DTIC ADA461856: Hop Reservation Multiple Access (HRMA) for Multichannel Packet Radio Networks

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by  Defense Technical Information Center

HopReservationMultipleAccess (HRMA)forMultichannel Packet RadioNetworks
(cid:3)
ZhenyuTangandJ.J.Garcia-Luna-Aceves
ComputerEngineering Department
SchoolofEngineering
UniversityofCalifornia
SantaCruz,CA95064, USA
ktang, [email protected]
theproblemofdesigningMACprotocolsthatuseveryslowfre-
Abstract quency hopping (i.e., an entire packet is sent in the same hop)
AnewmultichannelMACprotocolcalledHopReservationMul- asacombinationoftimeandfrequencydivisionmultiplexingof
tiple Access (HRMA) for packet-radio networks is introduced, the radio channel is very timely. Curiously, there is littlework
specifiedandanalyzed. HRMAisbasedonvery-slowfrequency- reportedonthissubject.
hoppingspreadspectrum(FHSS)andtakesadvantageofthetime TherearemanypriorexamplesofMACprotocolsforfrequency-
slottingnecessaryforfrequencyhopping.HRMAallowsapairof hopping radios, whicharetypicallybasedonapplyingALOHA
communicating nodes to reserve a frequency hop (channel) us- orslottedALOHAusingthesamehoppingsequenceforallnodes
ing a hop reservation and handshake mechanism on every hop or sender- or receiver-oriented code assignments [6, 8]. How-
to guarantee collision-free data transmission inthe presence of ever,theseapproachesassumethatradioshopfrequencieswithin
hiddenterminals. HRMAprovidesabaselinetoofferQoSinad- thesamepacketfrequentlytoachievecodedivisionmultipleac-
hocnetworksbasedonsimplehalf-duplexslowFHSSradios.We cess(CDMA).IEEE802.11[1]incorporatesaconvergencelayer
analyzethethroughputachievedinHRMAforthecaseofafully- that makes the characteristics of the physical layer transparent
connected network assuming variable-length packets, and com- to the MAC protocol. A concrete example of using very-slow
pareitagainstanidealmultichannelaccessprotocolandthemul- frequency-hopping radios is the MAC protocol used in Metri-
tichannel slotted ALOHAprotocol. Thenumerical resultsshow com’s Ricochet wireless data network [3], which assumes that
thatHRMAcanachievemuchhigherthroughputthanmultichan- eachreceiverhasitsownfrequencyhoppingsequenceandmakes
nelslottedALOHAinthetraffic-loadrangesofinterest,especially thesenderlearnthehoppingsequenceofthereceiver.Thesender
whentheaveragepacketlengthislargecomparedtoaslotsize, synchronizeswiththereceiver’shoppingsequenceandtransmits
inwhichcasethemaximumthroughputofHRMAisclosetowhat allitsdatapacketoverthesamefrequencyhoponwhichthere-
canbeobtainedwithanidealprotocol. ceiveristuned.Thedatapacketcanlastlongerthanafrequency-
hop dwell time. However, neither [1] nor [3] is exempt from
hidden-dterminalinterference.
WeintroducetheHopReservationMultipleAccess(HRMA)
1. Introduction
protocol,whichtakesadvantageofthetime-slottingpropertiesof
Becauseoftherecentaffordabilityofcommercialradiosandcon-
slow FHSS. Section 2 specifies HRMA in detail. HRMA uses
trollers based on microprocessors, multi-hop packet radio net-
acommon hopping sequence andpermitsapairof nodes tore-
works(i.e.,ad-hocnetworks)arelikelytoplayanimportantrole
servefrequencyhopsoverwhichtheycancommunicatewithout
in computer communications. Ad-hoc networks extend packet
interference. Afrequencyhopisreservedbycontentionthrough
switching technology into environments with mobile users, can
arequest-to-send/clear-to-sendexchangebetweensenderandre-
beinstalledquicklyinemergencysituations,andareselfconfig-
ceiver. A successful exchange leads to a reservation, and each
urable, which makes them very attractivein many applications,
reservedhopstartswithareservationpacketfromsenderandre-
including theseamlessextensionof theInternettothewireless,
ceiverthatpreventsothernodesfromattemptingtousethehop.
mobileenvironment.
Acommonfrequencyhopisusedtopermitnodestosynchronize
The unlicensed natureof ISMbands makes themextremely
withone another, i.e., agreeonthecurrent hop of thesequence
attractiveforadhocnetworks; furthermore, thereiswidespread
and the beginning time of a frequency hop. After a hop is re-
availability of commercial, affordable radios for the 915MHz,
served,asenderisabletotransmitdatabeyondthedwelltimeof
2.4GHz and 5.8GHz bands. Accordingly, developing medium
thereservedhop.Inthissection,wealsodemonstratethatHRMA
access control (MAC) protocols with which the nodes (packet-
guaranteesthatnodataoracknowledgmentpacketsfromasource
radios)ofad-hocnetworkscansharetheISMbandsefficientlyis
andreceivercollidewithanyotherpacketsinthepresenceofhid-
criticalforthefuturesuccessofsuchnetworks.
InISMbands,radiosmustoperateusingdirect-sequencespread denterminals.
Section3analyzesthethroughputofHRMA,anidealproto-
spectrum(DSSS)orfrequency-hoppingspreadspectrum(FHSS)
colinwhichitisassumedthatoneofmultiplesenderscompet-
[2]. ThispaperfocusesonthedesignofanefficientMACproto-
ingforareceiver isalways allowedtocapturethereceiver, and
colforad-hocnetworksbasedonFHSSradiosoperatinginISM
themultichannelslottedALOHAprotocolwithreceiver-oriented
bands.
ThemaximumdwelltimeallowedinISMbandsis400msec channel assignment (ROCA), for the case of a fully-connected
[2],whichat1Mbpsallowsentirepacketstobetransmittedwithin network andvariable-length packets. Although our analysis fo-
thesamefrequencyhop. Ontheotherhand, keepingthesender cuses on fully-connected networks for simplicity, it is relevant
and receiver synchronized on the same frequency hops while a forcomparative purposes, because HRMAdoesnot sufferfrom
packet isbeing transmittedisnot simplewhennodes moveand hidden-terminal interference, which makes the fully-connected
dataratesarehigh(1Mbps). Commercially-available radiosfor networkaworst-casescenarioforHRMAfromthestandpointof
ISMbandstodayareabletosynchronize onapacket bypacket channelreuse.
basis, but not on bit by bit basis. Given the FCC regulations Section4presentsthenumericalresultsofouranalysiscom-
for ISM bands and the characteristics of today’s COTS radios, paringthethreeprotocols;theresultsshowthatHRMAachieves
veryhighthroughputfortherangeoftrafficloadwithinwhichthe
(cid:3)ThisworkwassupportedbytheDefenseAdvancedResearchProjectsAgency networkisstable,whichcanbeenforcedinpracticewithsimple
(DARPA)undergrantF30602-97-2-0338. backoffstrategies.Section5presentsourconclusions.
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1. REPORT DATE 3. DATES COVERED
1998 2. REPORT TYPE 00-00-1998 to 00-00-1998
4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER
Hop Reservation Multiple Access (HRMA) for Multichannel Packet
5b. GRANT NUMBER
Radio 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
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 8
unclassified unclassified unclassified
Standard Form 298 (Rev. 8-98)
Prescribed by ANSI Std Z39-18
VariableDefinitions ProcedureRECEIVE() ProcedureXMIT()
=SlotLength Begin Begin
SL=FrameLength ; If(datalength )
FL=PacketDetected MHRoTrimeerPacket; 1 ThenBegin >FL
PD=TimerExpired While(HR TimFerLnotexpired ) Constructadatapacketoflength bytakingpartofthedata;
TE=LocalData Begin ^MorePacket fieldinpackFethLeader ;
LD =MaximumPropagationDelay Timer ; EndMorePacket 1
PBreogciWTTTIenfdi(mhppuirelrreerooS (PTpc)A=DR3PTr(cid:2)(^o)ceTFssELing;)lDisetleany; WITEEfhnls(hedTeinlIEBefEBles ((eLTeg)gicniDEna2ll)^P(cid:2)TAhSPeTSnIDpcVarEl)low(B)pa;AitC+;KOTFpFr()o;c IEETTfrilnmsa(dNenePMsBormue mtigotaoildnrrldaeettehdaleaaPpytdaaaact)itklTaclehittkn;heneeatehpnoafidpcekoltedoftt;ithnheepncaeocxkrrteetHshpReoanpddeerirniog da;ck0f;requency;
ThPenDBegin ReceivePacket; While( )Listen;
Receivepacket; DOCASEof(receivedpackettype) If( T)E^PD
DOCACEof(receivedpackettype) Begin ThePnBDegin
Begin DATA: Receivepacket;
Synchronizingpacket: If(DestinationID=LocalID) DOCASEof(eventtype)
Acceptthesynchronizingparameters; ThenBegin Begin
CallPASSIVE(); Passpackettoupperlayer; Moredata HRreceivedforthislink:
Default: If(lastpacket) Remov^ethedatasentfromdatabuffer;
CallSTART(); ThenBegin SendRTS;
End ; CallXMIT()atbeginningofnextslot;
End MHopotroethePcaorcrekspeotnd inga0ckfrequency; Nomoredata Ackreceivedforthispacket:
ElseBegin SendAcktosource; Removeth^edatasentfromdatabuffer;
Setthesynchronizingparametersandsendsynchronizingpacket; End If( )callBACKOFF();
CallPASSIVE(); End ElsLecDallPASSIVE();
End ElseBegin Default:
End If( )ThencallBACKOFF(); CallBACKOFF();
ElsLecDallPASSIVE(); End
ProcedureACCESS() End End
Begin Default: ElsecallBACKOFF();
SendRTStodestinationinRTSperiod; If( )ThencallBACKOFF(); End
ListenduringCTSperiod; ElseLcDallPASSIVE();
If(CTSreceivedfortheRTSsent)ThencallXMIT(); End ProcedureBACKOFF()
ElsecallBACKOFF(); End Begin
End End Calculatemaximumnumberofbackoffslots,m,
PBreogciDBendeOugriCBDEenAneuPgdArSiiCLIonEnSffgniaSs(oilHItHnlfeVRgSn(REeY;ovp(pfNe)eeinSrnrCitiyooHStnddyyc::p(nh)ec;p)heoriroHd:Rperiod inHRperiod) EndTIEEEfhnlns(eddMenIESLCBfBeliaesso(nleLegtldergiRcnniDHenaEdlRlCuP)PrEpTiAanaIhVcSgeckSnERekItcTV(ea)iSEnltalatt)(Bhn)t;hedAenCCeeKTxnSOtdHFpoRFefrC(ipo)Te;drS;iopde;riod; WBaTciecmhgoiielDBrnerdeOi (gnTigCBDERnAnteUuRogdrSEiisCLonEnA)ofgniamDsoilHNtHnlfeeoRgSn(RbeDY;oavppfcNeeeOknSrrCiotiyooMHftndfydc(:pa:)hl(;egp)0oe;rriitmohdm:;(cid:2)SL);
TheLnDcallACCESS(); ^PD If( inHRperiod)ThencallACCESS();
DuringRTSperiod: ProcedureSYNCH() DuringTRTESp^erioPd:D
Listen; Begin Listen;
BeginningofCTSperiod: Hopto ; BeginningofCTSperiod:
TIfh(eRnTBSergeicneived^DestinationID=LocalID) WHohpilteo(tfihn0eSnyenxcthfrpeeqruioedn)cydoacscyonrcdhiningftohremhaotipopninegxcphaatntegren;; TIfh(eRnTBSergeicneived^DestinationID=LocalID)
sendCTStosource; Returntocallingprocedure; SendCTStosource;
CallRECEIVE(); End CallRECEIVE();
End End
EndofCTSperiod: ElselistenduringCTSperiod;
If(( inRTSorCTSperiod) ( inHRperiod)) EndofCTSperiod:
ThenLcDallBACKOFF(); _LD^PD If( inHRperiod)ThencallBACKOFF();
ElsecallPASSIVE(); End TE^PD
End End
End End
Figure1:HRMASpecification
slot. Thefrequency on which nodes may tunetheir radios dur-
2. HRMA Protocol ingtheHR,RTSandCTSperiodsremainsthesameineachslot
HRMA is based on a common hopping sequence for the entire andvariesamong slotbyslotaccordingtothe
networkandrequireshalf-duplexslowfrequency-hoppingradios commonfrequencfyih;oip=pin1g;2s;e:q::u;eMnc;e.
with no carrier sensing to operate. HRMA can be viewed as a Aspecialslotisdefinedthatisofthesamesizeasanormal
time-slotreservationprotocolinwhichatimeslotisalsoassigned slot,butconsistsofonlyonesynchronizationperiodfixedon
aseparatefrequencychannel. for synchronization purpose. This special synchronization slfo0t
The pseudo code in Figure 1 presents the specification of followedby consecutivenormalslots,whichpassthroughall
HRMA.Wenotethatthemechanismusedtocontendforandre- the frequeMnciesinthehoppingsequence,makesupaHRMA
servefrequencyhopsinHRMAissimilarincomplexitytosuch framMe,asshowninFigure2.
simple MAC protocols as FAMA [4][7] and MACAW [5]. To
simplifyouranalysis,anon-persistentpolicyisusedforhopreser-
vations;persistentversionsofHRMAarealsopossible. CS BSHSNother
Beacons
Frame (M+1 Slots)
2.1.SynchronizingNodestoaCommonHoppingSequence S. Slot Slot
As in any MAC protocol operating with FHSS radios, time in
HRMAisslotted. HRMAuses one of the availablefrequen- f0 f0 fp3 f0 fp5 f0 fp4 f0 fp2 f0 fp1 f0 f0 fp3 f0 fp5
(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)
cies,whichwedenoteby ,asadedicatedsyLnchronizationchan- RTS Collision
(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)
nelonwhichallnodesexfc0hangesynchronizationinformationto
agree onthebeginning of afrequency hop andthecurrent hop. (cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)
Therestofthefrequenciesareorganizedinto RTS CTS DATA ACK
frequency pairs . FMor a=nyb(nLod(cid:0)e1),=t2hce
frequencyhop (ifsiu;fsei(cid:3)d);foir=sen1d;in2g;:o::r;Mreceivinghop-reserviation RTS CTS DATA fp3 DATA ACK
(HR)packets,rfeiquest-to-send(RTS)packets,clear-to-send(CTS) CS: Clock Synch Data
packets, and data packets, while frequency hop is used for BS: Beacon Synch Data
(cid:3) HSN: Hop Sequence Number HR RTS
sending or receiving acknowledgments to data pfacikets sent on fpi: Frequency Pair #i
frequencyhop .
Figure2:StructureofHRMAslotandframe
EachHRMfAislotconsistsofonesynchronizationperiod,one
HRperiod, oneRTSperiodandoneCTSperiod, eachofwhich
Whenanewnodebecomesoperational, itmustlistentothe
isused exclusively tosend or receive a synchronization packet,
synchronizationchannelforatimeperiodlongenoughtogather
an HR packet, an RTS packet, and a CTS packet, respectively.
thesynchronization informationabout hopping patternandtim-
Allthenodesthatarenottransmittingorreceivingdatapackets
ingofthesystem,sothatitcangetsynchronizedwiththesystem.
musthoptothesynchronizationfrequency andexchangesyn-
Ifthenewnodedoesnotdetectanysynchronizationinformation
chronizationmessagesduringthesynchronifz0ationperiodofeach
during that time, it finds an empty system. The new node can
broadcast itsownsynchronization informationandcreateanew information, and then hop to the next frequency hop of the
one-nodesystem. Anewnodecaneasilyjoinorcreateasystem frequenciesinthecommonhoppingpattern. M
withHRMA,becausethesynchronizationinformationisrepeated AdatapackettransmittedinHRMAcanbeofanylengthand
ineveryHRMAslot. Hence,nodesinthesameconnectedcom- the node can send multiple data packets as well. However, be-
ponentofanetwork,whichwecallgroup,aresynchronouswith causeHRMAoperatesintheISMband,adatapacketorpacket
eachother. Incontrast, nodesfromdifferentgroupsarediscon- traincannotexceedthemaximumdwelltimeallowedbytheFCC
nectedandasynchronous. [2].Thesourceanddestinationdwellonthesamefrequencyhop
LetthelengthofaHRMAslotandthesynchronizationperiod duringtheentiredatapacketorpackettrain.
ofanormalHRMAslotbe and ,respectively. Itcanbeseen When the data that need to be exchanged between sender
fromFigure3thatthedwel(cid:17)ltime(cid:17)osf atthebeginningofeach and receiver require multiple HRMA frames for their transmis-
frameis . Becausethesynchrofn0izationperiodisrepeated sion,thesendernotifiesthereceiverandthereceiversendsanHR
atthebeg(cid:17)in+nin(cid:17)gsofeachHRMAslot,theremustbeatleastone packetduringtheHRperiodofthesameslotofthenextframe.
synchronizationperiodoflength withinanyintervaloflengfth0 This informs the neighbors of the receiver that they cannot at-
.Therefore,anytwonodes(cid:17)frsomdisconnectedgroupsmust tempt to send RTSsin the HRMA slot occupied by sender and
(cid:17)al+wa(cid:17)yss have at least two overlapping time periods of length receiver. When the sender receives the HR from the receiver,
on withinanytimeperiod equal tothedurationof aHRM(cid:17)As itsends an RTStojamany possibleRTSsaddressed toitsown
framf0enomatterhowlargethetimingoffsetbetweenthedifferent neighbors, whichmay not hear the receiver. Thus, without fur-
groups is. Figure 3 shows the worst case overlapping time be- thercontention,thefrequencyhopisreservedagainbythesender
tweenasynchronoussystems.Therefore,HRMAallowsdifferent andreceiverforthefollowingHRMAframe.Bothsenderandre-
groupstomerge. ceiveraresilentintheCTSperiodoftheslot,andmoredataare
Asynchronizationprotocolbasedonalisten-before-transmit transmittedafterthatperiodoverthesamefrequencychannelof
policyforbeaconpacketssimilartothatadvocatedinIEEE802.11 theHRMAslot.Thefrequencyhopremainsreservedinasimilar
[1]canbeusedinthesynchronizationperiods.However,itwould fashion,untilthesenderrelinquishesit.
bedifficultforasynchronousgroupstomergein802.11networks, Afterthesourcesendsadatapacket, ittransitionstotheac-
because there is no equivalent to our proposed synchronization knowledgment frequencydefinedaccording tothefrequencyon
slotandfrequencyhop. which the data packet was sent, and the receiver sends an ac-
knowledgmentpacketbacktothesourceonthatacknowledgment
One frame frequency.
The different cases for access and reservation of hops are
f0 f0 f3 f0 f5 f0 f4 f0 f2 f0 f1 f0 f0 f3 f0 f5 showninFigure2.
AmoreefficientvariantofHRMAallowsthedataincluding
System A piggybacked acknowledgment toflowinbothdirectionsandes-
tablishsaduplexdatapipebetweenapairofnodes,withonenode
transmittingon andtheother on . Withthisapproach, the
(cid:3)
f2 f0 f1 f0 f0 f3 f0 f5 f0 f4 f0 f2 f0 f1 f0 f0 same hop reservfaition procedure isnfeieded whenever thedatain
System B eitherdirectionlastlongerthananHRMAframe.
Figure 3: Worst case overlapping time on synchronization fre-
quency
2.3. Correctness of HRMA
The following theorem proves that HRMA eliminates hidden-
terminalinterferenceproblems.Toprovethetheorem,weassume
thatallnodesaresynchronized,thatthereisnocaptureeffecton
2.2. Accessingand Reserving Hops anychannel,andthatanyoverlapoftransmissionsatanyreceiver
Assumingthatnodesareabletosynchronizeaccordingtoacom-
on any channel causes all packets to be lost. We assume that
mon hopping sequence, the rest of HRMA’s operation pertains
links are bidirectional, which is a requirement that stems from
tothewayinwhichnodesaccessandreservespecificfrequency
theRTS/CTSexchangeusedtoreservefrequencyhops.
hops. All nodes that are not communicating with other nodes
Aneighborofanode isanodethathasalinkto .Allthe
overreservedhopsarehoppingtogether, andweassumeanon-
neighborsofnode aredAenotedbytheset . A
persistentapproachtohopreservationinHRMA.
Theorem: HRMAA guarantees that no dNata(Ao)r acknowledge-
Whenanidlenodereceivesadatapacket totransmitbefore
mentpacketcollideswithanyotherpacketinthepresenceofhid-
theRTSperiodofagivenslothasstarted,thenodebacksoffifthe
denterminals.
HRperiodcontainsanHRpacket. Theback-offtimeisrandom
Proof: If no RTS is successful, then no data packet or ac-
andisamultipleoftheHRMAslottime,sothatthenodeisready
knowledgmentpacketissentandthusnodataoracknowledgment
toattempttransmissionatthebeginningofaslotaftertheback-
packetisinvolvedinanycollision.
off time elapses. Otherwise, if there is no HR packet claiming
Ifadestinationnode successfullyreceivesanRTSfroma
theslot,thenodesendsanRTStotheintendedreceiverandwaits
sourcenode onfrequenDcyhop inslot ,itmustbetruethat
fortheCTS,whichmustcomefromthereceiverduringtheCTS
nonodeotheSrthan in ifsktransmitmtingon intheRTS
period.WheneveranodereceivesanRTSintendedforit,itsends
aCTSbacktothesourceintheCTSperiodofthesameslotand periodofslot ;othSerwisNe,(tDhe)rewillbeacollisionfokfRTSsatthe
staysinthesamefrequencychannelwaitingforanydatapacket. destination m.Therefore,noothernodein canbeasource
IfanodethatsentanRTSreceivesnoCTSfromthereceiverin node on Dduring thefollowingHRMAfNra(mDe.) However, note
theCTSperiod,itbacksoffarandomnumberofslotsandtriesto that anyfokther node in could be or become a successful
senditsRTSagaininanotherslot. Thesourcenodetransmitsa destination onhop ifNi(tDis)not in . It must alsobetrue
datapacketifitreceivesaCTSfromthereceiver;thedatapacket that no node otherfthkan in Nc(aSn)receive a correct RTS
istransmitted inthesame frequency channel used for the RTS- addressed to it in slot D; for oNth(eSrw)ise the RTSfrom would
CTSexchange. interfere with it. Accomrdingly, no node other than iSn
Whenanidlenodereceivesadatapackettotransmitafterthe canbeorbecomeasuccessfuldestinationonhop DdurinNg(tShe)
RTSperiodofagivenslothasstarted,thenodesimplybacksoff. following HRMA frame, but it can be or becomefka successful
Thisisdonebecausesuchanodeisunabletorequestthecurrent sourceon ifitisnotin .Asaresult,duringthefollowing
slotanymore.
HRMAfrafmke, istheonNly(Dso)urceon in and isthe
AftertheCTSperiodofaslot,thenextslotstartsandallnodes
onlysuccessfulSdestinationon in fk . NTh(eDre)fore, tDheCTS
thatarenottransmittingorreceivingdatapacketshopto and
from anddatapacket(s)fromfk areNco(Slli)sionfree.
dwellon foraperiodoflength toexchangesynchronifz0ation
D S
f0 (cid:17)s
If the data packet lasts longer than a frame, the destination
sends an HR in the same (frequency) slot (slot ) of the next 3.2. HRMA Throughput
The length of HR, RTS or CTS is the same and is denoted by
frame,whichpreventsanynodein fromsmendinganRTS
, andthesizeofthesynchronization periodisamultipleof ,
on (inslot )andbecoming asNou(rDce)node. HRiscollision
(cid:13) . Thus, the slot size . For simplicit(cid:13)y,
freefkat ,becamuse istheonlydestinationon in . Af-
(gciv(cid:0)en1th)a(cid:13)tallprotocolsbeingcon(cid:17)sid=ere(dcr+ely2o)(cid:13)ntimeslottingand
ter reSceivesanHRR,itsendsanRTSonthesafmkefreNqu(eSn)cy
wouldbenefit fromthesamesynchronization solution proposed
(inSslot ), and thisprevents any node in fromcorrectflky
forHRMA,weignorethesynchronizationslotinourcomparative
receivingmanypossibleRTSon directedNfor(Sth)atnodeandbe- analysis andassume that the synchronization period of aslot is
comingadestination.Thereforef,kitistruethat istheonlysource muchlongerthanthesumofRTS,CTSandHRperiod.
on in and is the only successfuSl destination on WeuseaMarkovprocesstodescribetheoperationofHRMA,
in fk Ndu(rDing) anothDerHRMAframe. Alsonotethatnodesfikn whereeachstateoftheprocessrepresentsthenumberofchannels
N(Sb)utnotin canbecomesuccessfulsourcesandnodes beingusedtotransmitdatainaslot.Themaximumstateisthere-
iNn(S) butnotNin(D) canbecomesuccessfuldestinationson fore . ThestatetransitiondiagramfortheMarkov
Ndu(rDin)gthisfollowNi(nSg)one-frame-long periodoftime. There- chainKis=shobwN=i2ncFigure 4. Any state , , of the
ffokre,adatapacketfrom willbecollisionfreeinanysubsequent Markov chain can transit toany state k 0 (cid:20) k.<StaKte can
HRMAframe,untiltheSendofthedata. transittoallstates. i (cid:20) k+1 K
The ack packet for a data packet is sent on a different fre-
quencyofthecorrespondingfrequencypair, ;therefore,anack
(cid:3)
packetcanonlycollidewithotherackpacketsf.kHowever,asstated 0 1 2 K-1 K
above, notwosuccessful destinationsexistintheneighborhood
ofanysuccessfulsourceonthesamefrequencyhop, whichim-
pliesnoackpacketcancollidewithanyotherackpacket.
It follows from the above that HRMA guarantees that data
and ack packets are free of collision in the presence of hidden Figure4:MarkovprocessforHRMA
terminals.
2
Theprobabilitythatanynodehasdatatosendintheaccess
periodofaslot(i.e.,thesynchronizationorHRperiod)isgiven
3. Comparative Throughput Analysis by
(1)
F3.o1r.siSmypsltiecmity,MwoedaessluamnedaAfusslluym-cpontinoencstednetwork,whichcor- pa=1(cid:0)e(cid:0)c(cid:13)(cid:21)
Let betheprobabilitythat nodesattempttotransmitan
responds to a worst-case scenario from the standpoint of chan- (i)
nelreuseinHRMA,becauseHRMAensuresthatnointerference RTSinsAtakte ,wehave i
occursduetohidden terminals. Radiosarehalf-duplexandcan k
onlytuneontoonefrequencyatatime.Thereare nodesinthe
(2)
system and datachannels (frequency hops) avNailable, where (i) N (cid:0)2k i N(cid:0)2k(cid:0)i
. TMhisisthe case for a typical multi-hop packet radio Ak =(cid:18) i (cid:19)pa(1(cid:0)pa)
Mnetw>orkNoperating onthe ISMbands and using FHSSradios as
Let , theprobability thatonlyoneRTSarrivesduringthe
described in Section 1, where the number of neighbors of each
acceiss=pe1riodofaslotequals
nodeisusuallysmallerthantheavailablefrequencies.
Thechannelsareassumedtobeerrorfreeandhavenocapture
effect, so that collision of packets is the only source of errors,
arencdeimveorreletahdasntoonaecpoallciksieotnoavnedrlanpoppedacoknetsthienvsoalmveedcihnanitncealnatbea A(k1) =(N (cid:0)2k)(1(cid:0)e(cid:0)c+c2NG)(e(cid:0)c+c2NG)N(cid:0)2k(cid:0)1 (3)
receivedcorrectlybythereceiver. ThesuccessprobabilityofanRTSatanygivenstate , ,
Itisassumedthatdatapacketsarriveateachnodeaccordingto isequaltotheprobabilitythat:(a)onlyoneRTSarrivesdukrinPgStjhke
Poisonprocesswithaveragearrivalrate .Eachnodehasexactly accessperiodofaslot,(b)thecurrentchannelisnotreservedfor
onebufferforadatapacket. Thedestin(cid:21)ationofanydatapacket thefutureslot(s),and(c)theintendedreceiverisnottransmitting
fromeachnodeisassumedtobeuniformlydistributedamongall orreceivingadatapacket.Therefore,
itsneighbors.Allthenodesaresynchronizedandallchannelsare
slotted with the slot size equal to . Therefore, the total traffic (4)
(1)
loadnormalizedtoslotsizeisdeno(cid:17)tedby PSjk =Ak (1(cid:0)PRjk)(N(cid:0)2k(cid:0)1)=(N (cid:0)1)
where istheprobabilitythatthecurrentchannelisreserved
for thePfRutjukre slot(s) given that the system is in state . It can
G=N(cid:21)(cid:17)
Tosimplifyourcomparativeanalysis,weignoreanypropaga- beseenthatthisprobabilityislessthantheprobabilitykthatany
tiondelay,guardtimeoranyprocessingtime. Theseparameters otherchannelisreservedforthefuture,giventhatthesystemisin
can be easily taken into account if necessary, and their values state ,becausethedatapacketneedstolastlongeronthecurrent
arefarsmallerthanpacketlengthsinnetworksoperatinginISM channkel thanonanyotherchannel toreservethechannel. Thus
bands. BecauseIPpacketshavevariablesizes,weareonlyinter- wecanhaveanupperboundof byletting
estedinvariable-lengthdatapackets. Fortractability,weassume PRjk
thatanydatapacketistransmittedatthebeginningofaHRMA
slot andcanonly endattheend ofaslot; therefore, thesizeof k
PRjk = p
thedatapacket isamultipleoftheslotsize.Wefurtherassume M
that followsa(cid:14)geometricdistributionwithanaveragesizeof whichleadstoalowerboundofthethroughputofHRMA.This
slots(cid:14),whichimpliesthattheprobabilitythatadatapacketendsadt lower bound is very close to the actual value of the throughput
theendofaslotis .Wealsodenotetheprobabilitythata whenthenumberoftheavailablechannelsarelargecomparedto
datapacketdoesnoqt=end1=adtaslotby . the total number of nodes, which can be seen in the numerical
resultspresentedinSection4.
Throughput is defined as the thpe=ave1ra(cid:0)gequtilization of the
HRMAguaranteesthatanysuccessfulRTSleadstoasuccess-
receiver (or transmitter) per node, i.e., the average percentage
ful data transmission and the probability of a data packet com-
of timethat each node receives (or transmits) data packets suc-
pleting during a slot isq. At any given state , the
cessfully. Becauseweassumehalf-duplexradios,themaximum
throughputpernodeofanyMACprotocolis0.5. 1 (cid:20) i (cid:20) K
probabilitythatthenextstateissmallerthan isgivenby
i
i i
i j i(cid:0)j i j i(cid:0)j
(cid:11)i = PSji q p +(1(cid:0)PSji) q p 0 1 2 K-1 K
(cid:18)j(cid:19) (cid:18)j(cid:19)
Xj=2 Xj=1
(5)
i i(cid:0)1
= 1(cid:0)p (cid:0)iPSjiqp
BecausetheMarkovprocessisbalancedacrossacutbetweenany
state and ,weobtain
Figure5:MarkovprocessforidealprotocolandALOHA
k k+1
K
(6)
k
(cid:25)kPSjkp = (cid:25)i(cid:11)i probabilitythat nodes finishtransmittingatthe
i=Xk+1 endofslot isdnenotedb(y0 (cid:20)(nn).(cid:20)Thke)probabilitythat nodes
where istheprobabilityofstate and .Ifwe t haveDpakcket arrivalsandattemptmtotrans-
let (cid:25)k k 0(cid:20)k(cid:20)K(cid:0)1 m(0it(cid:20)inmthe(cid:20)neNxts(cid:0)lot2k) isdenotedby . Accordingtothis
(m)
(cid:25)i notation,wehave t+1 Ak
Qi=
(cid:25)K
(thus )afterarrangementEquation(6)becomes
QK =1 (11)
(n) k n k(cid:0)n
Ki=k+1Qi(cid:11)i (7) Dk =(cid:18)n(cid:19)q (1(cid:0)q) 0(cid:20)n(cid:20)k
Qk = k 0(cid:20)k(cid:20)K(cid:0)1 and canbeexpressedbyEquation(2)exceptthat isgiven
PPSjkp (m)
Because by Ak pa
(12)
K pa=1(cid:0)e(cid:0)G=N
instead of Equation (1). In slot , all the nodes in the system
(cid:25)i =1
canbepartitionedintofoursets: t ,whichconsistsofthenodes
ityields Xi=0 thataretransmittingorreceivingSdbataandwillnot finishinslot
,andhas members; ,whichcontainsthenodesthat
1 (8) taretransmi2ttkin(cid:0)go2rnreceivingdaStadbutwillfinishinslot ,andhas
(cid:25)K = K(cid:0)1 members; , which consists of the nodes that aretidle and
1+ i=0 Qi h2anvepacketarrSivaalsinslot ,andhas members;and ,which
andwecangetthestateprobabilitiesby containsthenodesthatareitdleandhamvenopacketarrivSalisinslot
P
,andhas members.Whencalculatingthetransition
(9)
tprobabilitiNes,(cid:0)w2ekw(cid:0)illmconditiononthenumberofmembersin .
(cid:25)k =(cid:25)KQk
For the transition from state in slot to state in slot Sd,
Finally,thethroughputofHRMAis
atleast nkodesmusttfinishselndingintsl+ot1;
thereforen^,= max,(a0n;dk(cid:0)l) nodesshouldbecomte
S = Kk=1(cid:25)kk (10) isnucscloetssfulns,ena(cid:21)ldlent^rhseimneslmom^tbet=r+sil1n(cid:0)an(dkomr(cid:0)(cid:21)n)wm^ill.nItotcabnebaveasielaebnlethfaotr,
P N receivintg+n1ewpacketswhileallSthbemSemabersin or willbe
availableforreceivingnewpackets. Therefore,tShietotSaldnumber
of nodes that will not be availablefor receiving new packets in
3.3. Throughput of Ideal Multichannel Slotted Access
Protocol slot is andthetotalnumber
For comparison purposes, weconsider thefollowing ideal mul- ofnotd+es1thaNtwnail(lkb;ena;vmai)la=ble2kfo(cid:0)rr2ence+ivimngnewpacketsinslot
tichannelslottedchannelaccessprotocol. Eachnodeisassigned
is .
auniquechannel(frequencyhop)towhichitistunedwhenitis
t+D1enoNteavb(yk;n;m)=Nth(cid:0)ep2rkob+ab2inlit(cid:0)ytmhat newarrivalsin
not transmitting, and the node tunes its radio to the channel of
slot willbesuSckc;ens;smfu(lm^in)slot giventhat,m^inslot , nodes
theintendedreceivertotransmitapacket,whichisusuallycalled
arestendingdataand ofthemtw+ill1finishand idlentodkeshave
receiver-orientedchannelassignment(ROCA).Whenanodehas
arrivals. Wecalculaten usingamapmpingconcept. To
apackettosend,itattemptstotransmitinthenextslot.Thereex-
have newsuccessfulSske;nnd;mer(sm^in)slot ,itshouldholdtrue
isttwopossibletypesofconflict. Oneisthattwoormorenodes
that m^ , and any nodte+in1 must be mapped
trytostartsendingpacketstothesamereceiveratthesameslot.
Theotheroneisthatthedestinationistransmittingorreceiving. (addrNesasve(dk);tno;omth)er(cid:21)nodm^esinsuchawaythatSeaxactly members
Weassumethatwhenthefirstconflicthappens,theidealprotocol in aremapped. Denoteby thetom^talnumber
canrandomlypickonecompetingsendertooccupythedestina- ofSsuic[hdSedsiredmappings. Ck;n;m(m^)
tion’schannelandtransmitifthedestinationisnotamongthese For , . Therefore, we
attemptingsendersandisreadytoreceiveinthenextslot;andit only neeNdatvo(kc;onns;imde)r t<hemc^aseSskw;nh;mer(em^) = 0 . If
willblockalltheattemptingsenderswhenthesecondcasehap- equals0, and mustNboatvh(kbe;n0;,mw)hic(cid:21)hmm^eans
pens. Therefore, thereisnocollisioninthechannels. Theonly tNhanta(k;n;m) . Ifm m^ equals 1, must be1;
issuethataffectsthethroughputisthepair-upofnodes. thereSfokr;en,;mal(lm^ne)ig=hbo1rsareNanvaa(ikla;bnle;man)dthus m if
WecanusetheMarkovchainshowninFigure5todescribe and if . InthefSokll;onw;min(gm^,)w=ec0on-
theoperationoftheidealprotocol,whereeachstateofthechain
ms^ide=rt0hecasSeskw;nh;mer(em^)=1 m^ =1 and .
represents the number of channels being used to transmit data
ItisalsoimmediatethNatav(k;n;m)(cid:21)m^ Nna(k;n;m)>1
packetsduringaslot.Let denotetheprobabilityofstate
. Ac(cid:25)ckordingtoourassumptions,eachk;s0ta(cid:20)te (13)
okf(cid:20)theKM;Kark=ovbcNh=ai2nccan transit to any state. A transition may Ck;n;m(0)=[Nna(k;n;m)(cid:0)1]m =(cid:2)k;n;m(0)
occurinthenextslotwhennodesfinishtransmittingoridlenodes
In general, for any , we can obtain , the
havearrivals.
total number of map0pi(cid:20)ngsiw(cid:20)hemr^eexactly given(cid:2)mke;mn;bmer(si)from
Before proceeding further we introduce the following nota-
i
tions. Assumethatinagivenslot thesystemisinstate . The
t k
aremapped,is Thesuccessfulreceivingprobabilityforanynode isequal
Si[Sd to the probability that: (a) only one packet is directeRd to node
fromitsneighborsinaslot,(b)allthecurrentpacket(s)being
i(cid:0)1 Rtransmittedtoorfromnode ifanyendduringthisslot,and(c)
m i
(cid:2)k;n;m(i)=[Nna(k;n;m)+i(cid:0)1] (cid:0) (cid:2)k;n;m(j) nootherpacket(s)willbetrRansmittedtoorfromnode during
Xj=0(cid:18)j(cid:19) (14) itsreceivingtime. Tokeeptheanalysistractable,weassRumethat
Itfollowsthat duringthereceivingtimeofanypacketat ,anynodecansendat
mostonepacket,whichleadstoanupperbRoundofthethroughput
ofALOHAwithROCA,becauseweunderestimatethecollision
(15) probability. Theprobabilitythatanidleneighborofnode has
Nav(k;n;m)
Ck;n;m(i)= (cid:2)k;n;m(i) nopacketarrivalfor in consecutiveslots,denotedby R,is
(cid:18) i (cid:19) R i Ei
Thereareatotalof possiblemappingsifthereare
m
arrivals.Therefore, (N (cid:0)1) m (cid:0)iG=N (20)
1(cid:0)e
Ei =1(cid:0)
N (cid:0)1
(16) Itfollowsthattheprobabilityof(c),when has idleneighbors,
Ck;n;m(m^)
Sk;n;m(m^)= m is R r
(N (cid:0)1)
Thetransitionprobabilityfromstate to isthengivenby 1 (21)
s(cid:0)1 s(cid:0)1 r
k l Cr = p q(1(cid:0)pa) Es(cid:0)1
k N(cid:0)2k (17) The throughput for aXsn=y1node that is not transmitting when the
(n) (m)
Plk = Dk Ak Sk;n;m(m^) packetarrivesis
nX=n^ mX=m^
Wecansolvetheglobalbalanceequationswith
N(cid:0)2 N(cid:0)k(cid:0)1 k k(cid:0)j
(22)
(m) (1) (j) j (n)
S1 = (cid:25)k Ak Bm Bk q Dk(cid:0)jCx
K
Xk=0 mX=1 Xj=0 Xn=0
(cid:25)l = (cid:25)kPlk where .
Xk=0 Anxy n=odNe(cid:0)inka(cid:0)slomt m+ujst+bene(cid:0)ith1er transmitting or not trans-
andthecondition mitting, and we can use a simple two-state Markov chain with
asthetransitionprobabilityfromthenon-transmittingstateto
K tphae transmitting state and as the transition probability for the
(cid:25)l=1 reverse direction to describqe its behavior. Solving this Markov
Xl=0 chain,wegetthetransmittingprobabilityforanynodeinaslotto
whichyieldsthethroughputofthesystemusingEquation(10). be
pa
Pt=
pa+q
3.4. Throughput of Multichannel Slotted ALOHA Therefore,thethroughputis
Prior MAC protocols based on slow FHSS assume ALOHA or
slottedALOHAaccesstothechannelandtypicallyassumeROCA
(23)
(e.g.,Metricom’ssystem[3]).WeconsiderhereaslottedALOHA
S =(1(cid:0)Pt)S1+PtqS1
withROCA.Tokeeptractable,wefurtherassumethattransmit-
tinghasthehighestpriorityandpreemptsanyreceiving. Whena
packetarrivesatanodenottransmitting,itwillbetransmittedat 4. Numerical Results
thebeginningofthenextslot. The numerical results are given in Figure 6 through Figure 11,
Foranygivennode(onaspecificfrequency)wecanconstruct whichdepictthethroughputpernode( )asafunctionofoffered
aqueuesystemwith customersand servers. The load( )withdifferentnumbersofnodSes( ),differentvaluesof
arrivalprobabilityateNach(cid:0)no1deinanyslotistNhe(cid:0)sam1easEquation averagGepacket length(APL)anddifferentNnumbers of channels
(12). Theservicetimeforeacharrivalisthepacket length. We available(forthecaseofHRMA)toreflecttheeffectofdifferent
canusethesameMarkovmodel(seeFigure5)asthatusedinthe choicesofthenetworkparametersontheperformance.
idealprotocoltoobtainthestateprobabilities ,
wherethestateisthenumberofbusyservers(cid:25)ikn;a0s(cid:20)lotk. H(cid:20)owNe(cid:0)ve1r, HRMA (M=20, N=10, APL in slots)
here we have states and the state transition probability from 0.5
APL=1000
state tostateNisgivenby: 0.45 APL=1000
k l APL=400
0.4 APL=400
k APL=100
(n+l(cid:0)k) (n) (18) 0.35 APL=100
Plk = Ak Dk APL=40
where nX=n^ put S 0.3 APL=40
gh 0.25
u
o
hr 0.2
(m) N (cid:0)k(cid:0)1 m N(cid:0)k(cid:0)m(cid:0)1 T
Ak =(cid:18) m (cid:19)pa(1(cid:0)pa) 0.15
isgivenbyEquation(11)and isgivenbyEquation(12). 0.1
(n)
DkDenoteby theprobabilitythpaat nodesaresendingpack- 0.05
(j)
etstonode gBivienthat nodesaretranjsmitting,whichcanbeen 0
expressedbRy i 0 2 4 6 8 10 12
Offered Load G
Figure6:ThroughputofHRMAwithdifferentvaluesofAPL
j i(cid:0)j (19)
(j) i 1 N (cid:0)2
Bi =
(cid:18)j(cid:19)(cid:16)N (cid:0)1(cid:17) (cid:16)N (cid:0)1(cid:17)
HRMA (M=40, APL=400 slots) Ideal protocol with ROCA (APL in slots)
0.45 0.5
0.4 20 nodes 0.45
16 nodes
10 nodes 0.4
0.35
0.35
0.3
put S 0.25 put S 0.3
gh gh 0.25
ou 0.2 ou
hr hr 0.2
T T
0.15
0.15 N=10 APL=40
N=16 APL=40
0.1 0.1 N=10 APL=400
N=16 APL=400
0.05 0.05 N=10 APL=1000
N=16 APL=1000
0 0
0 2 4 6 8 10 12 0 10 20 30 40 50 60 70 80 90 100
Offered Load G Offered Load G
Figure7:ThroughputofHRMAwithdifferentnumbersofnodes Figure9: ThroughputofIdealprotocolwithdifferentpopulation
andAPL’s
HRMA (N=10, APL=400 slots)
0.45 ALOHA with ROCA (APL in slots)
0.08
40 channels
0.4
20 channels
10 channels 0.07
0.35
0.06
0.3
S
hput 0.25 ut S 0.05 NN==1200 AAPPLL==22
oug 0.2 ghp 0.04 NN==1200 AAPPLL==44
Thr 0.15 Throu 0.03 NN==1200 AAPPLL==1100
0.1
0.02
0.05
0.01
0
0 2 4 6 8 10 12 0
Offered Load G 0 5 10 15 20 25 30 35 40 45 50
Figure8: ThroughputofHRMAwithdifferentnumbersofchan- Offered Load G
nels Figure10: ThroughputofALOHAwithdifferentpopulationand
APL’s
Figure6plotsthethroughputofHRMAwithdifferentvalues
ofaveragepacketlengthinslots,wherethesystemhas10nodes withthesameAPLalmostshowthesamethroughput,evenwith
and20availablechannels. Throughputgrowssignificantlywhen thedifferentnumberofchannelsavailable.
theAPLincreases,withthemaximumthroughputbeingcloseto Figure9andFigure10showthethroughputfortheidealpro-
the theoretical maximum value. This is because HRMA elim- tocol and ALOHA, respectively, each with different values of
inates data collisions; once successful, a large data packet can APLanddifferentnumbersofnodes.Inthispaperweassumethat
reserve the channel for a long time, which greatly reduces the thesystemshavefinitepopulationandmultiplechannels, where
overheadandimprovestheutilizationofthechannel. HRMAis pair-upisalsoanimportantissuethatcanaffectthethroughput.
more attractive with large packets or packet trains. The curves When the offered load is high, few nodes are available for re-
plottedwithdashedlinesshowtheupperboundsofthethrough- ceiving; therefore, the throughput decreases as the traffic load
put withtheassumptionthatthechannel isalwaysavailablefor increases, even for the ideal protocol. Due to the same reason,
theRTS-CTShandshake. Itcanbeseenthattheupperboundsare theperformanceoftheidealprotocolisbetterwithalargerAPL.
veryclosetoourapproximation. Incontrast,alargerAPLleadstomorecollisionsandthuslower
ThethroughputofHRMAwithaveragepacketlengthof400 throughputforthecaseofALOHA.ThethroughputforALOHA
slots and 40 available channels is displayed in Figure 7 for the isveryloweveniftheAPLissmall.
caseofsystemswith10, 16, and20nodes. Thecurvesindicate Figure11comparesthethroughputperformanceofthreepro-
thatthethroughput increasesasthenumber ofnodesdecreases, tocolsforthesystemswith10nodesand20channels.Thegraphs
which is expected. Because HRMA uses a common signaling showthatinthetraffic-loadrangeofinterestandwithlargeav-
channel,havingmorenodesinthesystemsleadstomorecollision eragepacket lengthcompared totheslotsize, HRMAperforms
onthesignalingchannel,whichreducesthethroughput. muchbetterthanALOHA.Moreover,HRMAhasthepotentialto
In Figure 8, we show the effect of changing the number of getclosetotheperformanceoftheidealprotocolwithverylarge
availablechannelsonthethroughput. Thesystemhas10nodes packetsizesorpackettrains.
and theAPLequals 400 slots. Adding channels addslittleper-
formanceimprovement. HRMAallowsidlenodestocontendfor
every unreserved hop by sending RTS’son theunreserved hop.
5. Conclusions
As long as the number of available channels exceeds the num- We have described a new multichannel MAC protocol for ad-
ber of nodes, the success probability for RTS’swill not change hocnetworks(multihoppacket-radionetworks)andanalyzedits
muchwithadditionalchannels.Again,weseethattheAPLplays performance. HRMAdynamicallyallocatesfrequency bandsto
averyimportantroleonperformance. Systemsinourexamples nodesusingacommonfrequency-hoppingpattern,suchthatdata
HRMA(M=20), Ideal and ALOHA. 10 nodes
0.5
0.45
0.4
0.35
ut S 0.3
p
gh 0.25 Ideal, APL=400
ou Ideal, APL=40
hr 0.2 HRMA, APL=400
T HRMA, APL=40
0.15 ALOHA, APL=2
ALOHA, APL=4
0.1
0.05
0
0 5 10 15 20 25 30
Offered Load G
Figure11:Throughputcomparison:HRMA,IdealandALOHA
and acknowledgements are transmitted without hidden-terminal
interference. HRMAallowssystemstomergeandnodestojoin
existing systems. HRMA’s features are achieved using simple
half-duplexFHSSradioscommerciallyavailabletoday.Ouranal-
ysisshowsthatHRMA’sthroughputperformanceissignificantly
betterthanslottedALOHAwithROCA,whichisrepresentative
ofthecurrentpracticeusingcommercialradios.HRMAcanachieve
amaximumthroughputthatiscomparabletothatoftheidealpro-
tocolinwhichareceiverisalwaysabletoreceiveonetransmis-
sionfrommultiplesenders,especiallywhendatapacketsarelarge
comparedtotheslotsizeusedforfrequencyhopping. Thishigh
throughputisobtainedwithouttheneedforcomplexcodeassign-
mentthroughaverysimplereservationmechanism.
Our work continues to analyze the performance of HRMA
in multi-hop packet-radio networks and to develop and analyze
variantsofHRMAwithimprovedperformance.
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