Wireless mesh networks for intelligent transportation systems

2006 IEEEInternational Conferenceon

Systems, Man, andCybernetics October8-11, 2006, Taipei, Taiwan

Wireless Mesh Networks for Intelligent

Transportation

Systems

Jane-Hwa

Huang, Li-Chun Wang, and

Chung-Ju

Chang,

Fellow,

IEEE

Abstract- Thewirelessmeshnetwork (WMN)is an econom-icalsolutionfordisseminating broadbandwireless information

in the intelligent transportation systems (ITS). This paper

investigates the issue of deploying access points (APs) in an ITS wireless mesh network, whereseveral adjacent APs form a cluster. Each AP in a cluster operates as a wireless relay

to forwardneighboring AP'straffictothecentral access point

connected to the Internet through cables. In general, access

pointsareplacedformaximizingcellcoverage.However, larger coverageofanAP leads to lower throughputand longerdelay

in the access link as well as in the relay link. To find the

optimal tradeoffs among delay, capacity, and coverage, we develop aphysical(PHY)/medium accesscontrol (MAC) cross-layer analytical model to evaluate the throughput and delay

of theconsidered ITSwireless mesh network. Weconsiderthe

carriersensemultiple access(CSMA) protocoland theimpact

ofhop distance on the data rate in the physical layer. Then,

we apply the mixed-integer nonlinear programming (MINLP) optimization approach to determine the optimal number of

APs in a cluster and the best cell radius ofeach AP, aiming

at maximizing the capacity and coverage of a cluster of APs

subjectto the delay andfairness requirements. I. INTRODUCTION

The wireless mesh network (WMN) is a promising

in-formation dissemination technology for the next-generation intelligent transportation systems (ITS) because it can

en-hancethroughput andcoverage with lesscablingengineering [1], [2]. Figure 1 illustrates the ITS wireless mesh network scenario considered in this paper. In this ITS wireless

net-work, several adjacentaccesspoints (APs) form acluster. In

each cluster of APs,only the central access point

APO

has a

wireline connection totheIntemet. OtherAPs communicate with the neighboring APs via wireless link. In addition, eachAPoperates asawireless relay toforward neighboring

AP's traffic toward the central

APo.

By using this multi-hop network architecture, theITS wireless networks can be

rapidly deployed inlarge scale withlesscablingengineering

work.

Inawireless mesh network, coverage extension,

through-putenhancement anddelay improvement are usually

contra-dictorygoals. On theonehand, maximizingthecellcoverage

of an AP can lower the total infrastructure costs. On the otherhand, alarger cell coverage leads tolower throughput

and longer access delay due to morecollisionsfrom a larger

This workwas supported jointly by MoE ATU Program, the National Science Council and the Program for Promoting Academic Excellence of Universities under thegrand numbers, EX-91-E-FA06-4-4, NSC 95-2752-E-009 -014-PAE, NSC 95-2811 -E-009-030, and NSC 95-2811 -E-009-060.

The authors are with the Department of Communication

En-gineering, National Chiao-Tung University, Taiwan, R.O.C. (e-mail: [email protected]; [email protected]; [email protected])

CeOitralAP Wireless link

Fig. 1. System architecture for an ITS wireless mesh network.

number of contending users. In the meanwhile, the larger

separationdistance between twoAPsalsodecreases the data

rates in the wireless relay link. Therefore, achieving the optimal tradeoffamong throughput, delay, and coverage for each AP is a key challenge for deploying the ITS wireless mesh networks.

In the literature, the issue of access point placement for outdoor WLANs has been studied in [1] and [3]-[8]. In

[3], anintegerlinearprogramming (ILP)optimization model

was proposed for the access point placement, where the

objective function was to maximize the signal level in the servicearea. In [4], anoptimization approach wasproposed

to minimize the areas with poor signal qualityand improve the average signal quality in the service area. The authors in [5] and [6]proposed optimization algorithmsto minimize

averagebit errorrate (BER). In [7], theWLANdeployment problemwas alsoformulatedasan ILPoptimization problem with the objective function of minimizing the maximum of channel utilization to achieve load balancing. However, in

[3]-[7] all the access points are connected to the backbone network through cables. Fewer papers have considered both throughput andcoverageperformanceissues whendeploying access points in theITS wireless networks. The work in [1] investigated the relation of throughput and coverage for an

ITS WMN in a single user case. In our previous work [8], the tradeoff between throughput and coverage in a multi-user ITS WMN was investigated. In [1] and [8], however,

the delayperformance issues were notconsidered.

In this paper, we investigate the AP deployment issue in the ITS wireless mesh network, as shown in Fig. 1. In this ITS wireless meshnetwork, accesspoints areconnected through wireless relays to ease deployment. To find the optimal tradeoffs among throughput, coverage, and delay,

cross-layer analytical model to evaluate the throughput and

delay for this ITS WMN,by incorporating the carrier sense multiple access (CSMA) MAC protocol and the impact of

hopdistanceon the datarate inthephysical layer. On topof

the analytical model, we apply the mixed-integer nonlinear programming (MINLP) optimization approach todetermine the optimal number of APs in a cluster and the best cell

radius foreachAP.Theobjective isto maximize the capacity and coverage of a cluster of APs with delay and delay faimess requirements.

Therest of this paper is organized as follows. Section II

describes the system architecture of the considered ITS

wireless mesh network. In Section III, we formulate an optimizationproblemtomaximize thecapacityandcoverage

of theITS WMNsubjecttothedelay and fairness constraints. Section IV discusses the channel activity in the considered

ITSwireless network.InSectionV,basedonthe channel ac-tivityconcept, wedevelopacross-layeranalytical throughput anddelay model for thisITS WMN.Numericalexamplesare shown in Section VI. Theconcluding remarks are given in SectionVII.

II. SYSTEM ARCHITECTURE ANDASSUMPTIONS

Figure 1 shows the considered ITS wireless mesh network.

Ineachcluster, only the centralaccesspoint

APo

connects to thebackbone network throughcables. Any twoneighboring

APs communicate with each other via wireless link. There-fore, each AP also operates as a wireless relay to forward neighboringAP's traffic to the central accesspoint

APo.

By doingso, thecabling engineering work fordeployingAPs in

the ITS wireless mesh network is reduced.

InthisITSwirelessnetwork,wesuggestutilizingtheIEEE

802.1la WLAN standard for data forwarding between APs, while theIEEE 802.1lb/g for dataaccess between APs and

user terminals. Recall that the IEEE 802.11a WLAN are assigned with eight non-overlapping channels for outdoor applications in the spectrum of 5.25 to 5.35 GHz and 5.725 to 5.825 GHz, while the IEEE 802.1lb/g WLAN

has three non-overlapping channels in the spectrum of 2.4 to 2.4835 GHz. To avoid the co-channel interference and

improve throughput, frequency planning is also applied to

ensure two buffer cells between thetwo co-channelAPs.

III. OPTIMAL ACCESS POINT PLACEMENT

A. Problem Formulation

All the performance issues of throughput, coverage, and delay are essential factors in the design of the ITS wireless mesh network. From the coverageviewpoint, thelarger cell can lower infrastructure cost due to fewer APs. From the

throughput standpoint, however, asmallercell is better since fewer users contend for thespectrum. In addition,the small-sized cell also leads to higher throughput in the wireless

relay link between APs. The main focus of this paper is on the frame delay consisting of contention delay and

queuingdelay in eachrelay node. Fromthe queueing delay perspective, a longer separation distance between two APs may be better due to fewer hops. Fromthecontention delay

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e MH-to-AP:IEEE3802.llbg \wtrhIRndterd d d d \ 1 J > 2 3 \A P AP AP2 AP H(d1) H(d2) 1(d3) H(d 11(r

R](r1

1(r2)\{ /

|RQT)

\

ii Y ~~~~WA W'b

Fig. 2. A cluster of APs in the ITS wireless mesh network, where only the single side of a cluster is shown since the APs in the other side are deployed symmetrically.

viewpoint, however, asmaller cellcoverflge ispreferreddue

tofewercontendingusers. Inthefollowing,weformulate an

optimization problem to determine the best number of APs in acluster and the optimal cell radius ofeach AP subject to the constraints on delay, throughput, andcoverage.

At first, referring to Fig. 2, we discuss the constraints in

the optimization problem for the considered ITS WMN:

* The access link capacity

R(rQ)

for one user

communi-cating with AP1 should be greater than the demanded traffic RD of each user. That is, R(r,) > RD, where

ri is the cell radius of APF, as shown in Fig. 2. This

constraintguaranteesthe minimumthroughput foreach user.

* Therelaylinkcapacity

H(di)

betweenAPF andAP11 should be larger enough to accommodate the carried traffic load Hr, of AP1, i.e.,

H(di)

>

H,i,

where

di

is the separation distance between

APi

and AP11. * The overall frame delay DT(i) for the user in the cell

of APF should meet the delay requirement Dreq i.e.,

DT(i) < Dreq,

* In a multi-hop wireless network, the further the user

from the central

APO,

the longer the overall frame

delay. To ensure the delay fairness in the considered

ITS wireless mesh network, it isrequired that DFI > DFreq where DFIisadelayfairness index and

DFreq

stands for the delay-fairness requirement in this ITS WMN.

* The cell radius r- of an accesspoint shouldbedesigned

from two folds. The cell radius should be less than

rMAX tomaintainanacceptabledataratein theaccess

link, while it should be larger than rMIN tolower the handoffprobability. Accordingly, rMIN <

ri

< rMAX. * The separation distance

di

= ri +ri 1 between APs

shouldbe less than the maximalreceptionrangedMAX

of the employed wireless system, i.e.,

di

<dMAX.

B. MINLP OptimizationApproach

According to theabove considerations, the AP placement issue for an ITS WMN can be formulated as a

mixed-integer nonlinear programming (MINLP) problem with the

following decisions variables n (the number of APs in the single side of onecluster) and rl, r2, ..., r,, (the cell radii ofAPs). The objective function is maximizing the capacity

MAX (Total throughput ofa cluster ofAPs n,ro,r,..,rr. n MAX 2

ro

++2Eri

DMRD n,ro,ri , [...,rl = subject to

R(ri)

> RD,

H(di)

>

Hr,ij

DT(i)

<

Dreq,

DFI >

DFreq,

rMIN < ri < rMAX,

di

< dMAX,

where assumethat the users areuniformly distributed onthe road with density DM (users/m);

R(ri), H(di),

DT(i),

and DFI are detailed in Sections V-B andV-C.

IV. CHANNEL ACTIVITYIN THEITS WIRELESS MESH NETWORK

From the viewpoint ofaparticular node (access point or

user terminal), there are five types of channel activities in the considered ITS wireless network:

(1) Successful frame transmission; (2) Unsuccessful frame transmission;

(3) Empty slot, where all nodes are backloggedor idle; (4) Successful frame transmission from othernodes; (5) Unsuccessful frame transmission from other nodes.

Forclarity, radiochannel activitiescanbelogicallydescribed

as a sequence of

effective

time slots [9]-[10]. Subject to the

backoff procedures, their durations aredefinedas '1 1

I,

'12

='15

=?I'

1,3' a, where a is the duration ofan empty slot,

Ts

and Tc are the successful transmission time and collision duration, respectively. Therefore, the average

duration J' ofan effective time slotcan be written as 5

'I =, vj'l. (8)

J=1

Here, vj is the corresponding probability for the channel activity type and iscalculated in the following.

A. Successful/Unsuccessful Transmission

One node can successfully deliver data frame only if no other node is transmitting in the same cell. Consider

a cell of radius ri with ki nodes. Suppose that T is the

transmission probability of an active node, and Po is the

averageprobability ofanodebeingidle duetoemptyqueue.

Then, the unsuccessful transmissionprobability Pu of a data frame can be computed by

Pu = 1

-[1

-T(1

p0)]ki-l

(9)

where the last term represents the probability that all other nodes are backlogged or idle. Consequently, given that the

considered node has anon-empty queue, theprobability that

this node successfully/unsuccessfully sends a data frame in

aneffective time slot can beexpressed as

V1 T(1-Pu) 'V2 = TPu (1)

(10)

(1

1) B. EmptySlot

(2) One node observes an

empty

slot when all the nodes

in the cell are silent. Therefore, from the viewpoint of the

(3) considered node, the empty-slot probability is (4)

(5)

(12)

where the firstterm means the probability of theconsidered

nodebeing backlogged, and the second termisthe probabil-ity that all the other nodes arebacklogged oridle.

C.

Successful/Unsuccessful

Transmission from Other Node When the considered node is backlogged at the current

effective time slot, the probability thatatleastonenodesends its data frame is equal to

Potr

1 [1- (1

p0)]ki-1.

Therefore, given that at least one frame is transmitted from other node, the conditional probability that the frame

trans-mission is successful canbewritten as

( 1

)T(1 -P0)[1

-T(1

p)]ki

2

(1.~

Pos _Potr

Then, from the viewpoint of the considered node, the probability of an effective time slot containing a success-ful/unsuccessful frame transmission from other node can be

given as

1/4

(1-

T)PotrPos

V5 =:::: (I

-T)Potr

(I

-Pos)

(14) (15)

V. CROSs-LAYERTHROUGHPUT AND DELAY ANALYSIS A. Background

Now we calculate the durations of a successful frame transmission and acollision. Recall that the data forwarding

in the wireless relay link between two APs follows the

IEEE 802.11a WLAN standard. Let I be the payload size of data frame, ma and

m,

be the transmission PHY mode for data frame and that for control frame, respectively. In

the wireless relay link between two APs, the successful frame transmission time

Is

and collision duration

I'l

can

be calculated by

I'S

=

1'DATA(l,

ma)

+6+SIFS

+TACK

(mc)

+6 +

DIFS,

1C =

1iDATA

(I,

ma)

+6+

EIFS,

(16)

(17) where6is thepropagation delay;the durations of short inter-frame space (SIFS), distributed interframe space (DIFS),

and extended interframe space (EIFS = SIFS +

i'ACK

(mC)

+

DIFS)

aredefined in IEEE802.1

la/b

WLAN

standard. Inaddition,

I'DATA(l,

ma)

is thetransmissiontime for a data frame with payload size I using PHY mode ma,

)

V3 = (I _,T)[I _,T(I p -

I.,

and TACK(Mi) isthetransmission timeof an

acknowledge-ment(ACK) controlframe usingPHYmodemi.The values ofI'

DATA(1,

ma)

and

'TACK(rn)

canbe

specified according

tothe IEEE 802.11 a WLAN standard.

In the wireless relay link between two APs, the datarate

and the transmission PHYmode ma will be affected bythe hopdistance, i.e., theseparation distance

di

betweenAPs. In

general, the radio signal suffers from path loss, shadowing

as wellas multipathfading.Considering these radio channel effectsalong withaproperfadingmargin,weassumethat the

average reception ranges for eightPHY modes inthe IEEE

802.1 la WLAN are

Dj,

j = 1,2,...,8, whereD1 >°2 > ... > D8. In principle, two APs with a shorter separation distance can transmit at a higher data rate. Therefore, the transmission PHY mode ma will be determined according

to the separation distancedi between twoAPs, i.e.,

ma =j, if

Dj+I

<d- <

Di

(8

In the wireless accesslinkbetweenAP anduserterminal, theIEEE 802.1lb WLANis used. Therefore, the successful frame transmission time Ts and collision duration

§1c

are expressed as

TS

I=DATA(I)

+6 +SIFS

+1ACK

+6+

DIFS,

(19)

TlC

= 1IDATA(I) +6+EIFS. (20)

B. Throughput

The MAC throughput is influenced by the backoff time. Consider a binary exponential backoff procedure with the initial backoff window size of W.LetPa be theunsuccessful transmission probability detailed in (9), and mbk be the maximum backoff stage. The average backoff time can be calculated by W 1 2W-Mbk(-Pa)

2mrnbk

W- 1

+pu

~~~2

+pu

(M+l)

(1 Pu)2rbkW

+1

2

[1

Pu

Pu(2Pu)TbklW

(1 2pu)

2(1 -

2pa)

Since anode transmits data frames every

(Bk

+

1)

slotson

average [11], the transmission probability T for a node can be written as

1 2

T (22)

Bk+I 1+W Pa

1(2pu)

(

From (9) and (22), we can obtain the unique solution ofT

and Pu for a given idle probability P0 of a node. The idle

probability P0 will be derived by the following queueing

model.

Figure 3 illustrates the proposed discrete-time queueing

model for a node (access point or user terminal), where the state variable s represents the number of frames queued

in the node. As defined in Section IV-A, in each effective

. (21)

1-X 1-xi. I'-X-V1 1 -X-v

0

x

2

x x

.7

x

Fig. 3. State transition diagram for a node (access point or user terminal), where the statevariablesis the number of framesqueued at the node.

time slot one node can successfully transmit its data frame with probability vl. Accordingly, the total contention delay

spent for a frame (i.e., the frame service time) will be a geometric random variable with the mean of

1/lv

effective

time slots. Inamulti-hop network,this phenomenon means

that the arrival process of relayed traffic is also Markovian

sincethe inter-arrival timeofrelayed traffic isgeometrically

distributed. Let I be the payload size of a data frame. It is reasonable to assume that the frame arrivals at one node

follow aPoisson process witha rate ofA =

RCII

frames/s.

Here, Rc is the total carried traffic load of the considered

node, which will be detailed as follows.

Specifically, in the wireless access link between AP and user terminal, the carried traffic load of a user equals the

demanded traffic, i.e., RC = RD. Moreover, since all the

data traffic will beforwarded toward thecentral access point

via wireless relays, the carried traffic load of each AP will

include the local traffic from users within the cell and the

forwarding traffic from otherAPs.Thus,inthe wireless relay

link between

APi

and

APi-1,

the carried traffic load

H0,i

of

APi

is equal to the aggregated traffic from

APi,

AP+1±,

... and

AP,

That is,

a

Hr,i

=

kDj

BRD j=i n j

2rjDMRD,

.11 (23)

where

kj

=

2rj

Dm

is the total number of users in the cell

of APJ and DM is userdensity.

From above considerations, the state-transition probabili-ties for the queue model can be defined as

Ps,s+1 Ps" s-Ps,s X Al'T VII 1

A[X

VI. (24)

Then, we can obtain the state probability P5 =

ps(1

-

pC),

where PC =

x/vl

and the idle probability ofa node can be

givenas Po (1

-P).

With theeffective time slotconcept,therelay link capacity

H(d1)

between two APs and the access link capacity

R(ri)

between AP and one user terminal can be respectively

calculatedby

(25)

vlola

I

1,

I

ilv

I-s

sv

wherev1 is theprobabilitythatone node successfully sends a frame in an effective slot, I isthe framepayload size, TT1 =

Ts is the time duration for successful frame transmission, and'T is theaveragedurationof an effectiveslot. From (8), and (10)-(15), vl, iT, and

P,

can be calculated by using an

iterative method.

TABLE I

SYSTIEMPARAMITIRSFORNUMI RICAI EXAMPIIES.

Symbol Item Nominal value Framepayload size, 1500 bytes

DAM Userdensity 0.05 users/m RD Traffic demand of each user 0.4 Mbps rmIIN Min.ofcell radius 75m

rMIAX Max.of cell radius 300m

dMIAX Max.distancebetween APs 300m

C. Delay and Delay Fairness

By Little's formula, the average frame delay (i.e., the

sojourn time for aframe spent in a node) canbe expressed

as

Z=O

SPs

1

X 1

C)

(26)

where Pc =

X/vl.

In (26), note that both the access

contention delay andqueueingdelayatthe nodeareincluded.

Inamulti-hop network, the overall frame delay is defined

as the elapsed time from the frame generated at the source

node to the successful reception by the central

APo.

Let

Dd(i)

be the frame delay in the wireless access link from

user to

APi;

and Dr(i) be the frame delay in the wireless relay link between

APi

and

APi-I.

Both Dd(i) and

Dr(i)

arecalculatedby (26). Then, the overall frame delay forthe

userin the cell of

APi

can be expressed as

DT(i)

Dd(i)

H+

E

Dr(j).

jlI

Then, we evaluate the delay fairness for the considered ITSwireless mesh network.Let

xj

be theoverall frame delay experienced by thejth user and N be the total number of

users in a cluster ofAPs. Referring to

[12],

we define the delay fairness index DFI for this ITS WMN as

DFI

(7N

1Xj)2

N

ENz1

X2

n

[koDT(O)

+2

E

kiDT

(i)]2

i=l

N[ko(DT(0))2

+

25

ki(DT(i))21

i=l

where

ki

=2ri

DM

isthe number ofusers inthe cellof

APi,

DM is the user density, and n is the number ofAPs in the single side of the cluster. Clearly, thetotal number ofuserin aclusterofAPsis N =

ko+2

12 k.By(28), DFI= 1is

achieved forperfect fairness,while DFI= 1/N forabsolute unfairness.

VI. NUMERICAL RESULTS

In this section, we investigate the interactions among

delay, capacity, and coverage in the ITS wireless mesh

network. This paper considers a simple case where all the cell radii forAPs are the same, i.e., ri = r, and then d,

d = 2r. The system parameters are summarized in Table

I.

The user density is assumed to be DM 0.05 (users/m).

The maximum of cell radius of each AP is limited to

rMAX = 300 (m), and thus all the users can communicate

with the APs at the data rate of 11 Mbps. In the wireless relay link betweentwo APsusing theIEEE 802.1laWLAN, the ACK frames are transmitted with PHY mode

m,

= 1

for reliability. Referring tothe measured results in

113],

the corresponding average receptionrangesforeightPHYmodes inthe IEEE802.1

la

WLANare

Dj

= {300,263, 224, 183, 146, 107, 68,

30}

(m). It is true that these reception ranges vary for different environments. Nevertheless, the proposed optimization approach is general enough to evaluate the performances for different ITS wireless mesh networks by adopting various reception ranges.

Figure 4 illustrates the capacity (total throughput) and coveragefor aclusterof(2n+1) APsunder different delay requirements. In the figure, n = 5 can achieve the optimal

capacity of 35 (Mbps) and coverage of 1748 (m) if without delay requirement. If setting the delay fairness requirement

DFreq

=0.9, theoptimal capacity and coverage foracluster remain unchanged for n = 5, while for n = 4 the optimal capacity decreases from32 to 31.8 (Mbps). Inaddition, one can observe that the delay requirement Dreq = 0.2 (s) can

be fulfilled at the expense that the optimal capacity for a cluster decreasesto33.7 (Mbps) witha coverageof 1683 (m)

at n = 5. In this figure, it is obvious that the more the number nofAPs, the better thecapacity and coverage ofa

cluster. However, the optimal solution is determined by the constraints on the linkcapacity, reception ranges, and delay requirements.

In Fig. 5, the overall frame delay DT(n) for the user in

the cell of

AP,

versusthecell radius ris shown. This figure shows that the frame delay canbe ensured by appropriately shortening the cell radius r. For example, the frame delay

can be dramatically reduced from hundreds of seconds to 0.1 (s), while the cell radius r merely decreases from 79.4

to 79.1 (m) at n = 5. In this ITS WMN, the phenomenon ofexcessive delay is due to the fact that the wireless relay link is fully utilized (especially for the link between

AP1

and

APO),

ifwithoutanydelay constraint. In themeanwhile,

forPc, 1, the frame delay grows toward avery large value

[14], asshown in(26).However, byshrinking thecell radius and then the separation distance between APs to raise link-capacity, the delay performancecanbeimproved atthe cost

of lower capacity and coverage of a cluster as shown in

Fig. 4.

In Fig. 5, it is also shown that the maximum cell radius

r of each AP decreases if the number of n increases. In

this ITS wireless mesh network, the total throughput for

a cluster also increases while n increases, as illustrated in

Fig. 4. Forhandling the incrementofforwarding trafficas n

increases, the separation distance d between APs (and then the cellradius r)shouldbereduced toimprovetherelaylink L capacity. Due to the constraint on the cell radius as in (6),

i.e., r =d/2> rMIN, there will exista maximum value of

n.

In this example, the maximum allowable numberof APs

3

Number ofAPs,n

Fig. 4. Capacity (totalthroughput) andCoverageforacluster of(2n+1) APs, underdifferentdelay requirement.

C 10' a) D 10 Co :3 10' a) 10 a)

20

a) 0 I I

~~~~~~~~I

i I ~ ~ ~ n=41 -0- n= 1 1+~~~~~~~~~~~~--n=51 75 80 90 100 110 120 130 140 150

Cell radius of each AP inacell,r(m)

Fig. 5. OverallframedelayDT(n)for theuserinthe cell ofAPnversus

the cell radius r.

in aclusteris na 5.

Figure 6 shows that theachieveddelay fairness indexDFI versusthe cell radius rof each AP. Oncan observe thatthe

delay fairness degradesas the cell radius r orthe numbern

ofAPs in acluster increases.Inthis ITSWMN,giventhe cell

radius r,thelargernwill causehighertrafficloadandlonger delay in the relay link between APs as shown in Figs. 4 and 5. Accordingly, the frame delay for the users in AP1,

AP2,

..., and

APR,

increase, while that for theusersin

APo

remainunchanged. Therefore, thedelay fairnessdowngrades

as n is increasing. In the same manner, the increment of r will also leadto higher delay in therelay link betweenAPs, thereby degrading the delay fairness.

VII. CONCLUSIONS

In this paper, we have investigated the access point placement problem for the ITS wireless mesh network. The

presentedmesh network architecture isappealingfor the ITS

applicationsdue to less cabling engineering work and lower infrastructure cost. An optimization approach to maximize the capacity and coverage for theconsidered ITS WMNhas been also presented.

In the presented ITS WMN, the frequency planning has

75 80 90 100 110 120 130 140

Cell radius of each AP in a cell, r(m)

Fig. 6. Achieved delay fairness index DFI versus the cell radius r of each AP.

been employed to effectively utilize the available multiple

channels. We have also proposed a PHY/MAC cross-layer

analytical mode toevaluate the delayand throughput of this ITS WMN. On top of the cross-layer model, the MINLP

optimization approach helps to analytically determine the

optimal number of APs in a cluster and the associated cell radius for each AP subject to the tradeoffs among delay,

throughput, andcoverage.

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