∅z(B1 , V 1), z x(x) 0, x

∈[B1 , BQ],

F max =

z(B1 , V P ), z x(x) 0, x∈

[B1 , BQ]

max (Z ∗), Z ∗ ∅z(BQ , V P ), z x(x) 0, x

∈

[B1 , BQ],

(A.3)

and 0 = (F max − F min )/ W n is obtained.




24

A B

D t c

Let random variables

{F 1 ,

F 2 ,

· · ·,

F N

}denote the relaying metrics of N relay candidates,

and F t = α 1 · (1 −d t

BQ) + α 2

E max · 1 − 1 −Q I d t

L+ α 3 ·

vt 2V P

is the relaying metric of node t .

Notice that the distances between the broadcast vehicle and other vehicles are not independent

variables because two vehicles can not locate in the same position. As a result, as the functions

of distances, the routing metrics {F 1 , F 2 , · · ·, F N }are not independently distributed either. In

a highway consisting of M lanes, at most M vehicles can choose the same block. Let events

A1 = { d 1 = B1 ∩ d 2 = B1 ∩ · · · ∩ d M = B1 ∩ d M + 1 = B2 , · · ·}, A2 = { d 1 = B1 ∩ d 2 =

B1 ∩·· ·∩d M = B2 ∩ d M + 1 = B2 , · · ·}, · · ·, A(M ·QN ) = { d 1 = BQ ∩ d 2 = BQ ∩·· ·∩d M = BQ ∩d M + 1 = BQ −1, · · ·}. Denote vt ,i(y) as the relative velocity between node t and the broadcasting

node, when F t = y and event Ai occurs. For example, d 1 = B1 in event A1, and therefore

v1,1(y) = 2V Pα 3 · y −α 1 ·(1 −

B1BQ

) −α 2

E max · 1 − 1 −Q I B1

L. Let ψ t ,m represent the number of

mini-slots that t backo ff s, and we have

ψ t ,m =

(

F t

− F min )/ 0 + 1, m = 0

[F t − F min −m−1k = 0 (ψ t ,k −1) · k ]/ m + 1, m

∈[1 , r max −1] , (B.1)

where m = 0/ (W n)m.

A. State transition probabilities of the backo ff timer

We denote N m as the set of contending relay candidates at the backo ff stage m, and initially

|N 0| = N . After receiving BRTS, relay candidate t starts its backo ff timer and prepares to reply

BCTS. The transition probability Pr [(0 , n, 0)|(0 , 0, 0)] , which denotes that t starts a backo ff timer




25

with initial value n, can be expressed as

Pr [(0 , n, 0)|(0 , 0, 0)] = Pr (ψ t ,0 = n)

= Pr [F min + (n −1) · 0 F t < F min + n · 0] (B.2)

=(M ·QN )

i= 1

Pr [F min + (n −1) · 0 F t < F min + n · 0 | Ai] ·Pr (Ai) (B.3)

=1

M ·QN ·

(M ·QN )

i= 1

Pr [F min + (n −1) · 0 F t < F min + n · 0 | Ai]

=1

M ·QN ·

(M ·QN )

i= 1

Pr vt ,i(F min + (n −1) · 0) vt < vt ,i(F min + n · 0) . (B.4)

Because the velocities of the broadcast node and relay candidate t are directional and ran-

domly distributed, the relative velocity vt is also randomly distributed among the (2 P −1)!

relative velocities {V 1 , V 2 , · · ·, V (2P−1)!}. In addition, since vt does not depend on events

A1 , A2 , · · ·, A(M ·QN ), for specic values vt ,i(F min + (n −1) · 0) and vt ,i(F min + n · 0), we can acquire

Pr [vt ,i(F min + (n −1) · 0) vt < vt ,i(F min + n · 0)], and therefore probability Pr [(0 , n, 0)|(0 , 0, 0)]

is obtained.

In the proposed scheme, when node t has started the backo ff timer and successfully backo ff

one more mini-slot, it means the initial values of all other nodes’ backo ff timers are larger than

the mini-slots that node t has elapsed. Therefore, the transition probability Pr [(0 , n, l + 1)|(0 , n, l)],

which represents l mini-slots has elapsed and t ’s backo ff timer can backo ff one more mini-slot,

can be expressed as

Pr [(0 , n, l + 1)|(0 , n, l)] =1, l = 0,

Pr j∈

N 0 ψ j,0 l + 1 , l∈

[1 , W n −1] ,(B.5)




26

where

Pr j∈

N 0

ψ j,0 l + 1

=(M ·QN )

i= 1

Pr j∈

N 0F j F min + l · 0 | Ai ·Pr (Ai)

=(M ·QN )

i= 1

Pr j∈

N 0

v j v j,i(F min + l · 0) ·Pr (Ai)

=1

M ·QN ·

(M ·QN )

i= 1 j∈

N 0

Pr v j v j,i(F min + l · 0) . (B.6)

Node t stops its backo ff timer and returns to the initial state (0 , 0, 0) when it or any other

relay candidate successfully transmits BCTS. In the former case, the number of elapsed mini-

slots equals to the initial value of t ’s backo ff timer, and less than the initial value of any other

timer. Whereas, in the latter case, at least one other timer’s initial value equals to the mini-slots

elapsed, and the initial value of t ’s timer is larger than the mini-slots elapsed. Therefore, the

transition probability Pr [(0 , 0, 0) | (0 , n, l)] is expressed as

Pr [(0 , 0, 0) | (0 , n, l)] =

0, l = 0

Pr j∈

N 0 , j t ψ j,0 l + 1 ψ t ,0 = l , l = n

Pr j∈

N 0 , j t ψ j,0 l ψ t ,0 l + 1 −Pr j∈

N 0 ψ j,0 l + 1 , l n,

(B.7)

where

Pr

j∈

N 0 , j t

ψ j,0 l + 1 ψ t ,0 = l =1

M

·Q

N ·

(M ·QN )

i= 1 j∈

N 0 , j t

Pr v j v j,i(F min + l · 0)

·Pr vt ,i(F min + (l −1) · 0) vt < vt ,i(F min + l · 0) ,

(B.8)




27

and

Pr j∈

N 0 , j t

ψ j,0 l ψ t ,0 l + 1 −Pr j∈

N 0

ψ j,0 l + 1

=1

M ·QN ·

(M ·QN )

i= 1 j∈

N 0 , j t

Pr v j v j,i(F min + (l −1) · 0) ·Pr vt vt ,i(F min + l · 0)

−1

M ·QN ·

(M ·QN )

i= 1 j∈

N 0

Pr v j v j,i(F min + l · 0) , (B.9)

If t ’s backo ff timer decreases to 0, it means the elapsed mini-slots equal to the initial value

of the timer. t can either successfully deliver BCTS and returns to the initial state (0 , 0, 0) as

expressed by Eq. (B.8), or transmit BCTS simultaneously with other relay candidates. In the

latter case, given that t ’s BCTS collides with those from other relay candidates, the probability

that t sets the its backo ff timer to be n in the next backo ff stage is given by

Pr [(1 , n, 0) | (0 , l, l)]

= Pr j∈

N 0 , j t

ψ j,0 l F t − F min −(l −1) · 0 1

= n −1

−Pr j∈

N 0 , j t

ψ j,0 l + 1 F t − F min −(l −1) · 0 1

= n −1

=1

M ·QN ·

(M ·QN )

i= 1

N

j= 1, j t

Pr v j v j,i(F min + (l −1) · 0) −N

j= 1, j t

Pr v j v j,i(F min + l · 0)

·Pr vt ,i(F min + (l −1) · 0 + (n −1) · 1) vt vt ,i(F min + (l −1) · 0 + n · 1) . (B.10)

For m 1, we have

Pr [(m, n, l+ 1)|(m, n, l)]

= 1, l = 0,

= N x1 = 2 · · ·

xm−1xm= 2 Pr j

∈N m ψ j,m > l | |N m| = xm

·Pr (|N m| = xm | |N m−1| = xm−1) · · · ·Pr (|N 1| = x1), l∈

[1 , W n −1] ,

(B.11)




28

where Pr j∈

N m ψ j,m l + 1 | |N m| = xm can be obtained similarly as Eq. (B.6), and Pr (|N m| =

xm | |N m−1| = xm−1) is given by Eq. (B.18). Conditioning on |N m|, |N m−1|, · · ·,|N 1|, we can acquire

Pr [(0 , 0, 0)

|(m, n, l)] and Pr [(m + 1, n, 0)

|(m, l, l)], respectively.

B. Calculation of T c

Let random variable Y = min (F 1 , F 2 , · · ·, F N ). Its probability mass function (PMF) is

F Y (y) = Pr (Y y) = 1 −Pr (Y > y)

= 1 −Pr (F 1 > y, F 2 > y, · · ·, F N > y)

= 1 −(M ·QN )

i= 1Pr (F 1 > y, F 2 > y, · · ·, F N > y | Ai) ·Pr (Ai)

= 1 −(M ·QN )

i= 1

Pr ( v1 > v1,i(y), · · ·, vN > vN ,i(y) | Ai) ·Pr (Ai)

= 1 −1

M ·QN ·

(M ·QN )

i= 1

N

j= 1

Pr ( v j > v j,i(y) | Ai)

= 1 −1

M

·Q

N ·

(M ·QN )

i= 1

N

j= 1

Pr ( v j > v j,i(y)). (B.12)

We represent S m and C m as successful transmission probability of BCTS and collision proba-

bility of BCTS at backo ff stage m, respectively. Let ψ 0 = (Y −F min )/ 0 and ψ m = (Y −F min −m−1i= 0 ψ i · i)/ m , where m

∈[1 , r max ]. Without loss of generality, we consider F t = Y as the

minimum value among {F 1 , F 2 , · · ·, F N }, and events K j,t ,m, H j,t ,m denote

K j,t ,m =(F j − F min −

m−1i= 0 ψ i · i)/ m > (F t − F min −

m−1i= 0 ψ i · i)/ m , m

∈[1 , r max −1]

(F j − F min )/ 0 > (F t − F min )/ 0 , m = 0,(B.13)

H j,t ,m =(F j − F min −

m−1i= 0 ψ i · i)/ m = (F t − F min −

m−1i= 0 ψ i · i)/ m , m

∈[1 , r max −1]

(F j − F min )/ 0 = (F t − F min )/ 0 , m = 0,(B.14)

and K j,t ,m(x, y, z), H j,t ,m(x, y, z) denote the events K j,t ,m and H j,t ,m under the conditions d j =




29

x, d t = y, vt = z. Therefore, for m = 0, we have

S 0 = |N 0|1 ·Pr

j∈

N 0 , j t

K j,t ,0

= N ·(M ·QN )

i= 1

Pr j∈

N 0 , j t

K j,t ,0 | Ai ·Pr (Ai)

=N

M ·QN ·

(M ·QN )

i= 1 j∈

N 0 , j t

Pr (K j,t ,0 | Ai)

=N

M ·QN ·

(M ·QN )

i= 1 j∈

N 0 , j t

Pr (K j,t ,0 | d j = d j,i, d t = d t ,i)

= N M ·QN

·(M ·QN )

i= 1 j∈

N 0 , j t

(2P

−1)!

l= 1

Pr (K j,t ,0 | d j = d j,i, d t = d t ,i, vt = V l) ·Pr ( vt = V l)

=N

M ·QN ·(2P −1)! ·(M ·QN )

i= 1 j∈

N 0 , j t

(2P−1)!

l= 1

Pr K j,t ,m(d j,i, d t ,i, V l) (B.15)

where d j,i, d t ,i denote the values of d j and d t in event Ai, respectively. For m∈

[1 , r max −1],

we have

S m =

N

x1 = 2

x1

x2 = 2 · · ·xm−1

xm= 2

xm

1 Pr j∈

N m, j t K j,t ,m | |N m| = xm ·Pr (|N m| = xm | |N m−1| = xm−1) · · ·

·Pr (|N 2| = x2 | |N 1| = x1) ·Pr (|N 1| = x1), (B.16)

where

Pr j∈

N m , j t

K j,t ,m | |N m| = xm =1

M ·QN ·(2P −1)! ·(M ·QN )

i= 1 j∈

N m , j t

(2P−1)!

l= 1

Pr K j,t ,m(d j,i, d t ,i, V l) ,

(B.17)




30

and

Pr (|N m| = xm | |N m−1| = xm−1)

= xm−1

xmPr

j∈

N m , j t

H j,t ,mj N m , j

∈N m−1

K j,t ,m−1

=xm−1xm

M ·QN ·

(M ·QN )

i= 1

Pr j∈

N m, j t

H j,t ,mj N m, j

∈N m−1

K j,t ,m−1 | Ai

=xm−1xm

M ·QN ·

(M ·QN )

i= 1 j∈

N m, j t

Pr (H j,t ,m | Ai) ·j N m, j

∈N m−1

Pr (K j,t ,m | Ai)

=xm−1xm

M ·QN ·(2P −1)! ·

(M ·QN )

i= 1 j∈

N m, j t

(2P−1)!

l= 1

Pr H j,t ,m

(d j,i

, d t ,i

, V l)

·j N m, j

∈N m−1

(2P−1)!

l= 1

Pr K j,t ,m(d j,i, d t ,i, V l) . (B.18)

whereas, for m = r max , we have

S m =N

x1= 2

x1

x2 = 2· · ·

xm−1

xm= 2

xm

1 ·1

W n

W n

k = 1

(1

W n −k )xm−1 ·Pr (|N m| = xm | |N m−1| = xm−1) · · ·

·Pr (|N 2| = x2 | |N 1| = x1) ·Pr (|N 1| = x1) , (B.19)

In the proposed scheme, if a relay candidate transmits BCTS simultaneously with other relay

candidates and introduces BCTS collisions, it will reply BCTS again after receiving a rebroadcast

BRTS until the retransmission times reach r max . Then, it will randomly select a mini-slot to reply

the BCTS, and any mini-slot has the same probability 1 / W n to be chosen. If a relay candidate

selects mini-slot k and successfully replies BCTS, other relay candidates should randomly select

mini-slots between k + 1 and W n , and Eq. (B.19 is obtained. Finally, we can acquire S m and

C m = 1 −S m. Let t m denote the average time taken for a relay candidate successfully replying

BCTS at backo ff stage m, which contains the backo ff time, delay of retransmissions caused by




31

BCTS collisions, and BCTS successful transmission time. Therefore, it can be represented as

t m =ψ m ·τ + t bcts + m(T b + t d i f s + t bcts ), m

∈[0 , r max −1]

W n

2 ·τ + t

bcts+ m(T

b+ t

d i f s+ t

bcts), m = r

max,

where ψ m = (Y −F min −m−1i= 0 ψ i · i)/ m is the mean of ψ m. Given the PMF of Y in Eq. (B.12), Y

and ψ m can be obtained. At the backo ff stage r max , a relay candidate uniformly selects a mini-slot

to reply BCTS, and the average number of mini-slots it backo ff s is W n/ 2. Given S m, C m, and

t m, we can obtain T c by Eq. (16).

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Efcient and Reliable Broadcast in Inter-Vehicle