DTIC ADA461597: Poll-before-Data Multiple Access

6 Pages·0.12 MB·English

by  Defense Technical Information Center

Poll-before-Data Multiple Access
AsimakisTzamaloukasand J.J.Garcia-Luna-Aceves
ComputerEngineeringDepartment
BaskinSchoolofEngineering
UniversityofCalifornia,SantaCruz,California95064
jamal,jj @cse.ucsc.edu
f g
Abstract—Weintroduceanewmediumaccesscontrol(MAC)protocolnamed Wepresentanewreceiver-initiatedMACprotocolthateliminates
PDMA(Poll-before-Data Multiple Access). Mostprior MACprotocols aimedat the performance limitations of MACA-BI, which we call the Poll-
avoidingcollisionsofdatapacketsinnetworkswithhiddenterminalsaresender- before-DataMultipleAccess(PDMA)protocol.PDMAturnstheRTT
initiated,inthatthesendertransmitsashortrequesttosend(RTS)askingthere-
usedinMACA-BIintoadual-usecontrolpacketcalledRT2(ReadyTo
ceiverforpermissiontotransmit.Incontrast,inPDMA,whenadatapacketarrives
ReceiveandTransmit). Whenanodehasdatatosendtoanintended
atthereceiver,thereceiversendsaready-to-receive-and-transmit(RT2)packetstat-
ingtheidentifiersofaspecificsenderandreceiver.AnodereceivinganRT2packet receiver, itsends anRT2using carriersensing, which weassume to
addressedtoitasasenderisenabledtosendadatapacket,ifithasone;otherwise, benon-persistentinthispaper. TheRT2specifiestwoneighbors: (a)
ifthesenderspecifiedintheRT2isquiet,thereceiverspecifiedintheRT2sends anintendedsourceofdata,whichischosenusinganypollingscheme
aclear-to-send(CTS)packet,enablingthesenderoftheRT2tosenditsowndata (e.g.,roundrobin),and(b)anintendedreceiverofthedatathenode
packetfreeofcollisions. PDMAisshowntoavoidthecollisionofdatapacketswith
hasfortransmission. TheRT2leadstoasuccessful transmissionof
anytypeofpacket.AnanalyticalmodelisusedtoshowthatPDMAachieveshigher
dataifeitherthepolledsourcehasdataforthesenderoftheRT2,orthe
throughputthanpriorcollision-avoidanceprotocolsforwirelessnetworks,namely
MACA-BI,FAMA-NCS,andMACA.AveragedelaysinPDMAarealsoshowntobe intendedreceiversendsaclear-to-send(CTS)tothenodeifthepolled
shorterthanthoseinCSMA. sourceremainsquiet. SectionIIdescribesPDMAindetail,andSec-
tionIIIshowsthatPDMAcorrectlyavoidscollisionsofdatapackets
withanyotherpacketsintheabsenceoftransmissionerrorsandfad-
I. INTRODUCTION
ing.SectionIVshowstheimprovementinthroughputoverMACA-BI
Therehasbeenasignificantamountofresearchondesigningeffi- andevenFAMA-NCSresultingfromthemodifiedcollision-avoidance
cientMAC(mediumaccesscontrol)protocolsforwirelessnetworks. dialogueofPDMAusingananalyticalmodel.
ThefirstattemptwasCSMA(carriersensemultipleaccess),whichis
basedonsensingthechannelbeforeattemptingtotransmitapacket. II. PDMA
KleinrockandTobagi[7]studiedCSMA’sbehaviorandidentifiedthe
Acriticaldesignissueinanyreceiver-initiatedMACprotocolisde-
hidden-terminalproblemofCSMA,whichmakesCSMAperformas
cidingonthefrequencywithwhichareceivermustpollitsneighbors
poorly as the ALOHAprotocol when the senders of packets cannot
forpackets. A polling ratethat istoo small renders lowthroughput
hear one another and the vulnerability period of packets becomes
andlongaveragedelays,becauseeachsenderwithapackettosendis
twicea packet length. TheBTMA (busytone multipleaccess) pro-
sloweddownbythepollingrateofthereceiver. Conversely,apolling
tocolwasafirstattempttosolvethehiddenterminalproblembyin-
ratethatistoohighalsorenderspoorperformance,becausethepolling
troducing aseparate busytonechannel [11]. Thesameauthorspro-
packetsaremorelikelytocollidewitheachotherandnosourcegets
posed SRMA [12], which attempts to avoid collisions by introduc-
polled. The basicsolution advocated inPDMAconsistsof twoele-
ing a collision-avoidance handshake between the sender and the re-
ments: (a)making thedatarateatthesourcesdeterminethepolling
ceiver.Anodewithadatapackettosendsendsfirstarequest-to-send
rateat thereceivers, and (b)eliminating wastedpolling packets. To
(RTS)packettotheintendedreceiver, whorespondswithaclear-to-
achievethedesiredclockingeffectofdatapacketsoverpollingpack-
send(CTS)ifitreceivestheRTScorrectly. Thesendertransmitsthe
ets,anodesendsanRT2(readytoreceiveandtransmit)packetwhen
datapacketafterreceivingtheRTSsuccessfully. ALOHAorCSMA
ithasdatatosenditself. Toavoidwastefulpollingpackets, theRT2
canbeusedbythesenderstotransmitRTSs.
servestwopurposes: it pollsaspecific neighbor asking for packets,
Several variations of the basic SRMA scheme to avoid collisions
anditaskspermissionfromanotherspecificneighbortosendpackets
ofdatapacketshavebeendeveloped;MACA[6],MACAW[1],IEEE
ifthepolledsourceremainsquiet.
802.11[5],andFAMA[2],[4]arejustafewexamples. Allofthese
InPDMA,everynodestartsoperationintheSTARTstate,inwhich
MACprotocols,andmostprotocolsbasedoncollision-avoidanceex-
the node waits twice the maximum channel propagation delay, plus
changestodate,aresender-initiated,inthatthenodewantingtosend
the hardware transmit-to-receive transition time ( ), before sending
adatapacketfirsttransmitsashortcontrolpacketaskingpermission
anythingoverthechannel. Thisenablesthenode(cid:15)tofindoutifthere
fromthereceiver.Incontrast,intheMACAbyinvitation(MACA-BI)
are any ongoing transmissions. After a node is properly initialized,
protocol[9],[10],thecollision-avoidancehandshakebetweensender
ittransitionstothePASSIVEstate. Inallstates,beforetransmitting
andreceiverisreversedandismadereceiverinitiated. InMACA-BI,
anything to the channel, a node must listen tothe channel for a pe-
a node with a packet to send must wait for the intended receiver to
riodoftimethatissufficientforthenodetostartreceivingpacketsin
sendapollingpacket,calledRTR(readytoreceive),addressedtothe
transit.Ifanode isinthePASSIVEstateandsensescarrier,ittransi-
node,beforeitcantransmitanything. Thisisaninterestingapproach;
tionstotheREMxOTEstatetodefertoongoingtransmissions.Anode
however, as we show in Section IV-B, it renders a low throughput,
inREMOTEstatemustallowenoughtimeforacompletesuccessful
unless the average rate of packets is high, because many RTRs go
handshaketotakeplace,beforeattemptingtotransitionfromremote
unanswered.
state.
Figure 1 illustrates the basic handshakes that occur in PDMA. If
ThisworkwassupportedbytheDefenseAdvancedResearchProjectsAgency(DARPA)underGrant
No.F30602-97-2-0338andbyagrantfromRaytheon. node isinPASSIVEstate and obtains an outgoing packet tosend
x
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does not display a currently valid OMB control number.
1. REPORT DATE 3. DATES COVERED
1999 2. REPORT TYPE 00-00-1999 to 00-00-1999
4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER
Poll-before-Data Multiple Access
5b. GRANT NUMBER
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
9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR’S ACRONYM(S)
11. SPONSOR/MONITOR’S REPORT
NUMBER(S)
12. DISTRIBUTION/AVAILABILITY STATEMENT
Approved for public release; distribution unlimited
13. SUPPLEMENTARY NOTES
14. ABSTRACT
15. SUBJECT TERMS
16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF 18. NUMBER 19a. NAME OF
ABSTRACT OF PAGES RESPONSIBLE PERSON

a. REPORT b. ABSTRACT c. THIS PAGE 5
unclassified unclassified unclassified
Standard Form 298 (Rev. 8-98)
Prescribed by ANSI Std Z39-18
toneighbor ,ittransitionstotheRT2state. IntheRT2state,node packetcollideswithotherpackets,hastobelargerthanthemaximum
uses non-pyersistent carrier sensing to transmit an RT2. If node propagationdelaybetweenanytwoneighbors.
xdetectscarrierwhenitattemptstosendtheRT2,ittransitionstothxe Toreduce theprobability that thesame nodes would compete re-
BACKOFF state, which makes the node back off immediately for a peatedlyforthesamereceiveratthetimeofthenextRT2,leadingto
sufficient amount of time to allow a complete handshake between a successivecollisionsofRT2s,theRT2specifiesabackoff-periodunit
sender-receiverpairtooccur;otherwise, sendsitsRT2. forcontention. ThenodesthatmustentertheBACKOFFstatecom-
The RT2 specifies two addresses: thxe address of a neighbor , putearandomtimethatisamultipleofthebackoff-periodunitadver-
which is the intended source being polled and can be chosen usinzg tisedintheRT2. Thesimplestcaseconsistsofcomputingarandom
anyneighborpollingschedule(e.g.,roundrobin,setting equalto ), numberofbackoff-periodunitsusingauniformlydistributedrandom
andtheaddressof astheintendedreceiver. z y variablefrom1to , where isthemaximum number ofneighbors
If receivestheyRT2correctlyandhasdatafor ,itimmediately forareceiver. Thedsimplestbdackoff-periodunitisthetimeittakesto
transiztions totheXMIT state, where ittransmitsaxdata packet to ; sendasmalldatapacketsuccessfully.
otherwise, transitionstotheBACKOFFstatetoremainquiet forxa
timeperiodzthatislongenoughtoallowthedesignatedreceiver start III. FLOORASSIGNMENTINPDMA
sendingaCTS,enabling tosendadatapacket. y Theorem1belowshowsthatPDMAensuresthatanypacketissent
If receivestheRT2cxorrectlyanddoesnothearanytransmission toitsdestinationwithinafinitetimeafteritbecomesreadyfortrans-
fromy foraperiodoftimeequaltoamaximumround-tripdelaywith mission,andthattherearenocollisionsbetweendatapacketsandany
anynezighbor,ittransitionstotheCTSstateandsendsaCTSaddressed othertransmissions,underthefollowingassumptions([4]):
to ifnocarrierisdetectedinthechannel. A0) AstationtransmitsanRT2thatdoesnotcollidewithanyother
xAnynodeinPASSIVEstatethatdetectsnoiseinthechannelmust transmissionswithanon-zeroprobability.
transitiontotheBACKOFFstate.Anynodeotherthan and receiv- A1) Themaximumend-to-endpropagationtimeinthechannelis
inganRT2transitionstotheBACKOFFstate. Anynodyeothezrthan .
receivingtheCTSfor transitionstotheBACKOFFstate. x A2)(cid:28) <Ap1acketsentoverthechannelthatdoesnotcollidewithother
Whennode receivxestheCTSfrom ,ittransitionstotheXMIT transmissionsisdeliverederrorfreewithanon-zeroprobability.
stateandtransmxitsadatapacketto . y A3) AllnodesexecutePDMAcorrectly.
Therefore, PDMA can have twoy types of successful exchanges, A4) The transmission time of an RT2 and a CTS is , the max-
whichareillustratedinFig.1(a)and(b).Thepollednode mayhave imum transmission time of a data packet is , an(cid:13)d the hard-
data tosend to (Fig.1(a)) or isidleand theintendedzreceiver waretransmit-to-receivetransitiontimeis (cid:14) . furthermore,
sendsaCTSsucxcessfully(Fig.1z(b)). y . (cid:28) (cid:20) (cid:15)
A5)2(cid:28)T<her(cid:13)e(cid:20)isn(cid:14)o<ca1ptureorfadinginthechannel.
Theorem1: PDMAprovidescorrectflooracquisitioninthepres-
(a)
enceofhiddenterminals.
Proof: The topology depicted in Figure 2 includes all the possible
RTR RTR
situations of hidden terminals withrespect tosource and receiver
x RRTTRR z x data z . Node representsalltheneighborsof thatcanbSehiddenfrom
RTR RandtheLreforewecanhaveinterferenceatS .Node representsall
y Rtheneighborsof hiddenfrom thatcancSauseinteKrferenceat so
that won’tbeaLbletofollowthSepacketexchangebetween anLd .
(b) LikeLwise,node isaneighbor of thatishiddenfrom S,causiRng
interferenceat X;andnode isanReighborof thatishiSddenfrom
RTR RTR data data ,preventing RfromunderYstandingthedialogXuebetween and .
x RTR y x CTS y x data y R X S R
RTR RTR data data
X S K
(c)
Y R L
RTR RTR
x RRTTRR y x BACKOFFy Fig.2. PDMAfloorassignment
RTR RTR
Theproofneedstoshowthat,ifnode sendsadatapacketto ,
noothertransmissioncancollidewithit,SindependentlyofthestatRus
Fig.1. PDMAillustrated ofallaforementionednodes.
Node cansendadatapacketto onlyafterreceivingasuccessful
WhenmultipleRT2saretransmittedwithinaone-waypropagation RT2fromS . WithoutlossofgenerRality,wecanassumethat,attime
delayacollisiontakesplaceandthenodesinvolvedhavetotransition ,node RsendsanRT2to . Becausethechannelhasaminimum
totheBACKOFFstateandtryagainatalatertimechosenatrandom, pt0ropagatiRondelaylargerthanS0,alltheneighborsof startreceiving
asshowninFig.1(c). ’sRT2atsometime . Node eitherreceivRestheRT2from
Node determinesthatitsRT2wasnotreceivedcorrectlybyeither Rintheclearattime t1 >t0 Xorithearsnoiseandmustback
X
or aftxeratimeperiodequaltothemaximumround-tripdelaytoits Roffuntil t2 (cid:20)t0+(cid:13)+(cid:28).
X
zneighyborsplusturn-aroundtimesandprocessingdelaysatthenodes. If ret2cei>vest0+’s2R(cid:13)T+2w(cid:14)i+th5e(cid:28)rr+ors(cid:15)orifacollisionhappenswitha
ThelengthofRT2sandCTSsisthesameand,toensurethatnodata transmSissionfromRanodethatishiddenfrom (e.g., ),then does
R L S
notsendadatapacket;inthiscase, backsoffuntil A. PDMA
S
seconds. Otherwise, Sreceives a cleart2RT>2ta0t+tim2e(cid:13)+
Thefollowingtheoremprovidesthroughputasafunctionofoffered
a(cid:14)n+ds5e(cid:28)nd+sa(cid:15)datapacketafterwaitinSgfor seconds.However,thiscatn1
loadforPDMA.
happenonlyafter hastransitionedtoal(cid:28)isteningmode,whichoccurs
Theorem2: ThethroughputofPDMAisgivenby
attime S .
S
At titm2e(cid:20)t0+(cid:13)+(cid:15)+(cid:28) node has
S (2)
receivedthet3da=tatp2ac+ket(cid:14).+Be(cid:28)ca(cid:20)uset0 +is(cid:13)in+th(cid:14)e+BA2C(cid:28)K+O(cid:15)FFstateRuntil (cid:14)
time X ,thXerearenopacketssentfromnode S = (cid:14)+(cid:28) + (cid:21)1 +((cid:13)+3(cid:28))(cid:1)e(cid:0)N(cid:21)(cid:13)2 +((cid:13)+2(cid:28))(cid:1)e(cid:21)(cid:28)
totn2od>et0;+th2e(cid:13)re+fo(cid:14)re+, t4h(cid:28)e+da(cid:15)ta packet sent from to , must be
Proof: To analyze the throughput of PDMA as a function of the
rXeceivedfroRm intheclear. S R
rate of data packet arrivals at nodes, we assume that all nodes have
InthecasetRhat receivesanRT2intheclearbutdoesnothaveany
thesamerateofpacketarrivalsandthatanodechoosestherecipient
datapacketstosenSdto , waitsfor ,untiltime
S ofadatapacketwithequalprobability. Therefore,thearrivalofdata
.If sensesthattRheSchannelisid2l(cid:28)eatthatmomte3nt=,ittt0ra+nsm(cid:13)i+ts
packetsatagivennodeforaspecificreceiveris . Becausenodes
(cid:15)a+CT3S(cid:28).NoSdes and receivetheCTSattime .If (cid:21)
S sendRT2swhentheyobtaindatapacketstosend,Nth2earrivalofRT2s
triestotransmiRtapackLetatthesametime,acollits4io<nhta3p+pe(cid:13)ns+an(cid:28)dboKth
isalsoaPoissonwitharateof RT2spersecond.
stationsbackoff;otherwise, receivesaclearCTSandmustbackoff (cid:21)
WithPDMAwheneveranRTN2istransmittedsuccessfullyapacket
for seconds,Kwhile waits tosendanydatapacket
willalwaysfollow,eitherfromthesenderorthereceiver. Therefore,
that(cid:13)it+m(cid:14)ay+ha4v(cid:28)e.+N(cid:15)ode alwaysrecSeivesacRlearCTSfrom asnode
theprobabilityofsuccess ,isequaltotheprobabilitywithwhichan
isintheBACKOFFRstate,untiltime X S . RT2istransmittedsuccesPsfSully. Becauseallnodesareconnected,an
FXinally,thedatapacketsentfromnode t2to>tw0i+lla2ls(cid:13)o+be(cid:14)in+th5e(cid:28)c+lea(cid:15)r
RT2fromnode issuccessfuliftherearenootherRT2stransmitted
as receivesthedatapacketattime SR S and within secondws from thestart of the RT2. After thisvulnerability
iSsintheCTSstateuntilatleasttimte3 <t0+2(cid:13)+(cid:14)+4(cid:28).+(cid:15) period (cid:28)of seconds, all the nodes detect the carrier signal and act
L In the special case that we have a ste0ri+es2o(cid:13)f+RT(cid:14)2+sc4o(cid:28)lli+din(cid:15)g inthe appropriate(cid:28)ly.Accordingly,
channel,let bethetimewhenagivennode receivesthefirstRT2
packetofthet0series.Inorderforthistohappenw,allthecollidingRT2s (cid:0)(cid:21)(cid:28) (3)
mustbetransmittednolaterthan ;otherwise wouldbeable PS =e
todetecttheexistenceofanothertR0T+2a(cid:28)lreadyinthewchannel. Ifsuch According to the PDMA specification, a successful transmission
a collision occurs, node should be able to detect it no later than occursintwocases: (a)whenthepolledsenderhasadatapacketto
. w send, or (b) when the sender has nothing to send and the intended
t0+2(cid:28) 2 receiversendsaCTSsuccessfully. Theprobability, ,withwhich
IV. APPROXIMATETHROUGHPUTANALYSIS thefirstcasehappensisequaltotheprobabilitythataPnSR1T2issentin
theclear,timestheprobabilitythatthereisatleastonepacketarrival
WeanalyzethethroughputofPDMAandMACA-BI([9],[10])us-
atthepollednodedestinedtothepollingnodeduring seconds,that
ingthemodelfirstintroducedbyKleinrockandTobagi[7]forCSMA
is: (cid:13)
protocolsandusedsubsequentlytoanalyzeMACA[6]andFAMA[4].
APDccMorAdianngdtoMtAhiCsAm-oBdIe:lthefollowingassumptionsaremadeforboth The timethat it takPeSs1to=trea(cid:0)n(cid:21)sm(cid:28)(i1t a(cid:0)seu(cid:0)ccN(cid:21)e(cid:13)s2s)ful packet in this ca(4se)
1. Thenetworkisfullyconnectedandhas nodes. is equal to the transmission time for a successful RT2 and the data
2. AsingleunslottedchannelisusedforalNlpackets,andthechan- packet,plusthepropagationtimeassociatedwitheach;thatis:
nelintroducesnoerrors.
3. Allnodescandetectcollisionsperfectly. (5)
4. Eachnodehasanindependent Poissonsourceofdatapackets, TS1=(cid:13)+(cid:14)+2(cid:28)
The second case of a successful busy period happens when the
withameanrateof datapacketspersecond.
(cid:21)
5. EachnodehasatmoNstonedatapackettosendatanygiventime. polled sender does not have a packet to send and therefore it sends
aCTSpacketbacktothesenderoftheRT2enablingthenodetosend
6. Thesizeforadatapacketis secondsandthesizeofanRTR,
RT2andanCTSis seconds.(cid:14) adatapacket. Theprobability thatthisscenario happens isequal to
7. Theturn-aroundtim(cid:13)e is0. theprobabilitythatanRT2issentintheclear, timestheprobability
8. Thepropagationdelay(cid:15)ofthechannelbetweenanytwonodesis thatthepolledsenderexperiencesnoarrivalsofdatapacketsdestined
forthepollingnodein seconds;thatis:
seconds.
(cid:13)
As(cid:28)wehaveshownintheprevioussection,PDMAensuresthatno
datapacketscollidewithothersundertheaboveassumptions,andthe PS2=e(cid:0)(cid:21)(cid:28)e(cid:0)N(cid:21)(cid:13)2 (6)
sameisalsotrueforMACA-BI.
Thetimeforasuccessfuldatapacketinthiscase, isequalto
Theaveragechannelutilizationis: thetransmissiontimeforasuccessfulRT2,CTSanddaTtSa2packet,plus
the waiting timeof needed for the polled sender, plus the corre-
(1) spondingpropagation2(cid:28)delays;thatis: .
U
S= AbusyperiodalwaysconsistsofatTlSea2s=tan2(cid:13)RT+2(cid:14)an+d5th(cid:28)eassociated
B+I
propagationdelay, i.e. . IftheRT2fails,thebusyperiodlasts
where is the expected duration of a busy period, defined to be a
, where (cid:13)is+the(cid:28)time between the start of the first and
periodBoftimeduringwhichthechannelisbeingutilized; istheex-
t(cid:13)he+la(cid:28)st+RTY2s of theYbusy period and is the same as in CSMA [11].
pecteddurationofanidleperiod,definedasthetimeintervIalbetween
Accordingly,afailedbusyperiodlasts
two consecutive busy periods; and is the average length of time
duringabusyperiodthatthechannelUisusedfortransmittinguserdata
successfully. 1(cid:0)e(cid:0)(cid:21)(cid:28) (7)
TF =(cid:13)+2(cid:28) (cid:0)
(cid:21)
Ifabusyperiodissuccessfulbecausethepolledsourcehasapacket Therefore,thelengthoftheaveragebusyperiodisgivenby
tosend, thebusyperiodlasts ,whichcorresponds tothe
durationoftheRT2,thedatap(cid:13)ac+ket(cid:14)a+nd2t(cid:28)heirpropagationdelays.Al- (cid:0)(cid:21)(cid:28)
ternatively,ifthebusyperiodissuccessfulwhenthepolledsourceis B=(cid:13)+2(cid:28) (cid:0) 1(cid:0)e
silent,itlasts ,whichcorrespondstoanRTR,aCTS,adata (cid:21)
packet,theirp2r(cid:13)o+pa(cid:14)g+ati5o(cid:28)ndelays,and waittimebeforetheCTSis +e(cid:0)(cid:21)(cid:28) (cid:1)(1(cid:0)e(cid:0)N(cid:21)(cid:13)2)(cid:1)((cid:14)+(cid:28))+e(cid:0)(cid:21)(cid:28) (cid:1)e(cid:0)N(cid:21)(cid:13)2 (cid:1)(2(cid:28))
speenrito.dFirsomgivtehnebabyove,itfollowsthatth2e(cid:28)durationoftheaveragebusy =(cid:13)+2(cid:28) (cid:0) 1 +e(cid:0)(cid:21)(cid:28) (cid:1) (cid:14)+(cid:28)+ 1 +((cid:28)(cid:0)(cid:14))(cid:1)e(cid:0)N(cid:21)(cid:13)2 (13)
(cid:21) h (cid:21) i
Thelengthoftheaverageidleperiodis asinPDMA,andthelength
(cid:0)(cid:21)(cid:28) 1
1(cid:0)e oftheaverageutilizationperiodis (cid:21)
B=(cid:13)+2(cid:28)(cid:0)
(cid:21)
+e(cid:0)(cid:21)(cid:28) (cid:1)h(1(cid:0)e(cid:0)N(cid:21)(cid:13)2)(cid:1)((cid:14)+(cid:28))+e(cid:0)N(cid:21)(cid:13)2 (cid:1)((cid:13)+(cid:14)+4(cid:28))i U =(cid:14)(cid:1)PS =(cid:14)(cid:1)e(cid:0)(cid:21)(cid:28) (cid:1)(1(cid:0)e(cid:0)N(cid:21)(cid:13)2) (14)
=(cid:13)+2(cid:28)(cid:0) 1 +e(cid:0)(cid:21)(cid:28) (cid:1) (cid:14)+(cid:28) + 1 +e(cid:0)N(cid:21)(cid:13)2 (cid:1)((cid:13)+3(cid:28)) (8) Thetheoremfollowsbysubstitutingthevaluesoftheaverageidle,
(cid:21) h (cid:21) i busyandutilizationperiodsinEq.(1).
When PDMA is used, the channel is only idle for a time period 2
equaltotheinterarrivalrateofRT2s,and 1.Theaverageutiliza- C. PerformanceComparison
tiontimeatnode istheproportionoftiIm=ein(cid:21)whichusefuldataare
sent,consequentlyw, (cid:0)(cid:21)(cid:28). TocomparePDMAwithotherwidelyknownMACprotocols, we
Equation (2) follUow=sf(cid:14)ro(cid:1)mPSsu=bs(cid:14)tit(cid:1)ueting , andEq. (8) intoEq. introducethefollowingvariables:
(1). I U
2 (normalizedpropagationdelay)
(cid:28)
B. MACA-BI a=
(cid:14)
(normalizedcontrolpackets)
MACA-BIisverysimilartoPDMA,withtheexceptionthat,when- (cid:13)
b=
everthesenderpolledbyanRTRhasnopackettosendtothepolling (cid:14)
(normalizedtransmittoreceiveturnaroundtime)
"
node,nospecialactionistaken.TheperformanceanalysisforMACA- c=
BIaspresentedin[9]doesnottakeintoaccounttheprobabilitythat (cid:14) (OfferedLoad,normalizedtodatapackets)
G=(cid:21)(cid:2)(cid:14)
an RTRsent intheclear may not result inadatapacket being sent.
Withthe above notation, we calculate the normalized throughput
Accordingly,theperformanceresultsshownforMACA-BIby[9]cor-
forPDMA,MACA-BI[9],non-persistentCSMA[7],MACA[6],and
respondtothecaseinwhichthereceiverknowsexactlywhenaneigh-
FAMA-NCS[4]asshownintableI.
borhaspacketforit,andisthereforeanunattainableupperboundon
performance. Inourcomparison,weassumeafully-connectednetworktopology
Our analysis of MACA-BI makes the same assumptions used for withapropagationdelayof ; 500 and1000 bytedatapackets; a
PDMA,assumesthatanRTRhasthesamelengthasanRT2,andthat length of 20 bytes for RTRs1,(cid:22)RsT2s and CTSs for PDMA; CTSs of
anodesendsanRTRtoaneighborwhenthenodehasdatatosend. length forFAMA-NCS;achanneldatarateof1Mb/s;andzero
Theorem3: The throughput for the MACA-BI protocol, is given preamb(cid:13)le+an(cid:28)dprocessingoverheadforconvenience.
by The performance demonstrated by PDMA is much better than
MACAandMACA-BI. Theupper bound fornon-persistent CSMA,
(cid:14)(cid:1)(1(cid:0)e(cid:0)N(cid:21)(cid:13)2) (9) which assumes an ideal channel over which acknowledgments to
S = (cid:14)+(cid:28) + (cid:21)1 +((cid:28) (cid:0)(cid:14))(cid:1)e(cid:0)N(cid:21)(cid:13)2 +((cid:13)+2(cid:28))(cid:1)e(cid:21)(cid:28) pPaDcMkeAtscaoremisnegntshinorzteoronlytimwehe[n7]t,hheaosffaerseidmilloaardthisrobuegtwhpeuetnc1u0r0veanads
Proof: The probability that a successful transmission occurs is 2000forafully-connectedtopology. Thenumberofnodesinthenet-
equaltotheprobabilitythatanRT2istransmittedsuccessfullytimes workdoesnotaffectthethroughputachievedbyCSMA,FAMA-NCS
theprobabilitythatthereisatleastonedatapacketarrivalatthesender andPDMAprotocols.
forthereceiverwithin seconds,thatis, As we can see in Figures 3 and 4, for a fully-connected network
(cid:13) with500and1000bytesdatapacketsPDMAandFAMA-NCSshow
PS =e(cid:0)(cid:21)(cid:28) (cid:1)(1(cid:0)e(cid:0)N(cid:21)(cid:13)2) (10) vinerFyAsMimAil-aNrCthSroisugalhwpauytscluersvsetshainnaolrleeqxupaelritmoethnets.onTehaechtihervoeudghwpiutht
Inthiscasethedurationofthebusyperiodis .
PDMA.
InMACA-BI,afailedbusyperiodcanoccurin(cid:13)t+wo(cid:14)c+as2es(cid:28):(a)when
thereisacollisionbetweenRTRs,and(b)whenanRTRissentinthe V. CONCLUSIONS
clearbutthepolledsenderdoesnothaveadatapackettosend. The
Wehavespecifiedandanalyzedthereceiver-initiatedmultipleac-
firstcaseoccurswithprobability:
cess (PDMA) protocol. We compared PDMA with non-persistent
(cid:0)(cid:21)(cid:28) (11) CSMA, MACA, MACA-BI and FAMA-NCS, and showed that the
PF1=1(cid:0)e throughputinPDMAismuchhigherthanMACA,alwaysbetterthan
ThedurationofsuchafailedbusyperiodisthesameasEq. 7. The
FAMA-NCSandMACA-BI,andbetterthannon-persistentCSMAat
probabilityofthesecondbusyperiodscenariooccurringisgivenby
highloads. Wealsoarguedthattheaveragepacketdelayexperienced
withPDMAislessthanthatwithCSMA.AssuchPDMAisthefirst
PF2 =e(cid:0)(cid:21)(cid:28) (cid:1)e(cid:0)N(cid:21)(cid:13)2 (12) MACprotocolbasedonareceiver-initiatedcollisionavoidancemech-
and the duration of such a busy period is , corresponding to anism that outperforms MAC protocols for wirelessnetworks based
the RTR, the propagation delay, and the ti(cid:13)me+n3o(cid:28)des must wait after onsender-initiatedcollisionavoidance.Ourworkcontinuestoextend
receivingtheRTRintheclear. theanalysisofPDMAforthecaseofamultihopnetwork.
Protocol Unslottedversion
np-CSMA[7] Ge(cid:0)aG
G(1+2a)+e(cid:0)aG
MACA[6] 1
e(2b+a)G(b+a+G1+F0)+ebG[b+a2+P0(a(cid:0)F0)]+1+32a+F0+P0(a(cid:0)F0)
where 0 ebG(cid:0)1(cid:0)bG and 0 e(cid:0)bG(cid:0)e(cid:0)G(a+b)
F = bG(1(cid:0)e(cid:0)bG) P = 1(cid:0)e(cid:0)G(a+b)
FAMA-NCS 1
b+4a+1+G1+eaG(b+4(cid:3)a)
(cid:0)bG
MACA-BI 1(cid:0)e N2
(cid:0)bG
1+G1(cid:0)e N2+(b+2a)eaG
PDMA 1
(cid:0)bG
1+a+G1+(b+3a)(cid:1)e N2+(b+2a)(cid:1)eaG
TABLEI
THROUGHPUTOFSENDER-INITIATEDANDRECEIVER-INITIATEDMACPROTOCOLS
a = 0.00025; b = 0.04; c = 0.005 a = 0.00025; b = 0.04; c = 0.005
1 1
NP−CSMA PDMA NP−CSMA FAMA−NCS PDMA
0.9 FAMA−NCS 0.9
0.8 0.8
0.7 0.7
MACA−BI MACA−BI
S (Throughput)000...456 S (Throughput)000...456
MACA MACA
0.3 0.3
0.2 0.2
0.1 0.1
0 0
10−3 10−2 10−1 100 101 102 103 104 105 10−3 10−2 10−1 100 101 102 103 104 105
Offered Load: G Offered Load: G
Fig.3. 500Bytedatapackets;1Mbit/secnetworkspeed Fig.4. 1000Bytedatapackets;1Mbit/secnetworkspeed
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