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DTIC ADA459345: Spatial Reuse and Collision Avoidance in Ad Hoc Networks with Directional Antennas PDF

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Spatial Reuse and Collision Avoidance in Ad Hoc Networks with Directional Antennas YuWang J.J.Garcia-Luna-Aceves DepartmentofComputerEngineering UniversityofCaliforniaatSantaCruz SantaCruz,CA95064 U.S.A. {ywang,jj}@cse.ucsc.edu Abstract—Thequestforefficientmediumaccesscontrol(MAC) However, these schemes usually force all those neighbors protocolsformulti-hopadhocnetworkshasarousedgreatinter- who overhear the transmissions between the sending and re- estinusingdirectionalantennas. SomeMACprotocolsusingdi- ceivingnodestodeferaccesstothesharedchannelduringthe rectionalantennashavebeenproposedinthepast,whichtradeoff whole handshake. This is required because any transmission spatialreuseandcollisionavoidanceviaacombinationofomni- directionalanddirectionaltransmissionmodes.Inthispaper,itis oftheseneighborscaninadvertentlycollidewiththeon-going arguedthatthebenefitofspatialreuseachievedbyaMACproto- handshake. Thus,theseschemesreducesubstantiallythepos- colthatusesdirectionalmodeinalltransmissionscanoutweigh sibilityofspatialreuseenabledbymulti-hopnetworksandcan the benefit of a conservative collision avoidance MAC protocol limitthemaximumachievablethroughput. thatsendssomeomni-directionalcontrolpacketstosilencepoten- tialinterferingnodes.Detailedsimulationexperimentsofthepop- Smartantennasoradaptiveantennashavebeenusedincel- ular IEEE 802.11 MAC protocol and its variants that make use lular networks to narrow transmitting or receiving to certain ofdirectionaltransmissionmodeinsufficientlyrandomnetworks directions while filtering out unnecessary interferences from are presented. It is concluded that, in contention-based MAC other directions and thus greater throughput can be achieved. protocolsformulti-hopnetworksinfestedwithhiddenterminals, Asaresult,someresearchers[4,5]haveconsideredusingthese theaggressivechannelaccessschemefeaturedbyall-directional transmissionsindeedoutperformsotherconservativeschemesin antennasinthedesignofMACprotocolsforadhocnetworks. termsofenhancedthroughputandreduceddelay. Alltheproposedschemesusedirectionaltransmissionmodein transmittingdataandacknowledgmentpackets,andthemajor differences among them lie in how control packets (RTS and CTS) are sent and how transmitting and receiving with direc- I. INTRODUCTION tionalantennasaremodeled. To address the inherent “hidden terminal” problem [1] in For example, Ko et al. [4] propose two schemes. In one multi-hop ad hoc networks that can degrade throughput dra- scheme, nodes use directional transmission of RTS packet matically, some coordination between a pair of sending and and omni-directional transmission of CTS packet for colli- receivingnodesandotherpotentialinterferingnodestoavoid sion avoidance. In the other scheme, nodes use both direc- collisionsismandatory.VariouscollisionavoidanceMACpro- tionalandomni-directionaltransmissionofRTSpacketsalter- tocols[2,3]havebeenproposedintherecentpast,andmostof natively. Theomni-directionalmodeisusedwhenthelocation thememployafour-wayhandshakebetweenapairofsending ofthereceiverisnotwellknownorallofthetransmittingan- andreceivingnodes. Thatis, theactualdatapackettransmis- tennasareunblocked. Itisclearthatinthesetwoschemesthe sionanditsacknowledgmentareprecededbyshortrequest-to- authors are weighing the tradeoff between the increased pos- send(RTS)andclear-to-send(CTS)packetsfromthesending sibility of simultaneous transmissions by neighboring nodes and receiving nodes respectively. The RTS and CTS control (scheme one) and the reduced possibility of collision of con- packets are used to silence those neighboring nodes that can trolpackets(schemetwo). overhear these packets. These protocols differ in the lengths Nasipuri et al. [5] also propose a different model for MAC ofcontrolpackets,whetherpacketsensingorcarriersensingis protocol enabled by directional antennas. In the authors’ used,andthechoiceofbackoffschemes. Thoughnotallpro- model, each node is equipped with M antennas whose orien- tocolscanensurecollision-freetransmissionsofdatapackets, tationscanbemaintainedallthetime,regardlessofthenodes’ generallytheyareshowntoalleviate,ifnoteliminate,thehid- movement. It is also assumed that nodes have directional re- den terminal problem and thus perform much better than the ceptioncapability,i.e.,nodescanactivatetheantennapointing carriersensemultipleaccess(CSMA)protocols[1]. to the direction of the desired source while deactivating an- tennas in otherdirections. Thus, the receiving node isnot in- ThisworkwassupportedinpartbytheDefenseAdvancedResearchProjects fluencedbysimultaneoustransmissionsfromotherdirections. Agency(DARPA)underGrantNo. DAAD19-01-C-0026andbytheUSAir Force/OSRunderGrantNo.F49620-00-1-0330. This is different from the model assumed by Ko et al. [4], in Report Documentation Page Form Approved OMB No. 0704-0188 Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. 1. REPORT DATE 3. DATES COVERED 2002 2. REPORT TYPE 00-00-2002 to 00-00-2002 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER Spatial Reuse and Collision Avoidance in Ad Hoc Networks with 5b. GRANT NUMBER Directional Antennas 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 whichantennasarealwaysactiveforreceivingandthustrans- GROUP 1 GROUP 2 missionstodifferentantennasresultinfailedreception. Inthe proposedMACprotocol,omni-directionalRTSandCTSpack- E etsarefirstexchangedbetweenapairofsendingandreceiving D B nodes and then antennas of these two nodes are directed to- A C wardseachothertoreceiveensuingdataandacknowledgment F packets. Itcanbeinferredthatcollisionavoidanceisweighed moreinthisschemebyusingomni-directionalmodeintrans- mitting control packets, though it also has the advantage that the locations of the sending and receiving nodes need not be knownbyeachotherinadvance. Theseschemeshavebeenshowntoperformbetterthanthe Fig.1. SpatialReusevsCollisionAvoidance existing omni-directional IEEE 802.11 MAC protocol on top ofwhichmostadhocroutingprotocolsarebuilt. However,the performanceevaluationsaredoneinrelativelysimple,regular hopneighbors1 ofthenodespartakinginahandshakearedis- networktopologiesanddonotprovidemuchinsightinthein- couraged from initiating handshakes with one-hop neighbors teractionbetweenspatialreuseandcollisionavoidance,where of the nodes. The effect is especially prominent when an ad theformeroptsfordirectionaltransmissionwhilethelateropts hoc network is composed of loosely coupled groups which foromni-directionaltransmission. Itisalsonotclearwhether are connected by a few “hub” nodes, as shown in Fig. 1. thecombinationofomni-directionalanddirectionaltransmis- In Fig. 1, the dashed lines show where inter-group commu- sionmodesfeaturedbytheproposedschemesindeedachieves nications take place. It is clear that, when omni-directional theoptimaltradeoffbetweenspatialreuseandcollisionavoid- RTS/CTSschemeisenforced,theinter-groupcommunications ance. Therefore, in this paper, we investigate the interaction can almost prevent other inner-group communications from betweenspatialreuseandcollisionavoidancewhendirectional taking place. Similarly, certain inner-group communications antennasareutilized. will also prohibit inter-group communications. Hence, the achievable throughput can be unduly low. The other problem Wefirstshowthattheuseofomni-directionaltransmission is that, with the increase of one-hop and two-hop neighbors, mode for control packets can largely nullify the spatial reuse itismoredifficulttogetallthenodescoordinatedwelldueto benefitofdirectionalantennasinSectionII. Wethenpropose therandomnatureofthechannelaccessandthelimitedinfor- that a scheme in which all transmissions are directional may mationavailabletoeachnode. Notknowingothernodes’con- perform better than other conservative schemes that transmit tentionstatus(busy,idle,deferringorbackingoff),nodesmay some control packets in omni-directional mode for collision havetochooseartificiallyverylargebackoffvaluestoshiftthe avoidance. InSectionIII,weelaborateontheantennaandnet- timesoftheirattemptstoaccessthechannelandthusmuchof workmodelstobeusedinoursimulations.TheninSectionIV, thevaluablechannelresourceiswastedinwaiting. simulationresultsofthreeMACschemesbasedonthepopular IEEE802.11MACprotocolarepresented. Itisshownthatthe The above discussion may lead to the conclusion that col- MACschemeinwhichalltransmissionsaredirectionalindeed lision avoidance becomes ineffective in relatively crowded achievesthebestperformanceamongthethreeintermsofen- multi-hop networks. In fact, the conclusion is supported by hanced throughput and reduced delay. Section V concludes priorwork[6,7]. thispaper. Some researchers have realized the benefit of spatial reuse enabled by directional antennas and their proposed schemes have been introduced in Section I. In these schemes, omni- II. SPATIALREUSEORCOLLISIONAVOIDANCE? directionaltransmissionofsomecontrolpackets(mostnotably, CTS packets) are unanimously used for collision avoidance. Itisapopularbeliefthatcollisionavoidanceisofparamount The effort to have a balanced tradeoff between spatial reuse importance in the design of MAC protocols for multi-hop ad andcollisionavoidanceisconspicuous. However,herewewill hoc networks due to the adverse effects of hidden terminals. show that the omni-directional transmission of CTS packets Collision avoidance schemes have been shown to alleviate, if can largely nullify the spatial reuse, even if other packets are noteliminate,thehiddenterminalproblem. Theseschemesre- transmitteddirectionally.ReferringbacktoFig.1,considerthe quire coordination from those overhearing neighboring nodes fournodesA–D.SupposeAandBhavepacketsforeachother whothenhavetodeferaccesstothesharedchannelduringthe andthesameisthecaseforC andD. Afteranexaminationof wholehandshake. this scenario, it is clear that only flows A → B and C → D However,therearepotentiallytwoproblemsassociatedwith cancoexistatthesametime,becausetheomni-directionalCTS these schemes. One is that spatial reuse is greatly reduced. Not only are the direct neighbors (or one-hop neighbors) dis- 1Herewerefertothosenodesthathaveatleastonecommonneighborwitha couraged from initiating any transmissions, but also the two- nodebutarenotdirectneighborsofthenodeasthenode’stwo-hopneighbors. from either A or C prevents the flow at the other side from In contrast with the rather regular network topologies used taking place. Even under the assumption of the capability of previously, where nodes are placed on a uniform grid, nodes directionalreception[5],thosenodeswhooverhearaCTSstill aredistributeduniformlyinplanarcircles(orrings)inournet- have to defer access to the channel for the whole handshake workmodel. Inthisway,nodesaredistributelymuchlessreg- accordingtothespecificationoftheprotocol. Thedirectional ularly, because nodes can have different number of one-hop reception capability just helps to filter out some interference neighborsandtwo-hopneighborsindifferentdirections. Tobe from others nodes that cannot receive the CTS clearly and it specific,weplacenodesinconcentriccirclesorrings. Thatis, doesnotimprovespatialreusemucheither. Thus,itisdubious given that a node’s transmitting and receiving range is R and iftheomni-directionalCTSschemeperformsmuchbetterthan that there are on average N nodes within this circular region, thebasicschemeinnetworkswithsufficientlyrandomtopolo- weplaceN nodesinacircleofradiusR,subjecttoauniform gies. distribution. Becausethereareonaverage22N nodeswithina However, in a scheme where all transmissions are direc- circleof radius2R, we place22N −N = 3N nodesoutside tional,flowsA→BorB →AcancoexistwitheitherC →D thepreviouscircleofradiusRbutinsidetheconcentriccircle or D → C and spatial reuse is maximized. Even though the ofradius2R,i.e.,theringwithradiiRand2R,subjecttothe useofdirectionaltransmissionsdoesnotforceallneighboring sameuniformdistribution. Then32N−22N =5N nodescan nodestodeferaccesstothesharedchannel,collisionswillnot beplacedinanouterringwithradii2Rand3R,andsoon. necessarilyhappeniftheseneighboringnodesdonottransmit Tofilteroutboundaryeffectsthatsomeboundarynodesface inthedirectionofeitherthesenderorthereceiver. Forexam- lesscontentionandmayattainhigherthanaveragethroughput, ple,inFig.1,nodesEandF donotdeferaccessforBandthe wejustfocusourattentionontheaverageperformanceofthe handshakebetweenthemwillnotaffectB ifthetransmission innermost N nodes. According to our experiments, conclu- beamwidthissufficientlynarrow. Obviously,theuseofomni- sionsdrawnfromacircularnetworkofradiusofmorethan3R directionaltransmissionofCTSpacketcanbequitedisruptive do not affect the conclusion to be drawn in the next section. inthesecases. Therefore,wepresentonlytheresultsforacircularnetworkof Based on the above arguments, we can reason that an all- radius3R. directionaltransmissionscheme2 mayachievebetterthrough- Toavoidsomeextremecases,weonlyusenetworktopolo- putthanthoseconservativecollision-avoidanceschemeswhen giesthatsatisfythefollowingrequirements: the benefit of spatial reuse outweighs that of collision avoid- • For the inner N nodes, each node should have at least 2 ance,whichweinvestigatehereafter. neighborsandatmost2N −2neighbors. • For the intermediate outer 3N nodes, each node should III. SIMULATIONMODELS haveatleast1neighborandatmost2N −1neighbors. Different assumptions can be made regarding the function- Tobespecific,evenwhennodesaredistributeduniformly,the alitiesofdirectionalantennas.Wemakethefollowingassump- numberoftheneighborsofanynodeinsuchnetworkscanstill tionsinourmodel: vary considerably. It is not uncommon for some innermost nodestohavenoneighborswhilesomeothernodeshavemore • Anodeisequippedwithantennassuchthat,whendirec- than3N neighbors,ifwedonotenforcesuchrequirements. tionaltransmissionwithabeamwidthofθ isused,nodes In our simulation, we investigate three typical MAC outside the beamwidth will not receive any signal from schemes. In the first one, all packet transmissions are omni- thenode. directional, which is just the scheme commonly used in tra- • When a node is transmitting with one of its antennas, it ditional MAC protocols that emphasizes collision avoidance. appears “blind” in other directions. This is also the case Forthesakeofsimplicity,wecallthisscheme“ORTS-OCTS.” when each node is equipped with only one steerable an- Though there are quite a few “dialects” of this scheme, we tenna. When a node is transmitting, it cannot sense any choose the IEEE 802.11 MAC protocol as the example. In otherchannelactivityatall. the second case, an RTS packet is transmitted directionally • Wedonotassumedirectionalreceptioncapability,which andCTSpacketistransmittedomni-directionallyandthendata is a node’s ability to receive transmissions from one di- packet and acknowledgment packet are transmitted direction- rectiononly,whiledeactivatingantennaspointingtoother ally. This is the scheme that tries to strike a balance between directionstoavoidunnecessaryinterference. collision avoidance and spatial reuse, and it is called “DRTS- Therationalebehindtheseassumptionsisthatthemajorityof OCTS” scheme. The third case is called “DRTS-DCTS,” in mobile nodes to be deployed in ad hoc networks in the near whichallpackettransmissionsaredirectional. Obviously,this future are unlikely to be equipped with multiple powerful di- schemeemphasizesspatialreuse. rectionalantennasonaparwithbasestationsincurrentcellular networks. IV. SIMULATIONRESULTS 2Despitethename’ssimilaritytoomni-directional,hereitreferstothespe- In this section, we investigate the performance of the three cificschemewhereallpacketsaretransmitteddirectionallyjustforthesakeof simplicity. schemesintroducedinSectionIII. WeuseGloMoSim2.0[8] TABLEI way of channel access to achieve spatial reuse, DRTS-DCTS IEEE802.11PROTOCOLCONFIGURATIONPARAMETERS scheme also enjoys on average less delay than the other two schemes, especially when N is large. In addition, it is also RTS CTS data ACK DIFS SIFS desirable to use narrower beamwidth in the DRTS-DCTS 20-byte 14-byte 1460-byte 14-byte 50µsec 10µsec scheme,evenwhenitdoesnotaffectthethroughputmuchfor contentionwindow slottime sync.time prop.delay thecaseofsmallN,becausenodesarelessaffectedbythesur- 31–1023 20µsec 192µsec 1µsec roundingsendingandreceivingnodesandthuscanspendless timewaiting. We also experiment with some configurations in which the as the network simulator. The traditional IEEE 802.11 MAC numberofnodesintheinnermostcircleofradiusR isdiffer- protocol just uses ORTS-OCTS scheme. We implement the entfromN andwedenoteitbyi.Bychoosingdifferentvalues other two schemes based on the existing IEEE 802.11 imple- ofi,wecanvarythecontentiondensitiesaroundthesenodes. mentation for fair comparison. Direct sequence spread spec- When i is more than N, the transmissions to and fro these trum(DSSS)parametersareusedthroughoutthesimulations, nodes loosely correspond to the inner-group communications whichareshowninTableI.Therawchannelbitrateis2Mbps. showninFig.1. WheniissmallerthanN,thenthetransmis- Inoursimulation,eachnodehasaconstant-bit-rate(CBR)traf- sions loosely correspond to the inter-group communications fic generator with data packet size of 1460-byte, and one of showninFig.1. Duetospacelimitation,Theresultsshowwe its neighbors is randomly chosen as the destination for each onlyshowtheresultsforthecasewhenN =5,i=3,5,10in packetgenerated. Allnodesarealwaysbackloged. Fig.4andmoreresultsareavailablefromtheauthorsuponre- We run simulations with N = 3,5,8 with beamwidth θ = 30◦,90◦ and 150◦. We generate 50 random topologies quest.ItisclearthattheDRTS-DCTSschemestilloutperforms undisputablytheothertwoschemes,evenwhenthecontention that satisfy the uniform distribution and then obtain averaged densitiesarenotuniform. throughput and delay for the N nodes in the innermost cir- cle ofradius R for eachconfiguration. The results areshown in Figs. 2 and 3. In these figures, the vertical lines show the V. CONCLUSION range of throughput achieved by each scheme, that is mean In this paper, we have discussed the tradeoff between spa- ± standard variance. These lines are shifted a bit for clarity. tial reuse and collision avoidance in contention-based MAC ItcanbeseenthatthethroughputoftheDRTS-DCTSscheme protocols for multi-hop ad hoc networks. It is shown that, doesnotdegrademuchinarelativelargerangeoftransmission whendirectionaltransmissionisused,itismuchbettertouseit beamwidthswhenN issmallandthethroughputoftheDRTS- throughoutthewholehandshake. Theomni-directionaltrans- OCTS scheme degrades very little regardlessof the transmis- missionofsomecontrolpacketsforcollisionavoidancewillin sion beamwidth. This can be explained as follows. When a factdefeatthepurposeofusingdirectionalantennastoachieve node has few neighbors, it usually does not make much dif- betterthroughput. Simulationresultsofsomesufficientlyran- ferenceifthenodetransmitswitheitheranarrowerorawider domnetworksvalidatethisargumentandshowthattheDRTS- beamwidth. For example, if a node has three neighbors that DCTS scheme indeed outperforms the other two conserva- are distributed around it, it can transmit with beamwidth of tive collision-avoidance schemes in terms of both enhanced either 30◦or 90◦. However, in reality, it is usually more de- throughputandreduceddelay. sirable to transmit with narrower beamwidth, because signal energyismoreconcentratedandahighersignal-to-noiseratio REFERENCES canbeachieved, thoughphysicallayerimpairmentotherthan [1] F.A.TobagiandL.Kleinrock,“PacketSwitchinginRadioChannels:Part Gaussianwhitenoiseisnotmodeledinthesimulations. Fig.3 II-theHiddenTerminalProbleminCarrierSenseMultiple-accessModes alsoshowsthatnarrowerbeamwidthtransmissionscanleadto andtheBusy-toneSolution,”IEEETrans.onCommunications,vol.23, no.12,pp.1417–1433,1975. reduceddelayintheDRTS-DCTSscheme. [2] J.J.Garcia-Luna-AcevesandC.L.Fullmer, “FloorAcquisitionMulti- The results reported in Figs. 2 and 3 clearly show that pleAccess(FAMA)inSingle-channelWirelessNetworks,”ACM/Baltzer the DRTS-DCTS scheme outperforms the other two MAC MobileNetworksandApplications,vol.4,no.3,pp.157–174,1999. [3] IEEE Computer Society LAN MAN Standards Committee, ed., IEEE schemes when beamwidth is narrow. In addition, it is also Standard for Wireless LAN Medium Access Control (MAC) and Physi- shownthattheDRTS-OCTSschemeperformsonlymarginally calLayer(PHY)Specifications. IEEEStd802.11-1997,TheInstituteof betterthantheORTS-OCTSschemeintherandomtopologies ElectricalandElectronicsEngineers,NewYork,1997. [4] Y.-B.Ko,V.Shankarkumar,andN.H.Vaidya,“MediumAccessControl investigatedhere. Thisshowsthattheunwittinguseofomni- ProtocolsUsingDirectionalAntennasinAdHocNetworks,”inIEEEIN- directional transmission of CTS packet can make almost all FOCOM2000,Mar.2000. [5] A.Nasipuri, S.Ye, J.You, andR.E.Hiromoto, “AMACProtocolfor overhearing but non-interfering hidden terminals defer access MobileAdHocNetworksUsingDirectionalAntennas,”inProceedingsof tothechannel,andthuscannullifyalmostallthespatialreuse theIEEEWirelessCommunicationsandNetworkingConference(WCNC) benefitthatdirectionaltransmissionsbringforth. Theseresults 2000,(Chicago,IL,U.S.),Sept.2000. [6] Y.WangandJ.J.Garcia-Luna-Aceves, “CollisionAvoidanceinMulti- confirmtheconjecturesmadeinSectionII. HopAdHocNetworks,”inProc.ofIEEE/ACMMASCOTS2002,(Forth It is also clear from Fig. 3 that, with a more aggressive Worth,Texas,U.S.A.),Oct.2002. Throughput comparison (N=3) Throughput comparison (N=5) Throughput comparison (N=8) 0.9 0.8 0.7 DRTS−DCTS DRTS−DCTS DRTS−DCTS DRTS−OCTS DRTS−OCTS DRTS−OCTS 0.8 ORTS−OCTS 0.7 ORTS−OCTS 0.6 ORTS−OCTS 0.7 0.6 0.5 0.6 0.5 Throughput00..45 Throughput0.4 Throughput00..34 0.3 0.3 0.2 0.2 0.2 0.1 0.1 0.1 00 1/6 1/3 Beamwidth1 /(2x p radians) 2/3 5/6 1 00 1/6 1/3 Beamwidth1 /(2x p radians) 2/3 5/6 1 00 1/6 1/3 Beamwidth1 /(2x p radians) 2/3 5/6 1 (a)N=3 (b)N=5 (c)N=8 Fig.2. ThroughputComparison–Set1 7800 Delay comparison (N=3) DDORRRTTTSSS−−−DOOCCCTTTSSS 120 Delay comparison (N=5) DDORRRTTTSSS−−−DOOCCCTTTSSS 116800 Delay comparison (N=8) DDORRRTTTSSS−−−DOOCCCTTTSSS 100 60 140 80 120 50 Delay (ms)40 Delay (ms)60 Delay (ms)10800 30 40 60 20 40 20 10 20 00 1/6 1/3 Beamwidth1 /(2x p radians) 2/3 5/6 1 00 1/6 1/3 Beamwidth1 /(2x p radians) 2/3 5/6 1 00 1/6 1/3 Beamwidth1 /(2x p radians) 2/3 5/6 1 (a)N=3 (b)N=5 (c)N=8 Fig.3. DelayComparison–Set1 00..78 Throughput comparison (N=5, i=3) DDORRRTTTSSS−−−DOOCCCTTTSSS 00..78 Throughput comparison (N=5,i=5) DDORRRTTTSSS−−−DOOCCCTTTSSS 0.04.54 Throughput comparison (N=5, i=10) DDORRRTTTSSS−−−DOOCCCTTTSSS 0.6 0.6 0.35 0.3 0.5 0.5 Throughput0.4 Throughput0.4 Throughput0.02.52 0.3 0.3 0.15 0.2 0.2 0.1 0.1 0.1 0.05 00 1/6 1/3 Beamwidth1 /(2x p radians) 2/3 5/6 1 00 1/6 1/3 Beamwidth1 /(2x p radians) 2/3 5/6 1 00 1/6 1/3 Beamwidth1 /(2x p radians) 2/3 5/6 1 (a)N=5,i=3 (b)N=5,i=5 (c)N=5,i=10 Fig.4. ThroughputComparison–Set2 [7] Y.WangandJ.J.Garcia-Luna-Aceves,“PerformanceofCollisionAvoid- SimulationofLarge-scaleWirelessNetworks,”inProc.ofthe12thWork- anceProtocolsinSingle-ChannelAdHocNetworks,”inProc.ofIEEE shoponParallelandDistributedSimulations,May1998. ICNP2002,(Paris,France),Nov.2002. [8] X.Zeng,R.Bagrodia,andM.Gerla,“GloMoSim: aLibraryforParallel

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