(a) Hidden Terminal Problem. (b) Direct Interference. (c) Self Interference

for Ad Hoc Networks 1

LichunBao

and

J.J.Garcia-Luna-Aceves

SchoolofEngineeringBE399

UniversityofCalifornia

SantaCruz,CA95064

E-mail: fbaolc,[email protected]

Version: 03/15/2002

Threetypesofcollision-freechannelaccessprotocolsforadhocnetworksarepresented.

These protocols are derived froma novel approachto contentionresolution that allows

contendingentitiestoelectoneormultiplewinnersfor channelaccessinanygiven

con-tentioncontext(e.g.,atimeslot)inadistributedfashion. Inmultihopwirelessnetworks,

the only requiredinformation for eachentity is the identiers of itsneighbors oneand

twohopsaway. Thenewprotocolsareshowntobefairandcapableofachievingmaximal

utilization of the channel bandwidth. The delay and throughputcharacteristics of the

contention resolution algorithms are analyzed, and the performance of the three types

ofchannelaccessprotocolsisstudiedbysimulationsandcomparedwiththatofoptimal

staticschedulingalgorithms.

KeyWords: Adhocnetwork,channelaccessscheduling,mediumaccesscontrol

(MAC),distributed computing.

1

This work was supported by the Defense Advanced Research Projects Agency

(DARPA)underGrantNo. F30602-97-2-0338andbytheUSAirForce/OSRunderGrant

Channelaccessschemesforadhocnetworkscanbecontention-basedor

sched-uled. Theadvantageofcontention-basedschemesisthattheyarerelativelyeasyto

deploy; this has resulted in many contention-based schemes for ad hoc networks

being proposed based on carrier sense multiple access with collision avoidance

(CSMA/CA), and the success of the IEEE 801.11(b) standard for wireless local

areanetworks[9]. Collision-avoidanceschemesareattractiveforadhocnetworks,

because they attempt to eliminate collisions of data packets, which degrade

net-workperformance. However,collision-avoidanceschemescannotpreventcollisions

ofsignalpacketsfromnear-farphenomena,fading,andcaptureeectsonthe

chan-nel [14,16]. Inaddition,itisdiÆculttoprovidequalityofserviceorfairnesswith

these channel accessschemes. Thispointsto theneedforchannel accessmethods

basedonscheduling.

Scheduledaccessschemesprearrangeornegotiateasetoftimetablesfor

individ-ual nodesorlinks,such that thetransmissionsfrom thesenodes oronthese links

arecollision-freewithintheeectiverangeofthetransmissionsonthetimeand

fre-quency axes. TDMA, FDMA,CDMA, SDMA,and theircombinationsarewidely

deployedincellularsystems[2,13]. However,thesesolutionsrequireacentralbase

station,andthepeer-to-peerschedulingneededinadhocnetworksismuchharder

to solve.

Thequestforoptimalsolutionstochannelaccessschedulinginadhocnetworks

(i.e., multihop packet radio networks)often resultsinNP-hardproblemsin graph

theory(suchask-colorabilityonnodesoredges)[10,11,24]. Insomecases,however,

theproblemscanbesolvedbyreducingthemtosimpleronesforwhichpolynomial

Manysolutionshavebeenproposedcombiningbothrandomandscheduled

ac-cessapproaches[6,7,27]. Specically,afewtimeslot assignmentalgorithmswere

presented by Cidon and Sidi [8], and Pond and Li [22] using a dedicated

con-trolsegmentofthechanneltoresolvecon ictsandbroadcastchannelreservations.

However, the complex resolution of neighbor schedules viamessage exchanges in

thechannelconsumeaconsiderableportionofthescarcebandwidthandintroduce

long delaysto obtainthe correctschedule. Several channel scheduling and

reser-vationprotocolshavebeenproposedbasedonin-bandsignaling(phaseddialogsor

RTS/CTShandshakes)beforetransmissions[28,30]tosecureatemporaryschedule

forchannelaccess. Becauseofthein-bandsignalingrequired,theseprotocolssuer

from unusedtimeslotswhensignalscollidebecauseoftheirrandomness.

Topology-transparentschedulingmethodshavebeenproposedbyChlamtacand

others [5, 19] to avoid theneed forthe in-bandsignalingof theabove

\topology-dependent" schemes. The basic idea of the topology-transparent scheduling

ap-proachisforanodetotransmitinanumberoftimeslotsineachtimeframe. The

times(slots)whennodeitransmitsinaframecorrespondstoauniquecode,such

that foranygivenneighborkofi,nodeihasatleastonetransmissionslotduring

which k and none of k's own neighbors are transmitting. Therefore, within any

giventimeframe,anyneighboroficanreceiveatleastonepacketfromi

collision-free. Thelimitation ofthetopology-independentschedulingapproachesdescribed

todateisthatthesenderisunabletoknowwhichneighbor(s)cancorrectlyreceive

thepacketitsendsinaparticularslot. Thisimpliesthat thesenderhastosendits

packet in thevarious slots in aframe, makingtheframe length(numberofslots)

Auniedframeworkforstaticchannelassignmentintime,frequency,andcode

divisionmultipleaccesscalledUxDMAwasdescribedbyRamanathan[23]to

com-pute a k-coloring of an arbitrary graph within polynomial steps. The heuristic

consistsof rstcoloringnodesor edgesrandomlyorsequentiallyaccordingto

ver-tex degrees,andthenconcludewithaminimumnumberofcolors,such thataset

of constraintsonthe nodesorlinks are satised. Theconstraintsonthe coloring

patternincludecommonlyknowninterferences,suchasdirectandhidden-terminal

interferences [29]. A limitation of this and similar schemes based on k-colorings

of graphsis that, inherently, topologyinformation needs to be collectedand

fre-quentschedulebroadcastshavetobecarriedoutindynamicnetworks,whichwould

consumeasignicantportionofthescarcewirelessbandwidth.

Toavoidtherepetitiousscheduleadjustmentsorredundantmultiple

transmis-sionsofdatapacketsduetothevolatilityofwirelessnetworktopologies,wepropose

that local topology be an integralingredientof the channel-accessscheduling for

eachnodeofanadhocnetwork.

Section 2 shows that the scheduling problems for node-activation and

link-activation channel access can be approached asa 2-coloring problem on graphs.

It presentsanew contentionresolution algorithmcalled neighborhood-aware

con-tentionresolution(NCR) whichworksbyeach node maintainingtheidentiersof

itsone-andtwo-hopneighbors,andmakinganewnodeorlink activationdecision

during eachcontentioncontext(e.g., eachtimeslot). Section3addressesthe

per-formanceofNCR, itsfairness,anditsproperoperation. Section4describesthree

channelaccessprotocolsbasedonnode-activationandlinkactivation-schemes.

concludes thepaper.

2. NEIGHBORHOOD-AWARE CONTENTIONRESOLUTION

Inmultihopwirelessnetworks,asingleradiochannelisspatiallyreusedin

dier-entpartsofthenetwork,andcontendingentitiesarenodesorlinks(edges)between

nodes. Collisionshappen in three cases, asillustrated in FIG. 1[26]. Nodes can

avoidsuchcollisions usingtopologyinformationwithin twohops.

(a) Hidden Terminal Problem

(b) Direct Interference

(c) Self Interference

FIG.1ExamplesofCollisionTypes

We assume that every entity knows the set of its contenders through some

appropriate means. One approach is for each node to broadcast periodically the

identiersofitsone-hopneighbors,asdescribedinSection5. Wealsoassumethat

each contentioncontext is identiable, which is reasonablein networks based on

time-division multipleaccessor frequencyhopping.

Weformulatetheproblemofcontentionresolutionwithneighborhood

informa-tionasfollows:

Givenasetofcontenders,M

i

,againstanentityiincontentioncontext

t,how shouldtheprecedenceofi bearbitratedinthe setM

i

[fig,such

thateverycontender yieldstoiwheneveridecidesthatitisthe winner

for thecommonchannel?

Todescribeoursolutionto theproblem,weassumethattheprimaryoperands

con-function that produces auniformly distributed randomnumber using byte-string

x astheseed[25]. Based onfunction MD(x), wedenethe priority ofnodei in a

contentioncontexttas:

p t

i

=MD(it)i: (1)

Thealgorithmforneighbor-awarecontentionresolution(NCR)isthefollowing:

NCR(entityi,contentioncontextt):

1. Computeapriorityp t

k

foreachmemberkinset M

i [fig: p t k =MD(kt)k;k2M i [fig : (2)

2. ExitifEq. (3)isnottrue.

8j2M i ;p t i >p t j (3)

3. Haveiaccessthecommonchannelduring t. 2

Note that, while the MD function can generate the same number on dierent

inputs,eachprioritynumberisunique,becausep t

k ;k2M

i

[figis appendedwith

k tothecorrespondingmessagedigest.

DescribingNCRintermsofatwo-coloringproblem,anentityigivesitselfcolor

r if its has the highest priority amongst its contenders in a contention context;

otherwise, i colorsitself with b. Nodes in color r areactive in thecorresponding

contentioncontext. Thecolorris extensivelyusedin each contentionsituationto

thesameamountofbandwidth. Inpractice,traÆcandbandwidthdemands from

dierent nodes can vary. NCR can be easily improved to accommodate variable

bandwidthrequirementsbyassigningmultiplepseudo identitiesto eachentity.

An entity i may claim pi

i

0 pseudo identities, and each pseudo identity of

i is dened as the concatenation of i with a number chosen from f1; :::;pi

i g.

Therefore, the l-th pseudo identity is denoted as il. To account for stability

of bandwidth requests, an upper bound can be placed on the number of pseudo

identitiesavailabletoeachentity,soastoallowreasonablegranularityofbandwidth

allocation.

Consequently,NCRcanbemodiedasfollowstosupportmultipleidentitiesfor

eachnode:

NCR-MI(entity i,contentioncontextt):

1. Computetheprioritynumbersonthepseudoidentities of each memberk2

M

i

[fig,thel-thprioritynumberofwhichisdenotedasp t k l : p t k l =MD(klt)kl; k2M i [fig;1lpi k (4)

2. ExitifEq. (5)isnottrue.

8j2M i ;9 m; p t im >p t jn ; 1<m<pi i ;1<n<pi j : (5)

q i = pi i P k 2Mi[fig pi k : (6)

Note that NCRis thespecial caseofNCR-MI with therestriction8k 2M

i [

fig;pi

k

=1. Forsimplicity,therestofthispaperaddressesonlyNCR.

3. BEHAVIOROFNCR

3.1. Correctness

Oncethenodesinanadhocnetworkhaveconsistentknowledgeoftheirtwo-hop

neighborhood,NCRachievesthefollowingthreegoals:

1. Avoidunintentional collisionsfromsimultaneous transmissions.

2. Fairsharingofnetworkbandwidthforeachnode,soastoavoidtheresource

starvationproblempresentin contention-basedschemes.

3. Permitconstant bandwidthutilization, even under heavy traÆc load, so as

tokeepnetworkdatatransmissionliveatalltimes.

Becauseitisassumedthatcontendershavemutualknowledgeandtis

synchro-nized, theorderofcontendersbasedontheprioritynumbersisconsistentatevery

participant. WhenentityihasthehighestpriorityinthesetM

i

[fig,eachk2M

i

respectstherightofi, andallowsito accessthecommonchannelcollision-free.

NCR basically generatesa permutation of thecontending members, theorder

of which is decided by the priorities of all participants. Since the priority is a

pseudo-randomnumbergeneratedfromaseedthatchangesfromtimetotime,the

q i = 1 jM i [figj : (7)

Anadhocnetworkhasanite numberofentities;therefore,NCRalways

pro-duces oneor multiple winners for each contention context because NCR gives a

uniqueprioritynumbertoeachentityandmultiplelocallymaximalprioritiesexist

in thenetwork. Accordingly,NCRallowsliveutilization ofthecommonchannel.

3.2. Delay And ThroughputAnalysis

When the arrival rate of the queuing system in a channel access scheduling

systemisbellowtheservicerate,wecananalyzethedelaypropertiesofthequeuing

systemusing asteady-stateM/G/1queue withservervacations,where thesingle

serverisanentity(nodeorlink).

WeassumethatdatapacketsarriveatanentityiaccordingtoaPoissonprocess

withrate

i

andareservedbyrst-come-rst-serve(FIFO)strategy. Serveritakes

avacationthat lastsforZ oflengthonetimeslotwhenthere isnodatapacketin

the queue; otherwise,i looks forthe nextavailable time slot to transmittherst

packet waiting in the queue. Because of the randomness in NCR and NCR-MI,

thenumberoftimeslots thatanentitymustwaitbeforeactivation isageometric

distribution with parameterq

i

, which is the probability of theentity i winning a

contention context (Eqs. (7) and (6)). Therefore, the probability of the service

timeX

i

foradatapacketfollowsPfX

i =kg=(1 q i ) k 1 q i .

Themeanandsecond momentsofrandomvariableX

Z =Z 2

=1.

So that the extended Pollaczek-Kinchin formula [4] for M/G/1 system with

vacations readilyyieldstheaveragewaitingtimein thequeueatentityi:

W i = X 2 i 2(1 X i ) + V 2 2V

Adding the average service time to the queuing delay, we obtain the overall

delayin thesystem:

T i =W i +X i = 2+q i 2 2(q i ) : (8) When i

=0,theleastexpectedsystemprocesslatencyis:

T i =1=q i +0:5 (9)

0

0.1

0.2

0.3

0.4

0.5

0

10

20

30

40

50

60

q=0.05

q=0.10

q=0.20

q=0.50

Arrival Rate

λ

(Packet/Time Slot)

Delay T (Time Slots)

Average Packet Delays in the System

FIG.2Average SystemDelayofPackets

Depending on whether the entity is a node or alink, the probabilitiesof the

entitywinning acontentioncontextaredierent,soarethedelaysofdata packets

i



i

. Tokeepthequeuingsystemin asteadystate,itisnecessarythat

i <q

i .

BecauseofthecollisionfreedomofNCR,thecommonchannelcanservecertain

loaduptothemaximumchannelcapacity. That is,thethroughputoverthe

com-mon channel isthesummationof arrivalratesatallcompetingentities aslongas

thequeuingsystemateachentityremainsinequilibriumonthearrivaland

depar-ture events. Accordingly, the systemthroughput S from eachand every entity k

that competesforthecommonchannelis:

S= X k min( k ;q k ) (10) where q k

is the probability that k may be activated, and 

k

is the data packet

arrivalrateat k.

4. CHANNELACCESSPROTOCOLS

4.1. TopologyAssumptions

Forsimplicity, weabstract thetopologyofapacketradio networkasan

undi-rectedgraphG=(V;E),whereV isthesetofnodes,eachmountedwithan

omni-directionalradiotransceiverandassignedauniqueidentier(ID),andEV V

is the set of links between nodes. Unless specied otherwise, a link (u;v) 2 E

indicates node uand v are within thetransmission range for each other, sothat

they canexchangepackets viathecommon channel, in which casethe twonodes

are called one-hop neighbors. Two distinctnodesthat arenot one-hopneighbors

but shareacommonone-hopneighborare calledtwo-hopneighborstoeachother.

Contentionsatanodeishouldberesolvedonthesubgraphcoveredwithintwo

hopsfrom thenodei, i.e.,N 1

i [N

2

i

,depending onnodeorlinkactivationschemes

and signalcoding methodsusedin thespecicchannel accessprotocols.

The following channel access protocols are described assuming that nodes

al-readyknowtheirneighborhood,i.e.,thattheyhaveexchangedthenecessary

infor-mation abouttheirtwo-hopneighborhood. Inaddition, these protocolsare based

on a distributed time division multiplexing scheme, which makes channel access

decisionsbasedonthetimeslot boundaries. However,wedonotaddressthetime

synchronizationissue.

4.2. Node Activation Protocol

Werstdescribeanode-activationmultipleaccess(NAMA)protocol,in which

thecontendersetofnodei isthesetofone-hopandtwo-hopneighbors,i.e.,M

i = N 1 i [N 2 i

. For each timeslot t, NAMA decidesthe activation of nodei based on

followingalgorithm:

NAMA(node i,timeslott):

1. Computethepriorityp t

k

ofeverynodekinthesetM

i

[figusingEq. (2).

2. ExitifEq. (3)doesnotholdfornodei.

3. Haveiaccessthecommonchannelduring timeslott. 2

NAMA is suitable for broadcast and multicast services in ad hoc networks,

where thereceiversofapackettransmissioninclude allorsomeofthetransmitter

itsone-hopneighborswithoutinterferencefrom itstwo-hopneighbor.

4.3. LinkActivation Protocol

The link activation multiple access (LAMA) protocol is a time-slotted code

division medium access scheme using direct sequence spread spectrum (DSSS),

togetherwithNCR.

InDSSS, code assignment canbebasedon atransmitter-oriented,a

receiver-orientedor a per-link orientedcoding scheme [15, 18, 21]. In LAMA,we opt for

a receiver-orientedcodeassignment,which is suitablefor unicastingusing a

link-activation scheme. Although many collision resolution protocols have relied on

codeassignmentalgorithmsto eliminate packet collisions [3,17]. Incontrast, the

codeassignmentforLAMAisrandomanddoesnotconsidercontentionresolution.

Instead, thecontentionsfortransmission onthecodeof theintended receiverare

resolvedbyadditionalcomputationsusingNCR.

Weassumethatapoolofwell-chosenquasi-orthogonalpseudo-noisecodes,the

set ofwhichisdenoted asC

pn =fc

k

g,areavailable foreach nodetochoosefrom,

where k =0; :::;jC

pn

j 1. A receiveriis assigned apseudo-noisecode c

i from

C

pn

bythe following hashingfunction, which utilizesthe messagedigest function

used inEq. (1): c i =c k ; k=MD(it) mod jC pn j (11)

Because wehave only alimited number of pseudo-noise codes to assign, it is

possibleformultiple nodestosharethesamecode. Ifwedenotethesetofi's

one-hopneighborsassignedwithcodecasn 1

i;c

,ourgoalinLAMAistodecidewhether

in n

i;c

during time slot t. Therefore, theset of contendersto node i includes the

one-hopneighborsofiandtheone-hopneighborsofnodesinthesetn 1

i;c

excluding

nodeiitself,asshowninEq. (12).

M i =N 1 i [ 0 @ [ k 2n 1 i;c N 1 k 1 A fig: (12)

Theresultinglink activationalgorithmisthefollowing:

LAMA(nodei,timeslott, code c):

1. Computethepriorityp t

k

ofeverynodek2M

i

[fig usingEq. (2).

2. IfEq. (3)holds,havei activatelink(i;j);j2n 1

i;c

in timeslott. 2

LAMA ensures that the transmissions on a given code in any time slot are

always collision-free at the receivers. Because multiple receiversmay be waiting

on the code, the transmitter can choose to deliver multiple packets or multicast

packetstothereceivingneighbors.

e

f

g

i

a

b

c

d

23

5

8

1

21

19

11

14

6

20

j

k

x

x

Non-contending Link

Contending Link

Active Link

FIG.3An ExampleofContendingResolution

FIG. 3 exemplies a contention situation at node i during time slot t. The

topology is an undirected graph. The number beside each node represents the

of thenodesaccordingto LAMA.Node ihas thehighestprioritywithin one-hop

neighbors, and higher priority than j and k as well as their one-hop neighbors.

Therefore,i canactivateeither (i;j)or(i;k)in thecurrenttime slott,depending

on back-loggeddata owsat i. Inaddition,nodeemayactivate link(e;d)ifdis

assigned acodeotherthancodex.

4.4. Pairwise Link Activation Protocol

Thepairwise-linkactivation multipleaccess (PAMA)protocol isbasedonlink

activation,usingatime-slottedcode-divisionmultiplexingschemewithDSSS. The

dierencebetweenPAMAandLAMAisthatacodeisassignedforagiven

transmitter-receiverpair,andcomputed everytime slot. UnlikeNAMA andLAMA,in which

contendingentitiesarenodes,linksaretheentitiescompetingforchannelaccessin

PAMA.LinksaredirectedinPAMAtosignifytransmissiondirections. Each

undi-rectedphysical linkisrepresentedbytwodirectedlinksin theoppositedirections.

PAMAassumesapoolof quasi-orthogonalpseudo-noisecodes,C

pn =fc k g. A pseudo-noisecodec u fromC pn

isassignedtoadirectionallink(u;v)attimeslott

accordingtothefollowinghashingfunction:

c (u;v) =c k ; k=MD(ut) mod jC pn j: (13)

Note that Eq. (13)doesnotinvolvev in thecodeassignment. Thisis becauseof

tworeasons: (a) anodecanactivateonlyonelink at atime, and (b)othernodes

donothavetoknowbothuandv todecidethecodeassignmentoflink (u;v).

PAMAdecideswhetheradirectedlink(u;v)canbeactivatedbynodeuintime

M

(u;v)

= f(x;y)j(x;y)2E;x2fu;vgg[

f(x;y)j(x;y)2E;y2fu;vgg f(u;v)g:

Theresultinglink activationalgorithmisthefollowing:

PAMA(link(u;v),time slott):

1. Computethepriorityp t

(x;y)

ofeverylink(x;y)belongingtoM

(u;v) [f(u;v)g using(14): p t (x;y) =MD(xyt) (14)

2. ExitifEq. (15)isnottrue.

8(x;y)2M (u;v) ; p t (u;v) >p t (x;y) (15)

3. Computetheprioritiesofeveryincident(incomingandoutgoing) link ofu's

one-hopneighbors using(14). IntroducesetL

u

tobethesubsetofincoming

linksofu'sone-hopneighbors,eachelementofwhichhasthehighestpriority

amongtheincidentlinks ofthecorrespondingone-hopneighbor. That is:

L u =f(x;y)jy2N 1 u ; y6=v;and x2N 1 y ; x6=u; and 8z2N 1 y ; p t (x;y) >p t (z;y) and p t (x;y) >p t (y;z) g (16) 4. Foreachlink(x;y)2L u

,computethecodeassignmentc

x aswellasc u using (13). Ifconditionc u =c x

holdsforlink(x;y),thenexit if:

(a) x2N 1

u

(b) x62N 1

u .

5. Havenodeuactivatelink(u;v)duringt. 2

ThersttwostepsinPAMAdeterminetheeligibilityoflink(u;v)foractivation,

whilestep3and4avoidpossiblehiddenterminalcon ictsonu'sone-hopneighbors.

Step3choosesthecandidateincominglinkofeachone-hopneighborforactivation,

and then step4 tries to avoidinterferenceto u'sone-hop neighbors if link (u;v)

is ever activated. Thetransmitter is the one that tries to avoid collisions on its

one-hopneighbors. Twoconditionsareconsideredin step4. Case4aoccurswhen

the end points of theactiveincoming link are bothone-hop neighbors of u, such

that uhas complete knowledge about their contention situation. Case4b occurs

whenuknowsonlyapartialcontentionsituationoftheactiveincominglink,such

that ugivesup(u;v)activationifonlytheactiveincominglink hasthesamecode

assignment.

PAMAis suitableonlyforunicastpackettransmissions, becausethe link

acti-vations arepurelybasedonpairsofnodesinthenetwork.

FIG. 4 shows a sample network, where the number next to each link is the

priorityof that link, and the numberbesideeach node is thecode assignmentof

that node. Link(a;b) and(u;v)(indicatedbysolidlines)are bothcandidates for

activationoncode5accordingtostep2. However,step4deactivatesutoavoida

collisionatb byuanda.

a

b

v

u

5

5

12

9

12

5

3

9

91

38

Inmobileadhocnetworks,thetwo-hopneighborinformationneededby

topology-dependentschedulingprotocols is notreadilyavailable to each node. Because no

neighborinformationcanbeassumedtoscheduletheexchangeofneighbor

informa-tion,theneighborprotocolutilizesarandomaccessapproachforthetransmissions

ofinformation. DuetothebroadcastnatureofNAMA, theneighborprotocolcan

also take advantage of the data packet transmissions to propagate the neighbor

information. Forsimplicity,weonlydiscusstheneighborprotocolforNAMA.

Random

Access

49

Scheduled Access

Time Slot

Signal Slot

1

2

FIG.5TimeDivisionSchemeinNAMA

As FIG. 5 illustrates, a special periodic time slot is allocated after every a

number of scheduled-access time slots for sending out signals. The number of

regular data slots and the special signalslot amount to fty in the gure, which

comprise aperiod in thetime division scheme. Thesignalslot is further divided

into multiplemini-slots forsignals.

srcAddr

dstAddr

seqNum type

#tot

#add

option

payload

4B

4B

4B

2B

1B

1B

1024B

Signal Frame Format

Data Frame Format

0~84B

FIG.6FormatsforSignalandDataFramesin NAMA

FIG.6showstheformatsofaregulardataframeandasignalframe,adoptedin

theimplementationofNAMA.Asignalisaspecialdataframethat haseveryeld

ofadatapacketbutthepayload. TheeldsrcAddranddstAddrcontainthesource

unicast, broadcast or signal data type. The eld #tot is used by the neighbor

protocol to suggest the total number of neighbor updates in the option eld, of

which#addupdatesaretheaddedorrefreshedneighbors.

Assuming that the bandwidth of the channel is 2 Mbps [1], and the sizes of

dierent elds are as in FIG. 6, the signal slot can contain six signal mini-slots,

accountingforbothradiopropagationlatencyandsignalprocessinglatencies.

Signalsareused bytheneighborprotocolfor twopurposes. Oneisforanode

to say\hello"to itsone-hopneighborsperiodicallyto maintainconnectivity. The

otheris tosendneighborupdateswhen aneighborisaddedordeleted.

A node waits for some mini-slots before transmitting its signals, so that the

probabilityofcollisionswithotherneighborsinamini-slotisreduced. Theinterval

betweensendingsignalsinthesignalslotsisdeterminedbythenumberoftwo-hop

neighbors.Weconsidertwo-hopinsteadofone-hopneighbors,becausetheir

trans-missions can allcollidewith that of agivennode. This situation wasformulated

asanoccupancyproblemincombinatorialmathematics[12,20],whichpursuesthe

probability of having m empty cells after randomly placing r balls into n cells,

where r correspondsto theinterval, andncorrespondsto thenumberoftwo-hop

neighborsofanode. Wedirectlyusetheresultontheprobabilityofleavingexactly

m cellsempty, whichis:

p m (r;n)=n r 0 B B @ n m 1 C C A n m X v=0 ( 1) v 0 B B @ n-m v 1 C C A (n m v) r (17)

Given theaveragenumberoftwo-hopneighbors nin anetwork,wesearch for

such an r that p

0

0

5

10

15

20

25

0

50

100

150

200

Number of Cells

Number of Balls

FIG.7NumberofBallsvs. NumberofCellsSuchThatp

0

(r;n)>0:99

FIG.7showstheminimumnumbersofballs(interval)toallowp

0

(r;n)>0:99,

givendierentnumbersofcells(two-hopneighbors). Inpractice,wesettheinterval

to 150, which allowsabout20 neighbors within twohopsfor each node. The150

signalmini-slotintervalcorrespondstoatimeperiodofabout5.6secondsbetween

consecutive\hello"signalsfrom thesamenode.

Inaddition,ajitterof25mini-slotsisaddedto theintervalnumberto avoid

signaltransmissionsynchronization.

Becauseof NAMA'sbroadcastingcapability, regulardataframesin the

sched-uled accesstimeslotsalsohavethesameeldstopropagateneighborinformation,

asshownin FIG.6.

Neighborupdatesaregeneratedin thefollowingthreesituations:

1. Anewneighborisdetectedatanodeandthewholeone-hopneighborsetof

thenodeneedsto bepropagatedtothenewneighbor.

2. Theone-hopneighborsetisrefreshed,whichoccurs periodically.

3. Aneighborislostafteraperiodofsilencefromthatneighbor,andaneighbor

deletion updatesin theoptioneld. A two-hopneighborcanbedeletedat anode

if the node does nothear update about the two-hop neighborfrom the common

one-hopneighborforacertainperiodoftime.

6. PERFORMANCEEVALUATION

6.1. Expected PerformanceDierences

In NAMA, contending members are nodes within two hops. Therefore, the

averagenumberofcontendingnodesin each timeslotis

jN 1 i [N 2 i j

InLAMA,contentionshappen oneach code. Whenanode itries to transmit

onacodetooneofitsneighbors,contentionoccursfrombothi'sone-hopneighbors

andtheone-hopneighborsofthereceiverspossessingthecode. Hence,theaverage

numberofcontendersto ionacodec is:

      N 1 i [ 0 @ [ j2n 1 i;c N 1 j 1 A       1 accordingtoEq. (12).

PAMAis moresensitiveto neighbor connectionsthanthe othertwoprotocols

becausetwo-hopneighborsaswellaslinksbetweentwo-hopneighborsbecomethe

contentionsources. Thecontendersofalink inPAMAareabouttwiceasmanyas

that ofLAMA,becauseofthedirectionaltreatmentoflinksin PAMA.

Supposethatthenetworknodesareuniformlydistributedonaninniteplanewith

density , and all nodes have the same eective transmission range r. A node

in NAMA hasapproximately4r 2

1contendingnodes withregardto two-hop

neighbors. InLAMA,anode would havearound 2r 2

1contending nodes for

activatingalink,consideringthetwoendpointsofthelink,andassumingone-hop

neighborsoftheendpointsarealwaysassigneddistinctivecodes. WhileinPAMA,

thenumberofcontendinglinks ofeachlink activationis4r 2

2,becauseofthe

directionaltreatmentoflinks.

Ifweexaminethenumberofactivelinkswhen anodemaytransmitpacket in

thecurrenttimeslot,NAMAcanactivateallofitsincidentlinks,andLAMA can

activatea subsetof its incidentlinks, while PAMA canactivate asingle incident

linkatalltimes. Inthecaseofunicasting,PAMAsustainsthehighestthroughput,

becauseofabetterspatialreuseofthechannel,asshownbytheresultsofsimulation

experimentsdescribedsubsequently.

Tobetterunderstandtheperformanceofdynamicschedulingprotocols,we

com-pare them with theoptimal staticschedulingalgorithm UxDMA that usesglobal

topologyinformation[23].

TheuniedframeworkUxDMAdenesaparametricalgorithmtoderivea

col-oring onagraphaccordingto thenetworktopologyandthetype ofentities. The

numberof colorsused onthegraphindicates theeÆciencyof thealgorithm. Ina

time divisionmultiple accessscheme,thenumberofcolorsutilizeddeterminesthe

lengthof atime frame,during which everyentityis activatedoncein atimeslots

ofthetimeframe.

relatedentitiesareassigned thesamecolorandactivatedat thesametimeduring

channelaccess. Accordingly,weselectanappropriatesubsetof theconstraintsfor

each of ourschedulingprotocols, asshown in Table1, corresponding to UxDMA

forNAMA, LAMAandPAMA,respectively.

TABLE 1

ConstraintSetsCorrespondingtoNAMA, LAMAandPAMA

Protocol TypeofEntities ConstraintSet

UxDMA-NAMA Node fV 0 tr ;V 1 tt g UxDMA-LAMA Link fE 0 rr ;E 0 tr ;E 1 tr g

UxDMA-PAMA Link fE

0 rr ;E 0 tt ;E 0 tr ;E 1 tr g

0

0

0

1

1

1

0

0

0

1

1

1

a

b

0

0

0

1

1

1

0

0

1

1

0000

0000

0000

1111

1111

1111

c

b

a

00000

00000

00000

11111

11111

11111

a

b

c

00000

00000

00000

11111

11111

11111

a

b

c

00000

00000

00000

11111

11111

11111

00000

00000

00000

11111

11111

11111

a

b

c

a

b

c

d

FIG.8ConstraintsUsedbyUxDMAforNAMA, LAMAandPAMA

FIG. 8 illustrates the prohibited schemes of node and link activations as

ref-erenced by UxDMA for NAMA, PAMA and LAMA, where solid dotsand thick

linesmeansimultaneousnodeandlink activations,respectively,thin linesindicate

interferences. However,becausebothLAMAandPAMAusecode-divisionchannel

access,constraintE 1

tr

isallowedwhenthetransmissioncodesaredierentfornode

aandc inPAMAandreceptioncodesaredierentfornodeb anddinLAMA.

Anoptimalordering,PMNF(ProgressiveMinimumNeighborsFirst)heuristic,

has been applied in each computation of thecoloringsonthe graphsin UxDMA,

WesimulateNAMA,LAMA,PAMAandthecorrespondingUxDMAalgorithms

instatictopologies. Theperformanceoftheprotocolsarestudiedintwoscenarios:

fully connectednetworkswith dierentnumbersofnodes,and multihop networks

with dierentradio transmissionranges. Thepacketarrivaland departureevents

are modeled as M/G/1 queuing systemswith vacations. Thedelayof packets at

eachnodeandthethroughputofthenetwork arecollectedineachsimulation.

Thesimulationsareguidedbythefollowingparametersandbehaviors:

 Thesignal propagationin thechannelfollows thefree-spacemodel and the

eective range of radio is determined by the power level of the radio. All

radioshavethesametransmissionrange.

 Thebandwidthofaradiotransmissionis2Mbps.

 A time unit in the simulation equals one time slot. A time slot lasts 4.5

milliseconds including the guard time, which is long enough to transmit a

1124-bytepacket.

 Eachnodehasanunlimited buerfordatapackets.

 In LAMA and PAMA, 30 pseudo-noisecodes are available for code

assign-ments,i.e.,jC

pn j=30.

 All nodes have the same packet arrival rate 

i

in each simulation. Unless

otherwisespecied,thedestinations ofthegeneratedpackets areevenly

dis-tributedonalloutgoinglinks.

slots),longenoughtocomputethemetricsofinterests.

6.2.1. FullyConnectedScenario:

0

0.1

0.2

0.3

0.4

0.5

0

20

40

60

80

Arrival Rate

λ

i

(Packet/Slot)

Delay T

i

(Time Slot)

q

1

=0.5, q

2

=0.5, 2 Nodes

NAMA

LAMA

PAMA

UxDMA−NAMA

UxDMA−LAMA

UxDMA−PAMA

Analysis 1

Analysis 2

0

0.1

0.2

0.3

0

20

40

60

80

Arrival Rate

λ

i

(Packet/Slot)

Delay T

i

(Time Slot)

q

1

=0.2, q

2

=0.07, 5 Nodes

0

0.1

0.2

0.3

0

20

40

60

80

100

120

Arrival Rate

λ

_i

(Packet/Slot)

Delay T

i

(Time Slot)

q

1

=0.1, q

2

=0.03, 10 Nodes

0

0.1

0.2

0.3

0.4

0

50

100

150

200

250

300

Arrival Rate

λ

_i

(Packet/Slot)

Delay T

i

(Time Slot)

q

1

=0.05, q

2

=0.0135, 20 Nodes

FIG. 9AveragePacketDelaysInFully-Connected Networks

Inthefullyconnectedscenario,simulationswere carriedoutin four

congura-tions: 2-,5-,10-, 20-nodenetworks,to manifestthe eectsof dierentcontention

levels. FIG.9showsthedelayvaluesunderdierentloadsinthefourcasesaswell

astwoanalyticalcurvesderivedfromEq. (8)withq

1

valuesforNAMAandLAMA,

q

2

valuesforPAMAasshowninthegures,respectively. Allprotocolsappeartot

wellwiththeanalyticalcurves. PAMAshowshigherdelaysinthesamesituations.

This isbecausethecontentionsourcesaredierentin PAMAthanin NAMAand

i q i = 1 4
jVj 6 (18)

ForNAMA andLAMA,q

i

inthesamescenariois:

q i = 1 jVj (19)

Takingthe10-nodenetworkasanexample,theq

i

valueforeachlinkis 1

410 6 =

0:029inPAMA,whichwouldresultinadelayofatleast36.5timeslotsbyEq. (9).

IncasesofNAMAandLAMA,nodesarethecontendingentities,andtheq

i values

foreachnodearebotharound 1

jVj =

1

10

=0.1,whichleadstodelaysofatleast12.5

timeslots.

Ineverysimulationsetting,UxDMAperformsbetterthanitscounterprotocol,

NAMA,LAMA,andespeciallyPAMA.ThisisbecauseUxDMAcanalwaysproduce

a more compactschedule where adynamic schedulingprotocol maygiveup due

to local prioritycomparisons. However,considering that UxDMA isacentralized

algorithm withglobal topologyinformation,NAMA, LAMA andPAMA tradeo

alittleperformanceformuchbettereÆciency.

FIG.10showsthethroughputofthethreeprotocols. AspredictedinEq. (10),

all protocols showlinearsystem throughputunder thedierent sustainableloads

and at throughput when network load exceeds the available channel capacity,

which is advantageous over any other randomized multiple access protocols that

experiencegreatlossinthethroughputwhenthenetworkloadgoesbeyondcertain

0

0.2

0.4

0.6

0

0.2

0.4

0.6

0.8

1

Arrival Rate

λ

i

(Packet/Slot)

Throughput S (Packet/Slot)

q

₁

=0.5, q

₂

=0.5, 2 Nodes

NAMA

LAMA

PAMA

UxDMA−NAMA

UxDMA−LAMA

UxDMA−PAMA

Analysis 1

Analysis 2

0

0.1

0.2

0.3

0.4

0

0.5

1

1.5

2

Arrival Rate

λ

i

(Packet/Slot)

Throughput S (Packet/Slot)

q

₁

=0.2, q

₂

=0.07, 5 Nodes

0

0.1

0.2

0.3

0.4

0

1

2

3

4

Arrival Rate

λ

_i

(Packet/Slot)

Throughput S (Packet/Slot)

q

1

=0.1, q

2

=0.03, 10 Nodes

0

0.1

0.2

0.3

0.4

0

2

4

6

8

Arrival Rate

λ

_i

(Packet/Slot)

Throughput S (Packet/Slot)

q

1

=0.05, q

2

=0.0135, 20 Nodes

FIG.10Packet ThroughputOf Fully-ConnectedNetworks

6.2.2. Multihop NetworkScenario:

FIG.11and12showthedelayandthroughputofthethreeprotocolsinmultihop

networks. The networks are generated by randomly placing100nodes within an

areaof10001000squaremeters. Tosimulateaninniteplane thathasconstant

nodeplacementdensity,theoppositesidesofthesquareareseamedtogether,which

visually turns thesquareareainto atorus. Bysetting thetransmissionrangesof

thetransceiveroneachnodeto100,200,300and400meters,respectively,wealso

changethetopologyandcontentionlevelsineachcase.

FIG. 11 demonstrates the advantage of LAMA over NAMA, obtained from

betterchannel reusewithin twohopsofeachnodebyapplying codedivision

mul-tiplexing in LAMA. PAMA produces higher delays than the other two protocols

fully-0

0.05

0.1

0

50

100

150

Arrival Rate

λ

_i

(Packet/Slot)

Delay T

i

(Time Slot)

Transmission Range=100

NAMA

LAMA

PAMA

UxDMA−NAMA

UxDMA−LAMA

UxDMA−PAMA

0

0.05

0.1

0.15

0

50

100

150

200

250

300

Arrival Rate

λ

_i

(Packet/Slot)

Delay T

i

(Time Slot)

Transmission Range=200

0

0.05

0.1

0.15

0.2

0

100

200

300

400

500

600

Arrival Rate

λ

_i

(Packet/Slot)

Delay T

i

(Time Slot)

Transmission Range=300

0

0.05

0.1

0.15

0.2

0

200

400

600

800

Arrival Rate

λ

_i

(Packet/Slot)

Delay T

i

(Time Slot)

Transmission Range=400

FIG. 11Average PacketDelaysInMultihopNetworks

connected scenario. However, PAMA appears to have slower increases in delay

when the network loadincreases, which explains thehigherspectrumand spatial

reuse ofthecommonchannelbypurelink-orientedscheduling.

Becauseof thedramatic dierencebetweenthethroughput ofNAMA, LAMA

andPAMA,FIG.12onlyshowsthemaximumthroughputavailableinthese

individ-ual protocols, insteadof showingthegradualthroughputvariationsin accordance

withtheloadchanges. Nexttoeachbarofthesedynamicschedulingprotocols,the

throughputofthecorrespondingUxDMAalgorithm isalsocontrasted. Exceptfor

therst simulationwhenthetransmissionrangeis 100meters,UxDMA performs

betterthanNCR.Thisisbecausenetworkconnectiondensitiesshowmorevariety

at lowertransmissionrange. WhileUxDMAschedules thenetwork channelaccess

1

2

3

0

10

20

30

40

NAMA

UxDMA

LAMA

UxDMA

PAMA

UxDMA

Throughput S (Packet/Slot)

Transmission Range=100

1

2

3

0

10

20

30

40

NAMA

UxDMA

LAMA

UxDMA

PAMA

UxDMA

Throughput S (Packet/Slot)

Transmission Range=200

1

2

3

0

10

20

30

40

NAMA

UxDMA

LAMA

UxDMA

PAMA

UxDMA

Throughput S (Packet/Slot)

Transmission Range=300

1

2

3

0

10

20

30

40

NAMA

UxDMA

LAMA

UxDMA

PAMA

UxDMA

Throughput S (Packet/Slot)

Transmission Range=400

FIG.12PacketThroughputOfMultihopNetworks

scheduleaccordingtolocaltopologyonly.

Althoughnotshowninthegure,thethroughputoftheseprotocolsstill

demon-strateslinearincreasesalongwithloadincreases,andlevelsowhentheloadvalues

approximateorexceedtheprobabilitiesthat anodeandlink maybeactivated,at

which point delaysincrease drastically,as shown in FIG. 11. Systemthroughput

is an indicationof the average channelreuse ratioin multihop wirelessnetworks.

PAMAachieveshigherloadsthantheothertwoprotocols.

7. CONCLUSION

We have introduced a new approach to contention resolution that eliminates

much ofthecomplexityofpriorcollision-freeschedulingapproachesbyusing only

cols were introduced for both node-activation and link-activation channel access

schedulingin packet radio networks using time-division scheme. The advantages

of the protocols are that (a) they do notneed the contentionphases orschedule

broadcasts adopted by manyother channel access schedulingalgorithms; and(b)

they onlyneed thelocal topologyinformationwithin twohops, which canbe

ob-tained bythe propagationof one-hopneighborinformation from each node to its

neighbors.Thiscontrastswithotherschedulebroadcastingalgorithmsthatrequire

complete network topologyfor collision-freechannel access scheduling. NAMA is

suitable for broadcastingand multicasting, while LAMA and PAMA are suitable

forunicastingusingspreadspectrumtechniques.

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