DTIC ADA461687: Collision Avoidance and Resolution Multiple Access for Multichannel Wireless Networks

9 Pages·0.14 MB·English

by  Defense Technical Information Center

1
Collision Avoidance and Resolution Multiple
Access for Multichannel Wireless Networks
RODRIGO GARCE´S J.J. GARCIA-LUNA-ACEVES
[e-mail] ComputerEngineeringDepartment
MetricomInc. UniversityofCalifornia
980UniversityAvenue Santa Cruz, California95064
Los Gatos,CA 95032 Networkingand Security Center
SunMicrosystemsLaboratories
Palo Alto,California94303
Abstract—WeintroduceandanalyzeCARMA-MC(forCollisionAvoid- protocols have been proposed that implement collision reso-
ance and Resolution Multiple Access MultiChannel), a new stable chan- lution using either control packets that are much smaller than
nelaccessprotocolformultihopwirelessnetworkswithmultiplechannels.
data packets, or are based on the ability of the transmitter to
CARMA-MCrelies ontheassignmentofauniquechannelandaunique
identifiertoeachnodetosupportcorrectdeterministiccollisionresolution abort transmission rapidly after detecting collision (e.g., [2],
inthepresenceofhiddenterminals. CARMA-MCdynamicallydividesthe [8],[14]).AmongthosestableMACprotocolsthatachievehigh
channelofeachnodeintocyclesofvariablelength; eachcycleconsistsof throughput, some build a separate queue for the transmission
oneormorereceiving periodsandatransmissionperiod. Duringthere-
of data packets, in addition to the stack or queue of the con-
ceivingperiod,stationswithoneormorepacketstosendcompeteforthe
righttoacquirethefloorofaparticularreceiver’s channelusingadeter- trol packets used for collision resolution. However, the stable
ministictree-splittingalgorithm.Eachreceivingperiodconsistsofcollision collisionresolutionapproachesreportedtodateoperateinfully-
resolutionsteps. Asingleroundofcollisionresolution(i.e.,asuccess,and
connectednetworksornetworksbasedoncentralbasestations.
idleoracollisionofcontrolpackets)isallowedineachcontentionstep.The
receivingperiodisinitiatedbythereceiverandtakesplaceinthechannel On the other hand, several reservation based protocols have
assignedtothereceiverstation. Thechannelutilizationandpacketdelays beenproposed(e.g.,[1],[10],[12],[14])whichprovidestabil-
arestudiedanalyticallyandbysimulation.
ity at high load levels, and efficient service at low load levels.
Resourceauctionprotocols,i.e., [1],[14],requireasignificant
I. INTRODUCTION
amountofoverheadforeachauctionperiodandaredifficultto
Collisions in a packet-radio network can be cause by direct implement.Ontheotherhand,PRMA [10]isrelativelyeasyto
or by secondaryinterference. Direct interferenceoccurswhen implementbutusesafixedframelengthwhichcanleadtostar-
twoneighboringnodestransmittoeachotheratthesametime. vationifthenumberofactivestationsislarge. Theseprotocols
Secondary interference occurs when two or more stations un- allrequireabasestation, anddonotoperateina networkwith
awareofeachother’sexistencetransmittothesamereceiverat hiddenterminals. Thelimitation ofthese schemesis thatmost
the same time or when a station is transmitting to its neighbor ofthemrequiretheuseofabasestationwhichisasinglepoint
and a third stations transmission to some other station causes offailure.
an interference. This problem was first introduced by Tobagi This paper presents an approach to utilizing collision reso-
andKleinrock[15]andisknownintheliteratureasthehidden lution in multihop wireless networks by taking advantage of
terminal problem. Several approaches have been proposed in uniquechannel(orcode)assignmentstonetworknodes. Inthe
the past to resolve the hidden terminalproblem, and collision- past, multichannelnetworkshave been constructed using mul-
avoidance protocolshave recently received considerable atten- tiple transceivers operating on separate fixed channels [21].
tion (e.g., [13], [6]). In a collision-avoidance protocol, sender Such devices were expensive to construct. However, current
and receivercollaborate trying to avoid data packets from col- transceivertechnology(e.g.,MetricomInc.newgenerationnet-
lidingwithotherpacketsatthereceiver.However,astrafficload workdevices),enablesradiodeviceswithasmanyas chan-
increases in the network, the collision of collision-avoidance nelstobecontrolledbyasingleDSP,enablingradios2t6o0switch
control packets increases and throughput in the system drops. fromonechanneltotheotherwithin1 sec. Thisallowsmulti-
A way to stabilize the operationof contention-basedprotocols channel networks to be constructed ine(cid:22)xpensively using a sin-
isbymeansofcollisionresolutionmechanisms. gle device at each station. In addition, using multiple chan-
Several stable MAC protocols have been proposed in the nelsrendersbetterdelaycharacteristicsthansingle-channelnet-
past based on tree-splitting algorithms for collision resolution works [16], [17], [19] and have better fault tolerance against
(e.g.,[4],[7],[20]). Thoseprotocolsinwhichdatapacketsare fading and noise [5], [17]. Early work in protocol design for
usedtoresolvecollisionsachievethroughputbelow [22]for multichannel networks used CSMA or ALOHA protocols in
a single channel and fully connected networks. Se0v:e6ral MAC slotted multiple channels [18]. A reservation protocol over
multiple channels is investigated in [16] for satellite commu-
TheworkatUCSCwassupportedinpartbytheDefenseAdvancedResearch
ProjectsAgency(DARPA)undergrantDAAB07-95-C-D157 nicationsystems. Asequentialmultichannelsystemwhichuses
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1. REPORT DATE 3. DATES COVERED
2000 2. REPORT TYPE 00-00-2000 to 00-00-2000
4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER
Collision Avoidance and Resolution Multiple Access for Multichannel
5b. GRANT NUMBER
Wireless Networks
5c. PROGRAM ELEMENT NUMBER
6. AUTHOR(S) 5d. PROJECT NUMBER
5e. TASK NUMBER
5f. WORK UNIT NUMBER
7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION
University of California at Santa Cruz,Department of Computer REPORT NUMBER
Engineering,Santa Cruz,CA,95064
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a. REPORT b. ABSTRACT c. THIS PAGE 8
unclassified unclassified unclassified
Standard Form 298 (Rev. 8-98)
Prescribed by ANSI Std Z39-18
2
CSMA/CA on each channel to dynamically assign stations to toanyofthefrequenciesassignedtoitsone-hopneighbors.
channelsispresentedin [3]. Analysisofmulti-hopmultichan- Weassumethatthereexistsamechanismthatensuresthatno
nel networks using CDMA in sparse networks with receiver- station is assigned the same receiving frequency as any of its
based,transmitter-based,pairwise-based,andcommonchannel two-hopneighbors.Eachstationhasknowledgeoftheassigned
assignmentispresentedin [11]. frequencies for all its one-hop neighbors. The assignment of
Inthispaperweintroduceanewstablereceiver-initiatedmul- frequenciescanbeachievedbyapplyingthedistributedassign-
tiple access protocol with collision resolution called Collision mentofcodesalgorithmproposedin [9].Thisalgorithmassigns
Avoidance and Resolution Multiple Access MultiChannel a different frequency to each station within a two-hops neigh-
(CARMA-MC) protocol. CARMA-MC operates in a multi- borhood,providedthatthenumberoffrequenciesavailablefor
channel network in which hidden terminals may exist. It as- assignment is at least , where is
2
sumesthateachnetworknodeisassignedauniqueidentifierand themaximumnumberonfo(cid:21)ned-mhoapxn(cid:0)eigdhmbaoxrs+th2atanystatdimonaxcan
a unique channel, at least within the two-hopneighborhoodof have. This mechanism eliminates co-channelinterference and
anynetworknode. CARMA-MCisareceiverinitiatedprotocol avoidsthehiddenterminalproblem.
that dynamically dividesthe channelassigned to each receiver Besides the assignment of a unique channel, each station is
into receiving and transmitting periods. The transmission pe- also assigned a unique identifier (ID), that is known by all its
riodhasamaximum-lengthdurationandeachreceivingperiod one-hopneighbors. ThiscanbeachievedbyexchangingtheID
consistsofcollisionresolutionsteps,i.e.,ofsuccess,idleorcol- informationatthesame timethatthereceivingfrequenciesare
lisionofcontrolpackets. Theprotocolmaintainsastackforthe assigned,i.e.,applyingthedistributedassignmentalgorithm.
transmissionofcontrolpacketsusedincollisionresolution. StationsinCARMA-MCarehalfduplex;theycanbesenders
DuringthereceivingperiodCARMA-MCusesadeterminis- or receivers. A station in the sender state participates in a
tic tree-splittingalgorithmandanRTR/RTS/CTS exchange. A collision-resolution interval (CRI) based on the deterministic
receivingperiodisinitiatedbythereceiversendingaready-to- tree-splitting algorithm introduced in [8]. The determinis-
receive (RTR) signal and takes place in the channel assigned tic tree-splittingalgorithmresolvecollisionsamongcompeting
tothereceiverstation. Duringcontentionintervalsastationat- senders. TheCRIevolvesintermsofcollision-resolutionsteps,
tempts to acquire the floor by sending an RTS to the intended wherethesizeofaCRIisboundedandisafunctionofthenum-
receiverwho,inturn,sendsaCTSifthereceivedRTSiserror- berofsenders(see [8]formoredetails). Weassumea ternary
free. RTSs are sent according to a deterministic tree-splitting feedbackmodel,i.e.,therearethreetypesofcollision-resolution
algorithm that resolves all the requests that arrive during the steps: collision, success, and idle. Collision-resolution steps
same receiving interval. A packet is transmitted from the sta- follows a handshake procedure meant to eliminate collisions
tion that has acquired the floor by successfully completing a among data packets. This procedureis knownin the literature
collision-resolution round. The control packets used in each as“flooracquisition”[6].Inasingle-channelnetwork,floorac-
contention step are much smaller than a single data packet. quisitionentailsallowingoneand onlyonestation ata time to
BecauseCARMA-MCusesadeterministiccollision-resolution send data packetswithoutcollisions. To achievethis, a station
mechanism,averagedelaysincurredinthenetworkarebounded that wishes to send one or multiple data packets must send a
andareafunctionofthenumberofone-hopneighborsofare- request-to-sendpacket(RTS)toanintendeddestinationandre-
ceiver. Instarkcontrasttopriorapproachestocollisionresolu- ceiveaclear-to-sendpacket(CTS)fromit,beforeitisallowedto
tion,CARMA-MCoperatescorrectlyinmultihopnetworkswith transmitanydata. RTSsarerequiredtolastaminimumamount
hiddenterminals. oftimethatisafunctionofthechannelpropagationtime.
Therestofthispaperisorganizedasfollows. SectionIIde- In CARMA-MC a station in the sender state is allowed to
scribes CARMA-MC in detail. In Section III we present the participateintheCRIintheuniquereceivingfrequencyassigned
worst case packet delay and channel utilization. Section IV toitsone-hopintendeddestination.
comparestheanalyticalresultswiththesimulation.Theanalyt- It is the responsibility of the receiver to initiate and gear
icalresultsareveryclosetotheresultsobtainedbythesimula- the collision-resolutioninterval (CRI). The receiver can be vi-
tion,andthisvalidatestheapproximationsmadeintheanalysis. sualize as the master of its one-hop neighbors. The receiver
OurresultsconfirmthatCARMA-MCisstableatanyloadlevel, uses the unique ID to resolve contentions among transmitters.
andthatitprovideshighthroughputandboundeddelaysbyfirst Like previous efficient MAC protocols based on tree-splitting
avoidingcollisionsofdatapacketsandthenefficientlyresolving algorithms, the receiver maintains a stack and two variables,
collisionsofcontrolpackets. and . and are respectively the
lLoowweIstDand higHhieIsDtIDLnouwmIbDersof thHeisItDationsthat are initially
II. CARMA-MC allowedtotransmit. Together,theydefinetheallowedIDinter-
val, . The allowed ID intervalis broadcasted
A. DefinitionsandAssumptions
byth(eLroewceIiDve;rHtoiaIlDli)tsone-hopneighborsinaready-to-receive
In CARMA-MC, the channelaccess time is divided into re- packet(RTR)atthebeginningofeverycollisionresolutionstep.
ceivingandtransmittingperiods. Eachstationhasa uniquere- While a station is a receiver, it transmits an RTR at the be-
ceiving channelthat is used by its one-hopneighborsto trans- ginningofeachcollision-resolutionstepandtransmitsCTSsin
mit packets. A station is allowed to transmitpacketsin anyof response to RTSs. It receives RTSs and data packets from its
theuniquereceivingchannelsassignedtoitsone-hopneighbors. one-hopneighbors. All packetexchangestake place in the re-
Therefore,stationsswitchfromtheirdefaultreceivingfrequency ceiversassignedchannel.
3
On theotherhand,astation inthe senderstate, waits onthe
intended receiver’s channel for RTRs and CTSs and transmits CH 1
RTSsanddatapacketsonthethesamechannel.
B. InformationMaintainedandExchanged CH 2
Informationismaintained,exchanged,andbroadcastedbythe
receiverstation. Eachstationisassignedauniqueidentifierand
CH 3
a unique receiving channel within the two-hop neighborhood
of any network node. The receiver station maintains a stack
and two variables and . Recall that is
the lowest ID numLbeorwtIhDat is allHowiIedDto send an RTLSoawnIdDit is CH 4
initially set to 1. On the other hand, is the highest ID
time
number that is allowed to send an RTHSiIaDnd it is initially set
to the largest number of one-hop stations allowed in the net-
work. and definetheallowedID-numberinter-
val,( LowID H,itIhDatcansendRTSs. IftheIDofastation Receiving Periods Transmission Periods
is notLwowithIiDn;thHeiaIlDlo)wedIDinterval, thenthestation isnotal-
Fig.1. Eachchanneliscomposedofreceivingperiodsandtransmissionperiods.
lowedto send its RTS. TheRTSs andCTSs specifythe IDsof
thesenderandoftheintendedreceiver. Finally,thestackisthe
storagemechanismforIDintervalsthatarewaitingforpermis-
Ifa station hasnolocalpacketpending,thenthestation can
siontosendanRTS.
initiatethereceivingperiodbytransmittinganRTRonthechan-
Throughoutthepaperweassumethateachstationknowsthe
nelassignedtoit. Thestationbecomesareceiverstationforits
maximum number of one-hop stations allowed in the network
one-hopneighborsby transmittingan RTR at the beginningof
andthemaximumpropagationdelay.
eachcontention-resolutionstep,i.e.,thestationmakesatransi-
tiontothereceiverstate. EachRTRcanbevisualizeasasmall
C. BasicOperation
packet indicating to other stations that the station transmitting
If a station does not have a data packet to send, it returns theRTRisreadytoreceivearequestforthefloor.TheRTRalso
to its receiving channel broadcasting an RTR initiating a new contains information regarding the allowed ID interval of sta-
CRI. The allowed ID intervalis broadcastedby the receiverto tionsthatcompetetoacquirethefloor. Since onlythe receiver
allitsone-hopneighborsinaready-to-receivepacket(RTR).An stationsendsanRTRinitscorrespondingchannel,collisionsof
RTRisalsotransmittedbythereceiveratthebeginningofevery RTRcanneveroccur. Thereceiverstateisthedefaultstatefor
contentionstep, allowingnew stationsto knowthe state of the allactivestations.
CRI.TheallowedIDintervalaswelltheuniquereceiverIDare A station in the receiver state with a local packet pending
embeddedwithintheRTR. makesatransitiontothesenderstate,ifthecurrentCRIiscom-
OnceastationinitiatesanewCRIitremainsasareceiveruntil pleted, i.e., the station must resolve all the contentionsfor the
theendofthecurrentCRI. IfattheendofthecurrentCRI the current CRI in its channel. Only then, it scans the destination
stationhasadatapackettosendthenitswitchestothechannel channelforatmostthemaximumdurationofaCRI.IfanRTR
of its intended receiver and becomes a sender, participating in isheardduringthisintervalandthestationsIDiswithintheal-
theCRIofitsintendedreceiver.Ontheotherhand,ifattheend lowedIDinterval,thenthestationcompetestoacquirethefloor
of the CRI the station does not have a packet to send, then it extendingits durationin theintendedreceiverschanneluntilit
remainsasareceiverinitiatinganewCRI.Anystationengaged acquiresthefloor.
inaCRIasasendermustremaininthereceiver’schannelforat A station acquires the floor by sending an RTS. The station
leastthedurationofamaximumCRI. follows a non-persistent CSMA strategy for the transmission
AsshowninFig.1,thechannelaccesstimeinCARMA-MC of RTSs. More precisely, the RTS is directed to the receiver
isdividedintocycles,consistingofreceivingperiodsandtrans- in the channel where the RTR was sensed. The sender of an
mission periods. The CRI in receivingperiodis a sequenceof RTS waits and listens for one maximum round-trip time, plus
collision-resolution steps, each initiated by an RTR. The one- thetimeneededforthedestination’sCTStoarrive. IftheCTS
hopstationsparticipatingintheCRIareassumedtoconstantly is not corruptedand is received within the time limit, then the
monitorthestateofthechannelwhiletheyarenottransmitting. stationacquiresthefloorandtransmitsitsdatapacketortrainof
It is assumedthatall one-hopneighborsare at most seconds datapackets. IftheCTSisnotreceived,allstationsmonitoring
apartfromeachother. Thedurationofacontentions(cid:28)tepvaries the channel detect a collision. Because the handshake occurs
accordingtothetypeofthecollision-resolutionstep. Itispossi- onthe receiver’schannel,a lostCTS ononeofthe contending
bleforachanneltohaveonlyreceivingperiods.Thisisthecase stationsdueto errorsor fading,leadsto a loss of feedbackbut
ifthestationownerofthechanneldoesnothavedatapacketsto not inconsistentfeedback. Notice that a station wishing to ac-
send. Suchastation remainsin thereceivingstateinitiate new quire the floor spendsat most the equivalentof two maximum
CRI, as is the case for the station in channel 2 ( as shown in CRI durations. The maximum CRI duration is determined by
Fig.1). themaximumnumberofone-hopneighborsallowed. Therule
4
isthatifwithinthefirstmaximumCRIdurationthestationdoes Case3–Collision: TherearetwoormorestationswithRTSs
(cid:15)
nothearavalidRTR,thestationtransitionsbacktothereceiver to send whose IDs are within the allowed ID interval. In this
stateandremainsinthisstateuntiltheendofaCRI. case, each of these stations sends an RTS creating a collision.
AlthougheachstationtransmitsanRTSonlyaftertheRTRis The stations in the allowed ID intervalare again split into two
receivedandonlyifthestationiswithintheallowedIDinterval, newIDintervalsandthestackandthevariablesforthereceiver
collisions of RTSs may still occur due to propagation delays. stationareupdated.
RTSs are vulnerableto collisionsfor time periodsequal to the Fig. 2 shows two stations contending for the floor. The re-
propagationdelaysbetweenthesendersofRTSs. CARMA-MC ceiverinitiatestheCRI.EachCRIiscomposedofasequenceof
usesadeterministictree-splittingalgorithm [8]toresolvecolli- collision-resolutionsteps,eachinitiatedbyanRTR.
sionsofRTSs,whicharedetectedbytheabsenceofaCTS.Each
stepoftheCRIisinitiatedbyanRTR.Therearethreetypesof III. CHANNELUTILIZATIONAND PACKET DELAY
steps, idle, collision, andsuccess. An idlesteps hasa duration
In this section we derive a lower bound on the average uti-
of , acollisionstephasadurationof , anda
lizationofthechannelaswellasanupperboundontheaverage
suc(cid:26)ce+ss2s(cid:28)tephasadurationof (cid:26)+, w(cid:13)h+er3e(cid:28) isthe
delay that a station experiences in transmitting a data packet.
sizeofanRTR, isthesizeof(cid:26)an+R2T(cid:13)S+orÆa+CT4(cid:28)S, isthe(cid:26)sizeof
Recall that, the channelutilization is defined as the amountof
adatapacket,an(cid:13)d isthemaximumchanneldelaÆy.
timethatthechannelisusedtotransmitdatapacketsdividedby
(cid:28)
thetotaltime.
D. CollisionResolutionInterval
Inordertosimplifyouranalysis,weassumethateachstation
CARMA-MCusesadeterministictree-splittingalgorithmto hasatmost one-hopneighborsandthateachstationhasa
resolve collisions. This algorithm was presented and analyzed differentrecdemivainxgfrequencyorchannelthanitstwo-hopneigh-
indetailin[8]. bors.Furthermore,weassumethatallthechannelshavesimilar
Wheneverastationhasalocalpackettosendandisnotcur- behaviorsandthisenableustostudytheutilizationofageneric
rently the receiver in a CRI, the following operations are exe- channel. Observethat,if thenthenumberofdistinct
cuted.First,thestationscansthechannelofitsintendedreceiver receivingchannelsis dmax > 2 .
2
foranRTR. RTRsinformcontendersthataresolutionstepcan Let denotethernec=eivdimngaxch(cid:0)andnmeal,x+t2hefrequencyassoci-
takeplace,allowingmultiplecontenderstorespond.IftheRTR atedwcithhrchannel and thereceivinfgrstation.Then,station
is detected, the station sends an RTS and waits for one maxi- istheintendedcrhecreivernfroratmost one-hopneighbors.
mum round-trip time plus the time needed for the destination Anrtthesametime,anyofthe one-dhmopaxneighborsisapoten-
tosendaCTS.IftheCTSisreceivedwithintheallocatedtime, tialreceiverforstation . Wdmeaaxlso let denotethe intended
thenthesenderacquiresthefloorandcanstartsendingcollision- receiverof regardlesnsrof whichofthnex one-hopneigh-
free packets. On the other hand, if the CTS is not received borsstationnr choosestosenditsdatapadcmkeatx. Thus, isthe
within the allocated time, then the station sender of the RTS transmittingnfrrequencyofstation and isthechafnxnelas-
and all the other stations competing for the floor detect a col- sociatedwithfrequency . nr chx
lision. Inthiscase, thecollision-resolutionalgorithmisstarted Finally,wedefine fx astheaveragesizeofthemaxi-
with the first round of RTS collisions. As soon as a collision mumdurationofaCRTI(fno;rdamraexc)eiverwithatmost one-hop
is detected, the receiverstation dividesthe allowed ID interval neighborsand uniquechannelswithinthetwo-dhompaxneighbor-
into two ID intervals. The first ID interval, hood of the nentwork node and at the same time the maximum
c(LalolewdItDhe;HbaicIkDof)f interval, is HiID+LowID , number of nodes in the deterministic tree. In order to derive
while the second ID interval, w(LhiocwhIiDs t;hde new a2llowedeI(cid:0)D1in)- , we make use of the analytical results obtained in
terval, is HiID+LowID . The receiver updates its [T8(]nf;odrmthaexn)umberofcollision-resolutionsteps.
stackbyex(edcuting2aPUSHe;stHacikIDco)mmand,wherethekeybeing Forall , where isthemaximumnumberof
pushedisthebackoffinterval.Afterthisisdone,thestationup- stationsannd(cid:21) dmiasxth>em1aximumnnumberofstationsparticipat-
dates and withthevaluesfromthenewallowed ingintheCRdIm,tahxeaveragenumberofcollisionstepsrequiredto
IDintLerovwalIbDroadcaHstiinIgDthisinformationonthenextRTR.This
resolveall collisionsis
marksthe beginningofthe nextcollision-resolutionstep. This dmax
operationisrepeatedeachtimethereisacollision.
Recallthateachstepofthecollision-resolutionalgorithm,and
(cid:23) (cid:11) (cid:12)
consequentlyeachcontentionstep,canbeeither: dmax(cid:0)i i
Case1–Idle: ThereisnostationintheRTSstatewhoseIDis C(n;dmax) = 1+ (cid:0) n (cid:1)(cid:0) (cid:1)C((cid:11);dmax(cid:0)i)
(cid:15) Xi=(cid:22) dmax
withintheallowedIDinterval.Thechannelremainsidleforthe
(cid:23) (cid:11) (cid:0) (cid:12) (cid:1)
(1)
durationofonepropagationdelay. Thestackandthe variables dmax(cid:0)i i
and are updated. Thereceiverstation executes + (cid:0) n (cid:1)(cid:0) (cid:1)C((cid:12);i)
Xi=(cid:22) dmax
aLoPwOIPDcommHanidIDin the stack updatingthe allowed ID interval
while the average number of(cid:0)idle s(cid:1)teps required to resolve all
withthenewvalues.
collisionsis
Case2–Success:ThereisasinglestationwithanRTStosend
(cid:15) dmax
whose ID lies within the allowed ID interval. In this case, a
single station is able to complete an RTS/CTS handshake suc- (cid:23) (cid:11) (cid:12)
dmax(cid:0)i i
cessfully,acquiringthefloorandtransmittingitsdatapacket. Z(n;dmax) = (cid:0) n (cid:1)(cid:0) (cid:1)Z((cid:11);dmax(cid:0)i)
Xi=(cid:22) dmax
(cid:0) (cid:1)
5
SENDER 0
RTS RTS RTS DATA
SENDER 1
RTS RTS RTS DATA
RECEIVER
RTR RTS RTR RTR RTS RTR CTS RTR CTS
CHANNEL
RTR RTS RTR RTR RTS RTR RTS CTS DATA RTR RTS CTS DATA
time
STEP 1 STEP 2 STEP 3 STEP 4 STEP 5
Fig.2. Receivingmode:TheintendedreceiversendsanRTRtoinitiatetheCRI.Noticethateachcollision-resolutionstepisinitiatedbyanRTRpacket.
CASE A RTR is within T(n,d_max) interval
(cid:23) (cid:11) (cid:12)
(2)
dmax(cid:0)i i
+ Xi=(cid:22) (cid:0) dmnax(cid:1)(cid:0) (cid:1)Z((cid:12);i) Receiver RTR CTS
where (cid:0) (cid:1)
; Sender Pkt to send Station Returns to its Channel
(cid:11) = dn=2e (cid:12) =n(cid:0)(cid:11)=n(cid:0)dn=2e
if RTS DATA
0 ifdmax (cid:20)(cid:11) time
(cid:22) =
(cid:26) dmax(cid:0)(cid:11) if dmax >(cid:11) T(n,d_max) T(n,d_max)
dmax ifdmax (cid:20)(cid:12)
(cid:23) =
(cid:26) (cid:12) dmax >(cid:12) CASE B
The number of success steps is .
Receiver No RTR arrives
can be calculated by mulSti(pnly;idnmgatxh)e n=umbdemraoxf
sTte(pns;dbmyatxh)e duration of a step for each of the three types of
collision-resolutionsteps.Anidlestepshasadurationof ,
Pkt to send Station Returns to its Channel
acollisionstephasadurationof ,andasucce(cid:26)ss+s2te(cid:28)p Sender
hasadurationof ,(cid:26)w+he(cid:13)re+3i(cid:28)sthesizeofanRTR,
isthesizeofan(cid:26)+RT2S(cid:13)o+rÆa+C4T(cid:28)S, isth(cid:26)esizeofadatapacket, time
a(cid:13)nd isthemaximumchanneldelÆay.Therefore, T(n,d_max)
(cid:28)
Fig. 3. Transmission period for CARMA-MC. In case A, the RTR arrives
T(n;dmax) = S(n;dmax)((cid:26)+2(cid:13)+Æ+4(cid:28)) withinthethetimeinterval ,therefore,thesendercontentsfor
thefloor.IncaseB,theRTRTd(one;sdnmoatxar)rivedwithintheallowableinterval,
+ Z(n;dmaxm)((cid:26)+2(cid:28))
(3) therefore,thesendermustreturntoitschannelandtransitiontothereceiving
+ C(n;dmax)((cid:26)+(cid:13)+3(cid:28)) mode.
Recallthata channeliscomposedofreceivingintervalsfol-
lowedbytransmittingintervals. Onceastationisinthereceiv-
ing mode (i.e., is a receiver) it remains in that mode until the otherhand,ifithearsanRTRitwilltransmititspacketwithinan
endofthecurrentCRI.Onlythen,thestationcanswitchtothe additional interval.Thisimpliesthatthedurationof
transmittingmodeifits transmittingqueuecontainsdatapack- thelongestTp(ons;sdibmleaxtr)ansmissionperiodis . Thus,
etsthatneedtobesent. We furtherassumethatwhenastation forourprotocolthebestpossiblereceiveris2tTh(eno;ndemtahxa)tspends
acquirestheflooritcanonlytransmitonedatapacket. all its time in the receiving mode, i.e., its transmission queue
We start by computing in Theorem 1 an upper bound on isalwaysempty,anda stationrequestingthe floorinthe chan-
the average delay that a station experiences in transmitting a nel of such receiver will always succeed in the request within
packet. Accordingto the CARMA-MC protocol,a station try- the time interval . On the other hand, the worst
ing to transmit a packet can wait at most time for possible receiver iTs(thne;domneaxt)hat spends most of its time in the
anRTR.IfduringthismaximumperiodofTtim(ne;ditmdaoxe)snothear transmittingmodeandtheleastamountoftimeinthereceiving
anRTR,itmustreturntoitschannelandinitiateaCRI.Onthe mode. Thatis, theworstpossiblereceiverwillconstantlyhave
6
idle steps (i.e., non of its neighborswill requestthe floor) and Bernoullitrialwithprobability . Eachtimethestationtriesto
receive a data packet in its transmission queue when found in sendadatapacket,thepacketwiqllbesuccessfulwithprobability
the receiver state. This will force the receiver to switch to the . Therefore,it can be representedby a geometricdistribution
senderstateandthentoremaininthisstateforaslongaspossi- fqunctionwhoseexpectedvalueis
ble. Now,sincethedurationofanidlestepis where is
thesizeoftheRTRpacketand isthemaxim(cid:26)u+m2c(cid:28)hannels(cid:26)de- 1
(8)
lay,andthedurationofthelonge(cid:28)stpossibletransmissionperiod y 1(cid:0)q
E[Y]= y(1(cid:0)q) q =
is , each time a sender targets the worst possible Xy=0 q
rec2eTiv(enr;itdsmparxo)babilityofsuccessis whichisequivalenttotheexpectednumberoffailuresbeforea
success.Thus,theaveragetimespendbystation transmitting
adatapacketcanbewrittenas nr
(4)
T(n;dmax)
Ps = <0:5
2T(n;dmax)+(cid:26)+2(cid:28)
anditsprobabilityoffailureis
1
y
Txmit (cid:20) (1(cid:0)q) q(y(T(n;dmax)+E[R])+
(5)
T(n;dmax)+(cid:26)+2(cid:28) Xy=0
Pf = >0:5
2T(n;dmax)+(cid:26)+2(cid:28) 2T(n;dmax)
Ingeneralwecanapproximatethiseventbyassuminganin-
dependentBernoullitrialwithprobability . Eachtimethesta- = (T(n;dmax)+E[R])E[Y]+2T(n;dmax)
(9)
tiontriestosendadatapacket,thepacketwqillbesuccessfulwith (cid:20) 2T(n;dmax)(1+E[Y])
probability . Thiscanbe approximatedbya geometricdistri- Nowobservethatthedatapackethadtobeoriginatedinthe
bution functqion whose expectedvalue is 1(cid:0)q. Recall last CRI in which the station was in the receiver state. If this
thatageometricrandomvariablecountstEhe[Ynu]m=berqoffailures wasnotthecasethestationwouldhaveremainedinthereceiver
before a success occurs. Thus, for the worst possible receiver stateandnotswitchedtothesenderstate. Therefore,weneedto
wehave and . Wearenowreadytoprovethe addto theexpecteddurationofthelastCRI(i.e.,
followingqt=he1o=re2m. E[Y]=1 Txmi)tbeforethestationswitchedfromthereceivEer[Rst]a(cid:20)te
Theorem1: Considerasystemwhereeachstationhasatmost tTo(tnh;edsmenadxe)rstate. Thethesisthenfollowsfromthefactthatfor
one-hopneighbors. Thentheaveragechanneldelay theworstpossiblereceiverwehave and .
edxmpaexrie>nc1edby a station trying to deliver a data packet can be In the next result we derive a loqw=er0b:o5und oEn[Yth]e=av1erage
upperboundedby channelutilization.
Theorem2: Considerasystemwhereeachstationhasatmost
(6) one-hopneighbors.Thentheaveragechannelutiliza-
D(cid:20)5T(n;dmax) tdimonaxis>bo1undedby
where isthemaximumpossibledurationofaCRI.
Proof:TT(on;ddemrivaex)Eq.(6)we assumethatforourstation the (E[X]+E[Y]+1)E[k]Æ
intendedreceiver is always the worst possible receiver thnartwe U (cid:21) E[R](E[X]+E[Y]+1)+T(n;dmax)(E[Y]+2)
(10)
can think of. Thus, each time the station tries to transmit
a packet it fails on average half of the timen.rAccordingto our
modelthisistrueifwithin thestationdoesnothear where isthenumberofCRI inwhichstation remains
anRTR.AfterafailedtransTm(inss;idomnathx)estationmustreturntoits intherEec[eXiv]erstatebeforeitleavesitschanneltotrannsrmitadata
channelandswitch fromthe transmittingstate to the receiving packet of its own on another channel; is the number of
stateinitiatinganewCRIasareceiver. AftertheCRIendsthe attemptsthatstation mustmake befoEre[Ytr]ansmittingits data
station transitions back to the transmitting state and tries once packet; istheexnperctednumberofdatapacketsreceivedby
moretoacquiretheflooronthechannelassignedtoitsintended station E[kp]erCRI; istheaveragedurationofoneCRIas
receiver. areceivnerr; E[Ris]themaximumdurationofaCRIand
Now, since each failed transmission has a total cost of isthesizeoTf(onn;eddmaatax)packet. Æ
(the time waiting for an RTR) plus , the ex- Proof:Thefrequencywithwhichstation triestosendadata
pTe(cnte;ddmdauxra)tionof the CRI (in which the stationEis[Ra ]receiver), packetisdeterminedbyitspacketdataratne.rOnceagainwecan
theexpecteddurationofaCRIcanbeupperboundedasfollows approximatethisprocedurewitha geometricdistributionfunc-
tion. AttheendofeachCRIacoinwithprobability istossed
dmax todecidewhetherornotduringthepreviousCRIstatiqon had
(7)
a packet to send and thus must switch from the receivenrrstate
E[R](cid:20) p(k)T(n;k)(cid:20)T(n;dmax)
Xk=0 to the transmittingstate. Hence, the expectednumberof CRIs
where is the probability of having a CRI with stations occurringbeforestation hasapackettosendis
competpin(kg)forthefloor,and isthecorrespondkingdura- nr
tiontoresolveall initialcoTlli(snio;nks). (11)
1(cid:0)q
Thesameprocekdureisrepeatedeachtimethestationfailsto E[X]=
q
deliveritsdatapacketandmustretryafteroneCRIasareceiver. Now, let be the numberof packetsreceivedduringa CRI,
Wecanapproximatetheretryeventbyassuminganindependent bethekprobabilityofhavingaCRIwith initialcollisions
p(k) k
7
and bethetimeneededtoresolveall collisions. Itis betweenstationsanddefinedthediameterofthenetworktobe
not dTif(finc;ukl)t to see that the expected durationkof a CRI can be mile. Underthese assumptions, the propagationdelay of the
upperboundedby c1hannels is . In order to accommodatethe use of IP ad-
dresses for d5e:4st(cid:22)insation and source, the minimum size of RTSs
andCTSs waschosento be bytes. TheRTR controlpacket
dmax
(12) wasassumedtobe bytes.T20hemaximumexpectedtheoretical
E[R](cid:20) p(k)T(n;k)
packetdelaywas 10 .
Xk=0
andthattheexpectednumberofpacketsreceivedinaCRIis 5T(n;dmax)=5T(14;4)(cid:20)98ms
dmax
(13)
E[k]= p(k)k: Pkt Delay versus Transmitting Load
80
kX=0
Sinceeachstationhasatmost one-hopneighbors,wehave
that . Observethattdhmeatoxtalduration inachan- 70
nel iks c(cid:20)omdmpoasxed of receiving periods and transTmtoittatilng periods
60
thatappearasidleperiodsinthechannel.Furthermore,sincethe
ntvoaulmtureabnefsromorfiatreogcneeoiavmninoegtthripecrerrciaohndadnsonbmeelfvoiasreridasebttaleteri,omnii.nene.,rdhbaysath,deaitteaxfopplealccoktweedst Delay: msec 4500
thatthe expectedarrivaltime for a packetis E[X] . Once Pkt 30
thepackethasarrived,station finishesasreEce[Riv]eEr[tXhe]current
CRIaddingonemore penrirodtothetotalduration. Thenit 20
switchestothesenderEsta[Rte].
10
Now,station makesseveraltrialsbeforeitisabletodeliver
its data packet.nArs explainedin Theorem 1, the trials are also 0
0 5 10 15 20
governed by a geometric distribution. Each failure has a cost Transmitting Load Rate: # Pkts/sec
of plus ,andthenumberoffailuresbeforethe Fig.4. ChanneldelayforCARMA-MC
datTa(pna;cdkmetacxa)nbedEel[iRve]redsuccessfullyis . Oncestation
hearsanRTRinthechanneloftheintendeEd[Yre]ceiver,ithasat Figure 4 shows packet delay as a functionof the number of
mnrost tocontentsuccessfullyanddeliveritspacket. data packets being transmitted per second on a channel. The
There2fTor(en,;thdemtaoxta)lperiodinthechannelcanbewrittenas loadappliestothereceivingchannel,i.e.,thenumberofpackets
that the receiver receives per second. The delay is measure in
msecandistheintervaloftimefromthearrivalofthepacketto
itsqueueuntilthepacketwassuccessfullydelivered.Thepacket
Ttotal (cid:20) E[X]E[R]+E[R]+
delayforeachindividualtrialwasalwaysbelowthetheoretical
(T(n;dmax)+E[R])E[Y]+2T(n;dmax)(14) upperboundpredictedbyEq.(6).
Infigure5wehavecomparedtheutilizationderivedfromour
where isthenumberofCRIinbetweentwotransmissions, analysistothatobtainedinthesimulationasafunctionofthere-
iEs t[hXe]expecteddurationof each CRI and is the ex- ceiversload.Toobtaintheutilizationofthechannelwecounted
pEe[cRte]d number of data packets transmitted in chEa[nkn]el per theintervalsoftimewhendatapacketsweretransmittedonthe
CRI. On averagethe amountof time thatchannel icshbreing channel divided by the total simulation time. The simulation
usedtotransmitdatapacketsis chr resultsvalidateouranalyticalresults.
(15)
(E[X]+E[Y]+1)E[k]Æ
ThethesisthenimmediatelyfollowsbydividingEq.(15)by
Eq.(14). V. CONCLUSIONS
CARMA-MCimplementscollisionavoidanceandresolution
IV. SIMULATION that workscorrectlyin multihopwireless networks. CARMA-
In order to verify the analytical results obtained in the pre- MCisareceiver-initiatedprotocolbasedonadeterministictree-
vioussection,simulationswithdifferentloadswereperformed. splitting algorithm; to operate, it requires each node to be as-
For the experiments we used a total of stations each sur- signed a unique identifier and a channel that must be unique
roundedbyatmost neighbors1.0T0herefore,themaxi- within the two-hop neighborhood of the node. CARMA-MC
mumnumberofchandnmealsxw=as4setto . resolves three mayor sources of packet failure. First, busy in-
2
Packetswerecreatedateachstationnu=sindgmianxd(cid:0)epdemndaexn+tP2o=iss1o4n terference is resolved since the intended receiver initiates the
generators. The simulations were repeated a number of times communication and remains as a receiver until the end of the
runningonaverageonehourpertrial.Weassumedahigh-speed CRI. A station will never send a data packet to a receiver that
network ( ) in which Ethernet data packets ( bytes) is not ready to receive it. Second, co-channel interference is
are transm1iMttedbp.sFurthermore, we have used the sam5e12distance not an issue for CARMA-MC since no station two hops away
8
Channel Utilization versus Receiving Load
100 [16] V.C. M. Leung,“Multichannelreservationprotocolforpacketmultiple-
access communications,” Electronic Letters, vol. 26, no. 20, pp. 1637-
90 1638,1990.
Analysis [17] C.G. Lof,“PacketdelayforCSMAandMulti-channelALOHAmulticast
80 Simulation schemesinWLANswithfadingandco-channelinterference,” IEEEInt.
ConferenceonUniversalPersonalCommunications,1996.
[18] A.M. MarsanandD. Roffinella,“Multichannellocalareanetworkpro-
U 70
Utilization: 60 [19] AtCoS.coMMlsA.,”/MCIEDarEspEarnoJtSaonAcdColF,s.v,”oNIlE.eSEriAE,C“TA-r1as,ninsm.ouC.l5oa,mtipompn.usn8t.u8,d5vyo-8lo.9fC7d,Oe1Ml9a8y-33i9.n,mnou.l1ti1c,h1an9n9e1l.
Channel 50 [20] Jm.uLn.icMataiosnsesy,”,i“nCMolulilstiiuosnerreCsoolmutmiounniaclagtoiornithSmystaenmds,raGn.dLoomngaoccEedss..cNoemw-
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40
[21] N. ShachamandP. King,“Architectureandperformanceofmultichannel
multihoppacketradionetwork,”IEEEJSAC,vol.SAC-5,no.6,pp. 1013-
30 1025,1987.
[22] B.S.Tsybakov,andN.B.Likhanov,“Upperboundonthecapacityofran-
20 dommultipleaccesssystem,”ProblemsofInformationTransmission,vol.
23,no.3,pp.224-236,July-Sept.1987.
60 80 100 120 140 160 180 200
Receiving Load Rate: # Pkts/sec
Fig.5. ChannelutilizationforCARMA-MC
will have the same receiving frequency. Third, contention in-
terference is resolved by using the deterministic tree-splitting
algorithm. Our analysis shows that the average channel delay
incurred in CARMA-MC is bounded and is a function of the
maximum number of one-hop neighbors; our simulation vali-
datethesimplifyingassumptionsthatwemadeonouranalysis.
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