About the Capacity of Flat and Self-Organized Ad Hoc and Hybrid Networks

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and Hybrid Networks

Hervé Rivano, Fabrice Theoleyre, Fabrice Valois

To cite this version:

Hervé Rivano, Fabrice Theoleyre, Fabrice Valois. About the Capacity of Flat and Self-Organized Ad

Hoc and Hybrid Networks. [Research Report] RR-5977, INRIA. 2006, pp.23. �inria-00095216v2�

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inria-00095216, version 2 - 18 Sep 2006

a p p o r t

d e r e c h e r c h e

Thème COM

About the Capacity of Flat and Self-Organized Ad

Hoc and Hybrid Networks

Hervé Rivano — Fabrice Theoleyre — Fabrice Valois

N° 5977

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Unité de recherche INRIA Rhône-Alpes

Hervé Rivano

∗

, Fabri eTheoleyre

†

,Fabri eValois

†

ThèmeCOM Systèmes ommuni ants ProjetMASCOTTE ARÈS

Rapportdere her he n° 5977September200623pages

Abstra t: Ad ho networkingspe i hallengesfosterastrongresear heortone ientproto olsdesign. Routingproto olsbasedonaself-organizedstru turehavebeenstudiedprin ipallyfortherobustnessand the s alabilitytheyprovide. Ontheotherhand,self-organizations hemesmayde reasethenetwork apa itysin e they on entratethe tra on privilegedlinks. This paperpresents four models for evaluating the apa ity of arouting s hemeson 802.11 likenetworks. Our approa h onsists in modeling the radio resour esharing prin iples of 802.11 like MAC proto ols asa set of linear onstraints. We have implemented two models of fairness. The rst one assumesthat nodes have afair a ess to the hannel, while the se ond one assumes that ontheradiolinks. Wethendevelopapessimisti andanoptimisti s enariiofspatialre-utilizationofthe medium,yieldingalowerboundandanupperboundonthenetwork apa ityforea hfairness ase. Ourmodels are independentoftheroutingproto olsand providethereforearelevantframework fortheir omparison. We apply ourmodelsto a omparativeanalysisof the well-known shortestpath base atroutingproto ol OLSR againsttwomainself-organizedstru tureapproa hes,VSR,andWu &Li'sproto ols. Thisstudy on ludeson therelevan eofself-organizedapproa hesfromthenetwork apa itypointofview.

Key-words: apa ity,self-organization,radio interferen es,adho networks, hybridnetworks

ThisworkispartlysupportedbytheEuropeanCommission,proje tIST-15964.Theviewsgivenhereinrepresentthoseofthe authorsandmaynotne essarilyberepresentativeoftheviewsoftheproje t onsortiumasawhole.

∗

I3S,UNSAINRIAMASCOTTEEmail:herve.rivanosophia.inria.fr

†

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Résumé : Lesréseaux adho on entrentuneortde re her heimportantsur la on eptiondeproto oles e a es. Lesproto olesderoutage baséssur une auto-organisationont étéprin ipalementétudiés pourleurs propriétésderobustesseetdepassageàl'é helle. Cependant,uneauto-organisationpourraitpeut-êtreengendrer unediminutiondela apa itéréseaupuisqu'elle on entreletra surquelquesliensradioprivilégiés. Cetarti le présentequatremodèlespourévaluerla apa itéd'unproto olederoutagedansdesréseauxieee802.11. Notre appro he onsisteàmodéliser ommedes ontrainteslinéaireslepartagederessour esradiodeproto olesMAC telsqueieee802.11. Nousavonsimplémentédeuxmodèlesd'équité. Lepremiersupposequelesn÷udsontun a ès équitable au analradio,tandisquele se ondsuppose uneéquité entreliens radio. Ensuite, nousavons développédess enariideréutilisationspatialeoptimisteetpessimistedumédiumradio, réantrespe tivement uneborneinférieureetsupérieuredela apa ité. Nosmodèlessontindépendantsduroutage,etfournissentainsi unframeworkpertinentpourleur omparaison. Nousavonsappliqué esmodèlesàuneanalyse omparativedu proto olede routageduplus ourt hemin (OLSR)et de deuxappro hesauto-organisées(VSR et Wu &Li). Cetteétude on luesurlapertinen edesappro hesauto-organiséesdupointdevuedela apa itéréseau. Mots- lés : apa ité, auto-organisation,interféren esradio,réseauxadho ,réseauxhybrides

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1 Introdu tion

MANet (Mobile Ad ho NETworks)are spontaneous topologiesof mobile nodes where ea h of them ollabo-rate in order to propose servi es likerouting, lo alization,et . Ea h terminal an ommuni ate viawireless links without pre onditioned xed infrastru ture [20℄. Moreover, the network must fun tion autonomously, without any humanintervention. Tosend pa kets from asour eto adestination, either thedestination is in the neighborhood of the sour e or intermediary nodes must relay the pa kets througha dynami route. To rea hthis goal,thenodesmust ollaborate andex hange ontrol informationto setuproutesin thenetwork. Indeed,ea hnodeisboth lientandrouter. Be auseofthenodesmobility,radiolinksare reatedanddeleted ontinuouslyleadingtotopology hanges. So,self-adaptationofthenetworktothedynami ityisamajorissue of MANet. Ad ho networks thanksto their exibilityare promised toa largespe trum of utilization. They ouldbeusefulformilitaryoperations,allowingradio onne tionsfromvehi lestosoldierswithoutsystemati al satellite ommuni ations. MANet ouldbeusedfor res ueoperations afteraearthquakehavingdestroyedall tele ommuni ationsinfrastru tures. Moregenerally,MANet ouldbedeployedinanys enarioofspontaneous informationsharing( onferen e, lassroom,home,...).

Adho networks anbe onne tedto theInternet, viaadedi ateddevi e, the wirelessa ess point(AP), onstitutingagatewaybetweenthewiredworldandtheadho network. Thesenetworksareoften alledhybrid networks onstitutingwirelessmultihops ellularnetworks. Wethinkthathybridnetworks onstituteanatural evolutionofa essnetworks.Thesenetworks ouldbeusedbytele ommuni ationsoperatortoextend heaply the radio overing area of their ellularnetworks. Hybrid networks ould also be intensively used in house automation networks, inter onne ting personal servi es gateways at home to the Internet and their servi es providers.

Adho andhybridnetworksremainalarges ienti domaintostudy. Classi alnetworkingsolutionsmust be re- on eivedbe ause of the parti ular onstraints of ad ho networks: radio links impli ate alow band-width, radiointerferen es,links instability reatingrapidtopology hanges,alowreliabilityandpa ketlosses. Moreover, ad ho networks are mainly onstituted by embedded terminals, presenting onstraints in power-energy, CPU, memory...The network must ollaborate to nd asuitablepower-energysavingpoli y. Several problemsremaintobesolved: addressesattribution,asolutiontose ure ommuni ations,ane ient inter on-ne tiontotheInternet,amobilitymanagementproto ol,aroutingproto olpresentinghighperforman eswith an a eptable overhead...Finally,the ooding in ad ho networks presentsimportantproblems of reliability, transmissionsredundan yand ollisions: thebroad ast storm problem[18℄.

Inour pointof view, self-organization ananswerto the abovekeyproblems. Theself-organization deals withvirtualtopologiesinordertosimplifyadho topologies. Forexample,virtualtopologies anbe onstituted byaba kbone[28℄,ora ombinationofaba kboneand lusters[24℄. Thegoalistooer ontrolontheMANet. Advantagesofvirtualtopologiesare:

Totake into a ount heterogeneousnodes, avirtual topology an lassifystrongest nodes asdominants andothersasdominatees. Dominantsparti ipateinthevirtualtopologyinordertominimizetheenergy onsumption(e.g.),hierar hizingthe ontributions.

to hideneighborhood hangesusing atop-levelviewof MANet. A virtualtopologystabilizesthe neigh-borhoodandsimpliesthenetworktopology

tofa ilitatetheintegrationofMANet inwireless/wirednetworksusing therootof thevirtualba kbone. It anbeviewedasaspontaneouswireless extensionof wiredinfrastru tures. It oersanaturalwayto managehybridnetworks

to improvethes alability: be auseMANet are onstitutedby manynodes, lusters ouldgroupmobile nodesand aba kbone ould on entrateooding pa ketsto minimizethebroad aststormproblem. So itispossibletoprovides alableroutingproto ols: alo alroutingproto ol restri tedto the luster only andaglobalroutingproto olusingtheba kbone

tooeraframeworktoimplementnewservi eslikemobilitymanagement,pagingandlo alizationservi es, nativemulti astsupport,et

Be ausetheself-organizationseemstobeaninterestingwaytomanageMANetandbe ausesomeprivileged links and nodes are sele ted, the apa ity of self-organized networks should be onsidered. When routing proto ols basedon self-organization arestudied [27℄, routes are often morerobustbut present asub-optimal length. Moreover,be ausesomenodesandlinksareprivileged,aself-organizationnotwell- on eivedorexploited

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ould reate bottlene ks in the network and, nally, the apa ity would de rease. Consequently, it would be interestingtostudytheimpa tofaself-organizationonthenetwork apa ityandhowthe apa ityismodied a ordingtoavirtualtopology.

Wefo ushereontheevaluationofthe apa ityofadho andhybridnetworks,i.e. thesumofthemaximum throughput of all owin thenetwork. Through this evaluation, we propose to omparethe apa ity of self-organizedandatnetworks. Thisarti lemakestwomain ontributionstotheunderstandingofadho networks. First,itprovidesa ompletemodelingofradiointerferen esusinglo alnodesintera tions,andgiveslowerand upper bounds on the a hievable apa ity, reating a distin tion for the upper bound between the broad ast and the uni ast tra . We hose to model afair medium a ess: ea h node hasthe same probability asits neighbors to transmitonepa ket. Se ondly, it provides two denitions of thenetwork apa ity and ompare atandself-organizedroutings hemes.

Next,wewillexposetherelatedworkabouttheevaluationofthe apa ity. Besides, weintrodu e lassi al and self-organized routing solutions. The se tion 3 provides a full model of radio interferen es and nodes intera tions. Lowerand upper bounds of the lo al apa ityare also introdu ed. The se tion 6 presents the studyoftwoparti ular ases: thelineandthegrid. Inthese tion5areproposedtwodenitionsofthenetwork apa itywithtwoasso iatedevaluation fun tions. Resultsaregiveninse tion7in orderto ompare apa ity ofatandself-organizedroutingproto ols. Finally,we on ludethearti leandexposesomeperspe tives.

2 Related Work 2.1 Capa ity Estimation

. Theauthorsdenethe apa ityastheaggregatea hievable throughput. Athroughputisa hievableifea hnodeinthenetwork ansendthisquantityofpa ketsa ording to spatial and s heduling onstraints. Theauthors onstru ta Voronoi Tessellation, reating ells. Two ells an ommuni ate dire tly if they have a ommon point. In the same way, two ells are interfering if there exist twopoints interfering with ea h other. A ording to the interferen e model, the number of interfering neighbors for a ell is in onsequen e bounded. Theauthors propose as hedulings heme, and then aroute onstru tion approximatinga shortestroute in length. Letn be thenumber of nodesin thenetwork. If the nodesare randomlypla edonthe sphere,thetra is randomlydistributed,and theradio range isidenti al forea hnode,the apa itypernodeis:

Θ

1 pn · log(n)

!

(1) Evenwhen

m

purerelaynodesareaddeduniquelyto forwardthetra ofthe

n

othernodes,the apa ityis:

Θ

n + m

n

_{p(n + m) · log(n + m)}

!

(2)

However,ifnodesareoptimallypla ed, hoosingoptimallytheirradiorange,the apa itypernodeis:

O

1 √

n

(3) In onsequen e,eveninanoptimal ase,the apa itypernodede reaseswhenthenumberofnodesin reasesin thenetwork. Intuitively,thein reasingnumberofnodesallowsanin reasingspatial on urren yandfrequen y reuse of the radio medium. However,the route lengthin reasesin

O(

√

n)

. Theaggregatethroughput of the networkin reasesin

O(

√

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Theauthors presentanasymptoti study of the apa ityof adho networks,independentof aparti ular routing proto ol, or any distributed s heduling te hnology. This onstitutes its strength and its weakness: this apa ity does not ree t the radio medium sharing of 802.11 for example. Moreover, the interferen e model entered on the re eiver is dierent from 802.11for example: MAC a knowledgmentsbeingrequired, a ommuni ation isde fa to (at leasttemporary)bidire tional. Finally, the apa ity is inherentlydependent from theroutingproto ols. Optimalrouteswillimprovetheglobalthroughput,shortestroutes ande reaseit [6℄. However,the authorsdon't take into a ount anot-optimal parti ular routingstrategy. In onsequen e, although astudy of the apa ityproposed by dierent routingproto ols ould beinteresting, su h awork is notdire tlyfeasiblewiththeproposition ofGupta&Kumar.

2.1.2 How to in reasethe apa ity ?

Afterthisdramati on lusion,[7℄proposestoimprovethe apa ityofadho networks,takingintoa ountthe mobility. Thegoalistode reasetheroutelength: thelesspa ketretransmissionso ur,themorethe apa ity is improved. A sour eis astati node and forwardsits pa kets to pure relay nodes. Relaynodesare mobile and forwardthepa ket dire tlyto thedestination when itis dire tly in the radiorange. Theroute lengthis in on lusion onstant. Asa onsequen e,the apa itypernoderemains onstantin

O(1)

. However,thedelay ould bearbitrarily high, whi h is in ompatiblewith themajorityof appli ations. Moreover,the mobilityof relay nodes is supposed ompletely random, whi h onstitutes a strong hypothesis. [1℄ tries to improve the apa ity per node in limiting the end-to-end delay. However, some strong assumptions are done. First, the destination must be astati node. Se ondly, the dire tion, speed and destination of the mobile nodes must beknownby thenode itselfand its neighbors,requiringaGPS. Finally, thelo ationof thedestination must beknownapriori, a ordingto as hemenotpresentedin thearti le. In on lusion,wethink su h as heme di ulttoapplyin realisti environments.

2.1.3 The apa ity of hybrid networks

Severalarti les[13,17,31℄proposetoextendtheworkofGupta&Kumar[8℄to hybridnetworks. [13,17,31℄ usethesameinterferen emodelaspresentedin[8℄. HybridnetworksallowtodeployA essPoints(AP)in the adho network. TheseAPare onne tedviawiredlinks: they onstitutegatewaystotheInternet,orshort uts in thenetwork. Hen e,these networks will surelybelargely deployedin the future fordomesti automation, for multihops Internet onne tivity [3℄...It ould beinteresting to study the apa ity evolution: it ould be improvedinusingthewiredba kbone,orinverselyredu edbe auseofthe reationofhotspots(AP ouldre eive tra frommany lientsand onstituteabottlene k).

[9℄presentsaperforman e omparisonof ellularandmultihopsnetworks. Theauthorsproposetomeasure the network apa ity in thefollowing manner: anode hooses arandom neighbor asdestination. Thus, the tra pattern reatesaMaximalIndependentSet. Allotherresultsin[9℄don'tmentionthetra pattern,and moreover,the apa ityismeasuredthroughsimulations. Hen e,thedependabilityofthesimulator,parameters, environment ouldbeproblemati . Theresultsarethus di ultlygeneralizable.

In[13℄,nodesandA essPoints(AP)arerandomlydistributed onadisk. Theauthors onstru taVoronoi tessellation. Finally,if theadho network isrequiredto be onne tedwithoutthehelp of theinfrastru ture, the apa ityis:

O

₁

log(n)

(4) Ifthenetworkis onne ted,potentiallythroughAP, the apa ityis:

O

1 pnlog(n)

!

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This onstitutesalittleimprovementin the apa ity,althoughthe apa ityisnotyetin

O(1)

.

In[17℄,

m

AParepla edonaregulargrid( onsequentlyimprovingthe apa ity),and

n

nodesarerandomly distributed onadisk. A Voronoitessellationis herealso onstru ted. Theradio rangeis uniform among the nodes. Therouting strategy is asfollows. The sour e sends dire tly thepa ket to the destination if it is in one ofthe

k

nearest ells. Else, the pa ket is sentto the nearestAP. This AP will forwardthe pa ket toan AP in the ellof thedestination. theparameter

k

allowsto proposealoadbalan ing among thead ho and infrastru ture nodes. The authors propose to study the global aggregated throughput. Hen e, the tra of parti ular nodes ouldbenull. Su h anunfairnessis in ontradi tion withthe denition ofad ho networks.

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Theimpossibilityto ommuni ateforanode ouldbeproblemati forseveralappli ations. Let

T (m, n)

bethe globala hievabletra . Theauthorsidentifydierents alingregimein thegrowthinthenumberofAP:

m = o(

√

n) ⇒ T (m, n) = Θ

r

_n

log

n

m

2 !

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m = Ω(

√

n) ⇒ T (m, n) = Θ(m)

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In [31℄, the authors propose to extend the work of [17℄ in studying one additional s aling regime for the growthof the numberof AP, in pla ingrandomly bothnodes and AP, introdu ing fairness among thenodes andinproposinganheterogeneousandadjustedradiorangeforAP.Let

λ(n, m)

bethe apa itypernodewith

n

nodesand

m

AP.

m ≤

r

_n

log n

⇒ λ(n, m) = Θ

₁

√

n log n

(8)

r

_n

log n

≤ m ≤

n

log n

⇒ λ(n, m) = Θ

m

n

(9)

m ≤ n/log n ⇒ λ(n, m) = Θ

₁

log n

(10) The authors remarkthat in therst regime (eq. 8), ommuni ationswill uniquelyuse thead ho mode, the numberofAPbeingtoosmall. Inthethirdregime(eq. 10),the apa ityrea hesanasymptoti maximumeven whenthenumberofAPbe omesarbitrarilyhigh. This orroboratestheresultsof[13℄.

2.1.4 Evaluation ofthe apa ity through simulations

In[16℄,thethroughputofthe hainandgridtopologiesarestudied. Theauthorsshowthroughsimulationsthat 802.11 does nota hievethe maximal theoreti apa ity. Finally, they propose atra pattern whi h allows a s alable apa ity: the problem beingan in reasing route lengthwhen the number of nodes in reases, it is su ientto limitthisgrowth. Theprobabilitythatanode ommuni ateswithanothernodeatthedistan e

x

is:

p(x) =

x

α

R

√

A

ǫ

t

α

dt

With Abeingthe surfa earea,

ǫ

theminimumdistan e from asour eto adestination and

α

aparameterof the tra pattern. The apa ityis in

O(1)

onlyif

α < −2

. However,su ha lo al tra pattern annotbe applied toallappli ations.

[14℄studiesthe apa ityofadho networksthroughsimulations. All nodesgeneratesometra a ording to arate

µ

S

i

will trytosend therstpa ket ofitsbuerwhi hisintended toonenodenotblo kedduring theslot

t

. This allo ations hemeseemsforusnearfrom the802.11behavior,asexplainedfurther. The apa ityestimationis basedonsimulationswithoutanalyti alstudy.

2.1.5 APpla ementto optimizethe apa ity

[22℄ dealswith theproblemof apa ityoptimization in thepla ementofAP. Theproblem isto minimize the numberofAPa ordingtothequantityoftra requiredbyea hnode. TheauthorsproposeaLPformulation of thedierent onstraints,and greedyalgorithmsallowingthepla ementofAP. Theypropose 3interferen e models. However,themostsophisti atedmodelproposesathroughputwhi hde reaseslinearlywiththeroute length,translatingama ros opi behavior,anddeletingthelo alproblemsofradioresour esharing,important in radiotransmissions.

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2.1.6 LP formulation ofthe problemof apa ity

In [11℄, lp helps to model the apa ity of ad ho networks. The authors fo us on the apa ity when the topology and the tra workload are given, whi h is theproblem wetreat. TheLP formulationmodels the apa ityproblemasamultiowsproblem. However,the omplexityofsu haformulationresidesinthe apa ity estimationofea hedge. Hen e,theauthorsproposealowerandanupperbound. A oni tgraphis onstru ted fromtheinitialgraph: avertexisasso iatedtoea hedge,andthereexistsoneedgeinthe oni tgraphbetween twoverti esifthe orrespondingedgesintheinitialgraphareinterfering. Themodelofinterferen esproposed by the authors take into a ount the Signal to Noise Ratio. The transmission from

u

to

v

is su essful if

SN R

uv

> threshold

, the thresholdbeingdependent of thenetwork ard. In the noiseis taken into a ount theambientnoise,andthesignalofothertransmittersre eivedin

v

. Inthelowerbound,theauthorsestimate that the maximum throughput is a hieved when a s heduling is ontained in an independent set. A linear ombinationof s hedulingsof edgesthat lie in anindependentset is alsoa hievable. Theauthors proposeto ndseveralindependentsetsandtoauthorizeatthetime

t

onesingleindependentset. The apa ityallo ated tooneedge

e

isthesumofa tiveindependentsetsinwhi hitappears. InafairMAClayer,ea hnodere eives abandwidth proportionalto thenumberof itsneighbors tryingto a essto themedium. In[11℄ theauthors proposetomodelanunfairMAClayer: alltheMISare onsideredequiprobable,althoughinafairMAClayer, the probability of sele tion of a MIS depends on the nodes whi h onstitute it and theirorder. We will see further that our approa h takesinto a ountsu h adistributed fair medium sharing, ree tingthe desirable intera tions ofadistributedMAClayer.

[15℄proposesas hedulings hememaximizing thethroughputfromagroupofsour esto agroupof desti-nations. Thearti ledealswithseveralinterferen esmodels:

Transmitter model: anode

u

an ommuni atewith anode

v

ifnonode

w

exists nearerthan

(1 + ∆) ·

(range(u) + range(w))

from

u

. Theradiorange anbeheterogeneousamongthenodes Proto olmodel: theinterferen emodelof[8℄

1

and

e

2

areinterferingwithoneedge

e

,the apa ityissharedamong

e

,

e

1

and

e

2

. However,

e

1

and

e

2

ouldperhapstransmitpa kets simultaneously. Our apa ityestimationproposesanerevaluationof thelo alresour esharingin studyingmorepre iselytheinterferen eintera tionsamongthe2-neighborhoodof anode. Finally,theauthorsproposeaninterestingmetri to modelthefairnessinadho networks: theylimit theratiooftheminimalthroughputandthemaximalthroughputinthenetworkbya onstant. Thisallowsto limitthedis riminationofsomeows.

2.2 Routing proto ols

Routingproto olsarevery loselyrelatedtothe apa ityofadho networks.A ordingtothesele tedroutes, anetwork willnota hievethesamethroughput. Ifaproto olsele tsshortestroutes in hops,thethroughput will notbemaximal. Oppositely,if aproto ol dis oversroutesin order todistribute theloadin thenetwork, avoidingtheformationof hotspotsand bottlene ks,theglobal throughputwillbeimproved. We presenthere ashortpanoramaof lassi alroutingproto olswhi hareusedinadho networks.

2.2.1 FlatApproa hes

Routing is one of the major issue in ad ho networks: a good delivery ratio with a low delay and overhead must bea hieved. Hen e,manypropositionsweredone[12, 21,5℄. Twomajorapproa heswereproposed: the rea tiveandtheproa tiveproto ols.

In the proa tive approa h, a node knowsa priori aroute toward ea h other node in the network. If the whole topology is known, it an ompute optimal routes using the Dijkstra algorithm for example. Su h a solution ouldbeinterestingif anode ommuni ates with severaldestinations, hangingfrequentlyalong the

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time. Moreover, the delay is redu ed and optimal routes ould be omputed a ording to several riteria (hops, ongestion,...). However, proa tive proto ols require the periodi al ooding of topologypa kets. As wesaid, oodings ausequi kly thebroad aststormproblem: the medium isheavilyloaded, many ollisions o ur...OLSR [5℄proposes asolutionto optimizethe ooding, theMulti Point Relays: anode hooses aset of 1-neighbors overingentirelyits2-neighborhood. Onlythese sele ted1-neighborsareauthorizedtoforward thetopologypa kets omingfromthisnode. Nevertheless,theoverheadremainsimportant.

Inthe rea tiveapproa h, anode does notknowinitially any route. It tries to dis overa newroute only whenneeded,ondemand. InAODV[21℄,anodewhi hwantstosendadata pa ketandwhi hdoesnothave aroutetowardadestinationsendsaRoute Request. Thisrequestisoodedinthenetwork: ea hnodewhi h re eivesthe pa ket forwardsit in broad ast. Any node whi h knowsaroute to thedestination (in the worst ase the destination itself) an send a Route Reply,forwardedalong the inverse route. Hen e, the rea tive proto olsrequireadelaytosetuptheroute,beforesendinganydata pa ket. However,theoverhead ouldbe redu edifanodehasonlyafew orrespondingnodes. Floodingbeingherealsousedmassively,thebroad ast storm ano urinthesameway. Someme hanismsmustbeproposed tolimittheimpa tofsu haooding.

Tomodelthe behaviorof aatapproa h,we onsider OLSR asa representativeproto ol. Sin e weuse a simplied representationofaroutingproto ol,onlysomespe ial hara teristi sareuseful: theshortestroutes omputedbyOLSRareextra tedfromthetopologyandtheaverageoverheadpernodeismeasuredandinje ted in ourLP formulation,asdes ribedlater.

2.2.2 Self-organized approa hes

Self-Organization throughthe onstru tion and themaintenan e of a virtualstru ture is an important topi in ad ho networks [23, 24, 28℄. A virtual stru ture onsists in onstru tinga virtual topologyon the radio topology: ea hnode ontrolstheidentityofitsvirtualneighbors,beingasubsetof itsradioneighbors. Inthe sameway,somelinksarenotused whereasoverareprivileged.

[28℄ proposes to sele tsome nodesto a t asba kbonemembers. The ele tionpro ess is ompletely lo al, reating a negligible overhead. This ba kbone ould be used for the ooding optimization: a node sends a pa ketinbroad ast,andonlyba kbonemembersareallowedtoforwardthispa ket. Hen e,thegainofsu ha stru ture forooding is

n

|BACKBONE|

,

n

beingthenumberof nodesin thenetworkand

BACKBON E

being theset ofba kbonenodes. A nodeisde lareddominatee, i.e. ba kbone lient,ifa onne tedset ofneighbors with an higher weight onstitutes a dominating set of its whole neighborhood. Else, it is dominator. The weight anbe basedon address,degree,energy...The ardinalityof thisCDS is learlynotthe ardinalityof the MinimumConne tedDominating Setofthe graph. However,this proposition isagood trade-o between ardinalityandoverhead. [30℄presentsaroutingproto olforsu hastru ture: anodeforwardsitsdatapa ket to the nearest ba kbone member. Then, a lassi alrouting proto ol is exe uted on the ba kbone topology. However, the ba kbone ould onstitute perhaps a bottlene k in the network,and more importantly su h a routings hemeisnotparti ularlyadapted tothevirtualstru tureorganization.

[24℄presentsavirtualstru ture omposedbybothavirtualba kboneand lusters. Theba kboneallowsto optimizeinformationoodingsandto reateadistin tionbetweenthe lientsandtheba kbonemembers,a ting asmasters. Clusters grouptogethernodesgeographi ally lose. These lustersrepresentexibleservi esareas, withoneleaderperarea,the lusterhead. In on lusion,su hastru tureself-organizesthenetworkandsimplies further servi esdeploymentlikerouting, addresses attribution...Distributed pro edures for onstru tionand maintenan e were proposed to adapt automati ally the stru ture to the topology hanges. Moreover, the algorithmsareself-stabilizing[25℄.

VSR [27℄ is arouting proto ol for ad ho networks adapted to su h a virtual stru ture. It is based and designedtodemonstratethataself-organizationisusefulto routepa kets. A nodeknowsroutesinits luster, usingaproa tiveproto olinsidethe luster. Oppositely,ifanodemustrea hadestination outsideits luster, a route is dis overedrea tivelyusing thevirtual ba kboneonly. A route is in this ase onstituted of alist of lusters id., stabilizing the route. The ba kbone is useful to optimize the ooding aused by the route dis overing. Hen e, someedges arenotused fortheooding. We proposehereto quantifytheimpa t ofthis topologyredu tion.

[26℄presentsaroutingandlo alizationproto olforhybridnetworks. Inhybridnetworks,theAP onstitutes thesingledestination: nodeswantto ommuni ateuniquelywithhosts intheInternet. Su h aroutings heme benetsfromavirtualba kbone.Inupload,aproa tiverouteisknownaprioritowardtherootoftheba kbone, the AP. In download, the AP andis overrea tivelya route toward one of its lients, the virtualba kbone helping to minimizetheimpa t ofooding. Moreover,agratuitousinverse routeis reatedon theywhen a nodeinitiatesa onne tiontotheInternet. Hen e,theoverhead ofrea tiveroutedis overingwillremainvery

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low. Besides,asanextension,aroutings hemeis proposedto routepa ketsdire tly inadho mode, without passingthroughtheAP.

As a virtual topology is a subset of the radio topology maintaining the same radio range, it ould be interestingto studythe apa ityasso iatedto self-organizationstru tures. Toevaluatetheimpa tofthe self-organizationonthe apa ity,westudyVSR[27℄,somom[26℄andWu&Li[30℄approa hes. Morepre isely,only a few hara teristi sof theproto olsare usefulin our models: theroutes a tually omputed andthe average overheadasso iatedtoea hnodein thenetwork.

3 Hypothesis

Inthisse tionweintrodu etwomodelsofradioresour esharingforwirelessieee

802.11

-likenetworks. Unlikeotherapproa hesdes ribedinSe tion 2,ourmodelsaimat evaluating the apa itythat isavailable to thenodesforaninput ouple(network,routingstrategy).

Morepre isely, adis rete-eventsimulationpro essprovidesfor theinputdata ofourmodels: thenetwork topology,theroutesdened bythe hosenroutingproto ol,andtheratesofthe ontroltra whi hislo ally broad asted byea hnodetotheirneighborhoods.

Eventually,ourapproa hisbasedonthefollowingkeystatements:

Theradioresour eavailabletoanodedependsonthea tivityofitsneighborsandontheMACproto ol. Wefo usona knowledgedproto ols(and onsequentlyto bidire tionallinks).

Theseresour esharingpro essesindu elo alized setsof onstraintsonthebandwidthavailable forea h node. Thepessimisti andoptimisti modelsmainlydierbythese onstraints.

We onsidertheendtoendtra asnetworkowsthatindu eloadonthelinksthey ross,hen e network-wideglobal onstraints. Thisglobalviewofthenetworkspares onsideringea hdatapa ketindividually, resultingin anaggregated,highlevelviewofthedatatransportation.

Combining global and lo al onstraints yields a linear model for the transport apa ity of the whole network.Dierentnotionsof apa itymightbedened,asdetailedbelow,dependingonthe hara teristi s ofthenetworkthat isstudied.

Thelinear onstraintsmayexploit ombinatorialandmathemati alresultsonwirelessnetworks. Mostof theseresultsarebasedongraphtheoryandsto hasti analysis,andallowtosavethousandsofpa ket-level simulationiterations.

Ourlinear programingmodels t the generi form des ribed aslp 1. Radioresour esharing onstraints aredened forea hnode. Thedataowload onstraintsaddedforea hroutedeneglobal onstraintsonthe transport apa ityof thenetwork.

Thesetof theroutes isgivenas

P = {p = (s, u

1 , . . . , d)}

,with

s

beingthesour e,

d

thedestination, and

u

i

the

i

th

intermediary nodein thepath. Theobje tivefun tion givesthe apa itythat wewantto evaluate. Tra managementequationsdes ribetheowsthatare tobe arriedbythenetwork whendata aresenton apath

p

.

Linear Program 1(Generi model)

Maximize Obje tive fun tion onP Subje t to Resour esharing onstraints

∀

node u

around

u

Tra managementfor p

∀

path p

Inthefollowing,werstdes ribesomehypothesisandnotations. Then,wepresentasetofresour esharing onstraintswhi hgivesapessimisti modeloftheMAClayerbehavior,resultinginalowerboundontheoverall apa ityofthenetwork. Finally, wegiveanoptimisti model,hen eresultinginanupperbound. Thismodel isbasedon ombinatorialandsto hasti onsiderationsontheMAClayerbehavior.

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3.1 Common hypothesis and notations

Inordertodevelopalinearmodel oftheradioresour esharing,weneedtoassumesome lassi hypothesison theMAClayer. Moreover,weassumeatypi al lient/servertra model,asfollows:

1. Perfe tradio hannel: weassumethat themedium deliversa onstantbandwidthand doesnot orrupt datatransmissions.

2. Ideal MAC layer: there are no ollision, the bandwidth an be optimally used, and the probability to a esstothemediumisuniform.

u

through a lo al broad astpreventing all nodes within2hopsof

u

(2-neighbors)fromsendingorre eivinganykindoftra .

Weareusing thefollowingnotations:

bwis the availableradio bandwidth. This givesthemaximumamountof data that anbe sent by one terminal.

f (p)

isthethroughputof thedatasentonthepath

p

.

Let

u

beanode.

T (u)

isthetotalamountoftra sentby

u

:

T (u) =

P

v∈Γ(u)

T (u, v) + T

c

(u)

with

Γ

k

(u)

isthe

k

-neighborhoodof

u

,i.e. thesetofthenodesatmost

k

hopsfarfrom

u

.

istheuni asttra onthephysi allink

(u, v)

.

T

c

(u)

isthebroad asttra for ontrolandtopologymaintenan esentby

u

toitsneighborhood. Notethatitisstraightforwardtowritethetra management onstraintsoflp 1fromthe ompositionof

T (u, v)

.

4 Models of radio resour e sharing

Weproposetwomodelsofradioresour esharing: thenode-orientedfairness,andthelink-orientedfairness. In therstmodel, ea hvertexwhi htriesto a esstotheradiomediumre eivesthesame apa ity. Thismodels well the lassi alMAClayer proto ols. ieee 802.11 introdu esa random ba k-o delay for thenodeswhi h wantto a esstothemedium. Inoptimal onditions,allthenodeswill havethesameprobabilityto havethe medium. Inthelink-orientedfairness,ea hradio linkin aninterferen eareawillre eivethesamequantityof apa ity. A ordingtous,this allowstoavoidbottlene ks: somenodeshavemanylinks,and mustforwardan important quantity of tra . If these nodes re eivea apa itynot proportional to the number of neighbors, theywill onstituteabottlene k.

For ea h model of fairness, we propose apessimisti radio resour esharing onstituting alowerbound of the apa ity,andanoptimisti radioresour esharing onstitutinganupperbound.

4.1 Node-oriented fairness

4.1.1 A pessimisti resour e sharings enario

Alowerboundinglinearprogramisobtainedwhenlo alradioresour esharing onstraintsmodelapessimisti behavioroftheMAClayer. Indeed,twosimultaneous ommuni ations(A

→

B) and(C

→

D)area hievableonly if(A,C),(A,D), (B,C)and(B,D)arenotneighbors. A2- ontentionexists.

Thus, a pessimisti resour e sharing is a hieved if the transmission of one node is blo king all its 2-neighborhood (g. 1). If the enter or one of its 2-neighbors transmits a data pa ket, no other node in the 2-neighborhood ofthe enter isallowedto send pa kets. Tomodel anode-orientedfairness, thesame a-pa ityis allo atedto ea h 2-neighbors ofthe enter. Naturally,thisrepresentsaworst ase,sin eforexample the ouples(A,B)/(D,E) or(K,B)/(H,I) an ommuni atesimultaneouslyinthegure1.

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Figure 1: The2-Neighborhoodofonenode

One annoti e thatstopping anyradio a tivityin ludes refusinganyin oming onnexion request,sin eit requires tosendana knowledgmentforthere eivedpa ket, reating ollisions.

Applyingtheworst aseof ontroltra todata ommuni ationsleadstoapessimisti MAClo albehavior asfollows. Letbeanode

c

, alledthe enterof its2-neighborhood.

Theradiobandwidthisuniformlydistributed betweenallnodesin potential ontention: the enter

c

and itswhole2-neighborhood,

Γ

2 (c)

:

∀c, ∀u ∈ Γ

2 (c),

T (u) ≤

BW

∆

2 (c)

(11) Note,thatforea h enter

c

,asetof

∆

2 (c)

equationsisgiven. In onsequen e,the apa ity

T (u)

allo ated toanode

u

is onstrainedby

∆

2 (u)

equations(oneforea hpossible enter).

Inthe apa ityallo atedtoonenode,allthe ontroltra andtheuni asttransmissionsmustbe s hed-uled. Additionally,anodeallo atesanequal apa ityto ea hofitsneighbors:

∀u, ∀v ∈ Γ(u) − {u},

T (u, v) ≤

T (u) − T

c

(u)

∆(u) − 1

(12)

Theequationset(12)modelsthewayea hnodemanagesitsavailablebandwidth,whileset(11)modeltheway theradiomedium apa ityissharedamongthenodes.

Finally,we anremarkthattwonodes an senddatasimultaneouslyonlyiftheyaresu ientlydistant,at least 3hops, and aless loaded node is given thesame bandwidth than afully loaded one. This set of lo al onstraintsyieldslp 2,whosesolutionslowerbound thetotalamountoftra supportedbythenetwork. Linear Program 2(Pessimisti model)

Maximize Obje tivefun tion onP Subje t to Equation set(11 ) node , the enter Equation set(12 )

∀

node

u

Tra managementfor p

∀

pathp

4.1.2 Anoptimisti resour e sharings enario

The pessimisti radio resour esharingmodeltends to over-estimatethe interferen es. Some ommuni ations ould be possible in a realisti proto ol, but are forbidden in our model. Hopefully, many proto ols, like ieee 802.11, a hievea better repartition. All the 2-neighborhood is not blo ked. Forexample, in g.1, the

(15)

u

′

wantstosendapa ket. If

u

′

isneitherneighborof

u

norof

v

.

u

′

ansenda pa ket. Butitmust hooseadestination

v

′

whi hisnotneighborof

u

or

v

. Wemodelthemediumasa entral entitywhi hallo ates apa itytoea hedge,andavoidinginterferingedgestotransmitpa ketssimultaneously. This hypothesisisstronglylinkedtothe ombinatorial on eptofindependent set.

Indeed,su ha ontention-free ommuni ationsetisanindependentset,maximalforin lusion,ofthegraph

L

1,2

(L (G

c

))

,dened asfollows:

G

c

isthegraphofthe2-neighborhoodof

c

.

LG = L(G

c

)

is thelinegraphof

G

c

,thatis thegraphwithonevertexperar of

G

c

,andanedgebetween anytwoverti eswhose orrespondingar sareadja ent.

L

1,2

(LG)

is the graph with the same verti es as

LG

, and an edge between any two neighboring or 2-neighboringverti es(its2- losure).

Independent verti es (i.e. pairwise non adja ent verti es) of

L

1,2

(L (G

c

))

orrespond to ontention-free ommuni ations. An in lusion-wise maximal independent set is therefore an in lusion-wise maximal set of ommuni ationsthat anbea tivatedsimultaneously.

Eventually,theMAClayera hievesafair sharingof thebandwidthamongthemaximal independentsets. fairnessofthenodesmustberespe tedforthissharing. Let

BW (I)

bethebandwidthgiventotheindependent set

I ∈ I

, the set of all maximal independent sets of

L

1,2

(L (G

c

))

.

BW (I)

is proportional to

P (I)

, the probabilityof

I

tobesele ted,andthebandwidthin theneighborhoodof

c

issharedasfollows:

BW (I)

=

P (I) ·





BW − T (c) −

X

u

∈Γ(c)−{c}

T

c

(u)





⇒ BW ≥ T (c) +

X

I

∈I

BW (I) +

X

u

∈Γ(c)

T

c

(u)

Thetotalbandwidthallo atedtoa ommuni ationlink

(u, v)

isthesumofthebandwidthallo atedtoea h independentsetin luding

(u, v)

:

T (u, v) ≤

X

I

∋(u,v)

BW (I)

T (u, v) ≤





BW − T (c) −

X

x

∈Γ(c)−{c}

T

c

(x)





X

I

∋(u,v)

P (I)

Moreover,

P

I

∋(u,v)

P (I)

isexa tlytheprobabilityforthe ommuni ationlink

(u, v)

tobea tivatedbythe anal. Thisquantityishen edenoted

P (u, v)

in thefollowing.

∀(u, v) ∈ Γ

2 (c) − {c},

T (u, v) ≤





BW − T (c) −

X

x

∈Γ(c)−{c}

T

c

(x)





P (u, v)

(13)

(16)

Unfortunately,onarbitrarynetworktopologies,

P (I)

and

P (u, v)

annotbe omputedunlessthewholeset

I

is known, and

I

has an exponential size. We therefore build a sto hasti estimation of

P (u, v)

, denoted

f req(u, v)

in thefollowing.

These frequen ies

f req(u, v)

mustabsolutely takeintoa ountthefairness amongthenodes. Wepropose in onsequen ethefollowingalgorithmto onstru tanindependentset:

Whileat leastonenotblo kednodeexists,takerandomlyone,say

u

hoserandomlyoneneighbor

v

of

u

whi hisnotblo ked

If

v

exists,a tivatethe ommuni ation

(u, v)

andmarkalltheneighborsof

u

and

v

asblo ked else,mark

u

asblo ked

Ifthisalgorithmisrepeated

n

4.1.3 Flexibilityof the models

We use thetransmitter-re eivermodel for therepresentation ofinterferen es [15℄: twolinks anbe a tivated simultaneouslyiftheyareat least2hopsfarinthelinegraph

L (G

c

)

. However,ourapproa hisgeneri forany otherinterferen emodel. Inthelowerbound,we an onstru ttheset ontainingonenode

C

andallthenodes whi h aninterfere withitstransmissions. Thelowerbound willdistribute thesame apa itytoea hnodein this set.

Inthesameway,theupperbound ouldbe onstru tedwithanyinterferen emodel. Thelinegraph

L (G

c

)

willsimplyberepla edbyany oni tgraph(twoedgesareneighborsina oni tgraphiftheyareinterfering). Twoedges anbesimultaneouslya tivatediftheyarenotneighborsinthe oni tgraph. Thus,in omputing frequen ies

f req(u, v)

,anode

n

is onsideredasblo kedifnoedge

(n, x)

exists su h that

(n, x)

and

(u, v)

are notneighborsin the oni tgraph.

Inthe previousmodels, we hose to present onlythe transmitter-re eiverinterferen emodel for asakeof larityfortheexpli ations.

4.2 Link-oriented fairness

Here arepresentedlowerandupperboundswithafairnessorientedonedges. Insteadofdistributing anequal apa itytoea hnodein ompetitiontoa esstothemedium,hereisdistributedmu h apa itytonodeswhi h

(17)

havemoreneighbors,andthusmoretra toforward. In onsequen e,isproposedherealink-orientedfairness. Sin ethepreviousmodelsinse tion4.1areverysimilar,we hosetopresentonlythemajordieren es.

Letintrodu ethefollowingnotation:

LG

: thelinegraphof

G

1

γ

k

: thek-neighborhoodin

LG

ofoneedge

e

in

G

. Ea hlink

e

isdire ted.

δ

k

:

|γ

k

|

4.2.1 A pessimisti resour e sharings enario

We keepon proposing apessimisti radio resour e sharing. However, instead of distributing the apa ity to verti es,we onstru tforea hedgein thegraphtheset ofitsneighborhoodin the oni tgraph. If oneedge isa tive,itispotentiallyin oni twithea hedgeinthisset. Moreover,thesame apa ityisallo atedtoea h edge. In onsequen e:

∀e ∈ E, ∀f ∈ γ

2 (e),

T (f ) ≤

BW −

P

(u,x)∈γ

2 (e)

T

c

(u)

δ

2 (e)

(14)

Additionallytodatapa kets,anodemustsend ontroltra . Theequation12ofthepreviouslowerbound keepsonholding. Finally,weobtainthefollowinglinearprogramlp4:

Linear Program 4(Pessimisti model)

Maximize Obje tivefun tion onP Subje t to Equation set(14 ) edge e Equation set(12 )

∀

node

u

Tra managementfor p

∀

pathp

We anremarkthat thelowerbounds withlink-orientedandnode-orientedfairnessarenot omparable. A dierent behavior of the MAC layeris modeled. Thus the apa ity of the network depends on the proto ol hosentoallow on urrenta ess tothemedium.

4.2.2 Anoptimisti resour e sharings enario

The upper bound with an link-oriented fairness knows less modi ations. The only detail to hange is the amountof apa itytodistribute toea hedge. Indeed,only thealgorithm omputingthe

f req(u, v)

( apa ity allo ated to ea h link in the 2-neighborhood of onenode) must be hanged. We propose the following new algorithm:

f req(u, v)

.

1

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5 Evaluation fun tions

Wedenedinthepreviousse tionamethodtomodeltheradiomediumutilization. Theradioresour esharing wastranslatedinlo al onstraints,intheformofinequalities. Therefore,anytopology an ondu ttoalistof inequalitiesexhibitingtheradio resour esharing. Theobje tiveof theworkisto modelthenetwork apa ity. Consequently,fun tionstoevaluatesu ha apa itymustbeproposed. Weproposeheretwoobje tivefun tions: therstdealswiththe lassi aldenitionof apa ityandthese ondfun tion introdu esthefairness.

5.0.3 Max-Sum fun tion

The apa ity is often des ribed as the maximal throughput a hievable in the network. Thus the obje tive fun tion anbe:

M ax





X

p

∈P

f (p)





(15)

Insu hanapproa h,thenetworkis onsideredinitstotality: theobje tiveisnotindividual. Thus,anetwork privilegessomeowswhi hpresentthelowest onstraintsontheradiointerferen es. In onsequen e,someows will surely be null,be ausethey onsumetooresour es. Parti ularly, aow anbe multihops,meaning that a pa ket of thisowmust be forwarded,and reate moreinterferen es. Consequently, thetra pattern will surelybe onstitutedbyanindependentsetofsinglehopows. Therefore,adeterminedsour eanddestination ouple an be impossible. A ording to us, this ould onstitute a misinterpretation of the real apa ity of an ad ho network for many appli ations. Nevertheless, thisformulationgivesan upper bound of theglobal a hievable apa ity.

5.0.4 Max-Min fun tion

A fairnessamongtheows an beintrodu ed. Insu ha ase,theobje tivefun tion anbeformulatedas:

M ax (M in

p

∈P

f (p))

(16)

In su h anapproa h, aminimalbandwidth isguaranteedfor ea h ow inthe network in su h away that the multihops ows are not handi apped. The global a hievable throughput will surely be inferior to the max-sum fun tion ase,sin emoreinterferingowsmust ohabit. Nevertheless,weassumesu h anapproa hmore representativeofthegeneralexpe tedbehaviorofanadho network.Additionally,thefairnessratiointrodu ed in [15℄ ould very well beadapted in this approa h, although we hose to notgivethe orresponding results heresin eitrepresentsmoreatuning parameter.

6 Spe ial-Case Study: the line

Weproposeinthisse tiontostudythe asesofthelinetoillustrateourproposition. The apa ityisevaluated through the twoobje tive fun tions max-sum and max-min. To simplify the expli ations, the ontrol tra is onsidered null. Inthesameway,the apa ityis equaltoone unit. In themax-min ase,

x

representsthe throughputofea hnode.

Letbethetopologyillustratedingure2. TheA essPointispla edontheleftextremity. Theline ontains

n

nodes,andtheap.

5

ofthemedium apa ity. Thehalfofthis apa ityisreservedforthe edge(1,AP),andtheotherpartfortheedge(1,2). Finally,max-sum

=

1

10

.

10 ≤ (n − 1)x + x

. Finally,max-min

=

1 10n

Optimisti model

max-sum: thenode

1

sendsallitstra totheap. Ifthe enteristhenode

1

,allitstra andthetra sent through(2, 3)

2

...

k

n Figure3: The aseoftheline(optimisti model)

max-min: the node

1

will onstitute here also the bottlene k. It sends

x

tra and must forward the tra of

(n − 1)

nodes. The most- onstrained set is the 2-neighborhood of the node

2

. The following holds:

Throughthelink

(1,

ap

)

mustbesentthetra

x(n)

Throughthelink

(4, 3)

mustbesentthetra

x(n − 3)

Thenode

2

mustadditionallysend thetra

x(n − 1)

The frequen ies omputed forthe max-sum obje tivedo not hange. Thus, we havethe following on-straints:

x(n) ≤ [1 − x(n − 1)] ·

1 ₂

3 (17)

x(n − 3) ≤ [1 − x(n − 1)] ·

1 ₂

4 (18) Finally,max-min

=

1 3n−1

2

Thebandwidthissharedamonga enterandallits2-neighbors 3

Sin ethe enteris

2

,thetra allo atedto

(1,

ap

)

mustbeinferiortothebandwidthminusthetra of

2

multipliedbythe frequen yofthelink

(1,

ap

)

4

Sin ethe enteris

2

,thetra allo atedto

(4, 3)

mustbeinferiortothebandwidthminusthetra of

2

multipliedbythe frequen yofthelink

(4, 3)

(20)

ap

, 1)

. Thus,max-sum

=

1

10

max-min: The node

1

must send its own tra and forward the tra of the line,

n − 1

nodes. In onsequen e,max-min

=

1 10n

.

We anremarkthat fortheline,themax-min remainsun hangedwhateverthefairnessis(vertex-oriented oredge-oriented).

Optimisti model Sin ethe frequen ies donot hange, theupper bound remainsun hanged for theedge orientedfairness.

7 Results

7.1 Input Parameters

Ourobje tiveistoestimatethe apa ityinherenttodierentroutingproto ols. Torea hthisgoal,thebehavior of someroutingproto olsweresimulatedwithOPNETModeler[19℄. Morepre isely,topologiesfrom 20to60 nodes with an average degree of 20 nodes were generated. Then, OLSR, Wu & Li, somom and VSR were implementedandsimulatedonthesetopologies. The omputedroutesandtheoverheadweredire tlyextra ted from thesimulations to be used in our lpformulation. We hose to model2 dierent tra patterns: in an ad-ho network,allthepossibleroutesare omputed,inanhybridnetwork,onlyroutestowardtheA essPoint are omputed.

Tohavearepresentativeviewofthedierentroutingapproa hes,3mainproto olsweresimulated:

OLSR: thisproto ol isrelevanttorepresentthebehaviorofatroutingproto ols. Parti ularly, shortest routesare omputed,andtheoverheadisextra teddire tlyfromthesimulations. Otherroutingproto ols omputingthesamerouteswillsurelyoerasimilar apa ity.

Wu & Li - Routing via the ba kbone: Only the ba kbone topology is used, radio links between two ba kbone lients being onsidered logi ally dea tivated. It is important to noti e that in this ase, the uselessradiolinks keepon reatingradio interferen es,de reasingpotentiallythe apa ity. Besides, the original algorithm of Wu & Li[29℄ proposesto omputea ba kbone su h that theshortest routes pass throughtheba kbone. However,in thisarti le,weusedthemoste ientalgorithm [4℄: itoptimizesthe ba kbone ardinality,redu ingtheba kboneredundan y. However,inthis ase,theba kboneroutesare notshortestroutes. Theoverheadgeneratedbyalink-stateroutingproto olwouldbeinthis aseredu ed buttheroutelength anin rease.

VSR & somom: In the ad ho approa h (VSR version), routes use the luster topology, potentially longerthanthe shortestradio routes. Inthehybridapproa h(somomversion), routesuseuniquely the ba kbonetopology,forwhi htheAPrepresentstheroot. Finally,theoverheadisdire tlyextra tedfrom thesimulations.

Finally,thefollowings hemewasproposedto omputethenetwork apa ity: 1. Onetopologyof

x

nodeswassimulated(

x ∈ [20..60])

2. Aroutingproto olwas simulatedgivingoverheadsandroutes(eitherin ad-ho orinhybridmode) 3. Startingfromthetopology,the onstraintsmodeling theradioresour esharingwereextra ted 4. The onstraintsmodelingtheowswereobtainedfromtheroutes

5. The apa ityis nally omputedwithCplex [10℄from this listof onstraintsand theobje tivefun tion (either

max − sum

or

max − min

fun tion, f. se tion5).

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0 0.0001

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0.9 Capacity per flow

Throughput

Number of nodes

Lower bound - OLSR - max-min

Upper bound - OLSR - max-min

Lower bound - OLSR - whole traffic

Upper bound - OLSR - whole traffic

Figure4: Comparisonoftheobje tivefun tionsinanad-ho networkusingatrouting(link-orientedfairness)

7.2 Results

In this se tion, we investigate the apa ity of the at and self-organized stru tured routing proto ols. We assume that the radio bandwidthis normalizedto 1. First,general remarkson theevolutionof the apa ity with anin reasingnumberofnodesisgiven. Then, the apa itiesinherenttodierentroutingproto olsinan ad-ho andhybridnetworkare ompared.

7.2.1 General evolutionof the apa ity

First,thegeneralevolutionofthe apa ityinMANETisevaluatedwiththelink-orientedfairness,maximizing theminimum apa ityallo atedtoea howinaatnetwork(g. 4). InaMANET,allthepossibleroutesare omputed. Thus,ifthenetwork omprises

n

nodes,

n(n − 1)

pathsare omputed. Withaatroutingproto ol, we anremarkthat the apa ityperowde reases whenthenumberof nodesin reases: thenumberofows grows, reatingpotentially more ontentions. Consequently, thebandwidth allo atedto ea h ow will surely de rease, orroboratingtheresultsof[8℄. Oppositely, thetotalaggregatedthroughputsenta rossthenetwork remains onstant: manyowswill withhighprobabilitypassthroughthe enterof thenetwork sin eshortest paths are used. Thus, the enter will represent abottlene k, limiting the spatial reutilization of frequen ies. Finally,we annotethattheoptimisti andthepessimisti resour esharingpresentavery lose apa ity. 7.2.2 Ad-ho networks

The apa ity of ad-ho networks a ording to dierent routing proto ols is evaluated. In a rst time, the apa itywith the max-min obje tiveand with a link-orientedfairness bandwidth sharingis studied (g. 5). We anremark for thesame reasonas des ribed previouslythat the apa ityde reases when the numberof nodesin reases. Theatroutingproto olpresentsthehighest apa ity: shortestroutesin theinitialnetwork limittheroutelength,and onsequentlypresentlessinterferen es. TheVSRproto olwhi husestheba kbone only for ooding, and omputesshortestroutes on the luster topologydoes notin rease greatlythelength. Thus, the apa ity ofVSR and aatroutingproto olare very losein MANET. Oppositely, Wu& Liwhi h omputes shortestroutes throughthe ba kbonetends to lengthenthe averageroute. Besides, onlyba kbone nodeswillroutepa kets, reatingabottlene kinthenetwork. In onsequen e,Wu &Liproto ol presentsthe lowest apa ity.

Inase ondtime,the apa ityisevaluatedwiththenode-orientedfairnessbandwidthsharing(g. 6). The apa ityof OLSR and VSR is veryslightly impa ted by adierent fairnessmodel. On the other hand, the apa itypresentedbyWu &Liis lower: theba kbonenodes on entrateall thetra . Thus, theba kbone lientsre eiveadisproportionedbandwidth, reatingoppositelyabottlene kin theba kbone.

Finally, we maximize the global network throughput using the max-sum obje tive (g. 7). With su h a maximization, short routes will be advantaged sin e they reate less radio interferen es. Thus, the global apa itydoesnotde reasewhenthenetwork ardinalityin reases. We anevenremarkthatwiththeoptimisti bandwidth sharing,theglobal apa ity in reases: the degreebeing onstant,thediameter in reases, allowing a spatial reutilization of the radio medium. This orroborates the results of [8℄. Oppositely, the pessimisti

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0 5e-05

0.0001

0.00015

0.0002

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0.00035

20

25

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35

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55

60 Capacity per flow

Number of nodes

Lower bound - OLSR

Upper bound - OLSR

Lower bound - VSR

Upper bound - VSR

Lower bound - Wu and Li via cds

Upper bound - Wu and Li via cds

Figure5: Capa ityofanad-ho networkwiththemax-minobje tive(link-orientedfairness)

0 5e-05

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Lower bound - OLSR

Upper bound - OLSR

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Upper bound - VSR

Lower bound - Wu and Li via cds

Upper bound - Wu and Li via cds

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Number of nodes

Lower bound - OLSR

Upper bound - OLSR

Lower bound - VSR

Upper bound - VSR

Lower bound - Wu and Li via cds

Upper bound - Wu and Li via cds

Figure 7: Capa ityofanad-ho networkwiththemax-sumobje tive(link-orientedfairness)

0

0.002

0.004

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0.01

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0.014

20

25

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50

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60 Capacity per flow

Number of nodes

Lower bound - OLSR

Upper bound - OLSR

Lower bound - VSR

Upper bound - VSR

Lower bound - Wu and Li via cds

Upper bound - Wu and Li via cds

Figure8: Capa ityofanhybridnetworkwiththemax-minobje tive(link-orientedfairness)

resour esharing tendsto over-estimatethe interferen es,limiting thespatial re-utilizationin smallnetworks. Besides, we anremark that OLSR and VSR present a very lose apa ity, whatever the obje tive fun tion is. The apa ityofWu&Liremainsmu h lower. Furthermore,the apa ityin anoptimisti resour esharing doesnotin reaseas fastas in OLSRorVSR.In on lusion,inan adho network,aself-organizations heme doesnotimpa t severelyon the apa ity: OLSR and VSR oeraverysimilar apa ity. Although routesare sometimeslonger,andsomenodesareoverloaded,thenetworkdoesnotexhibitseverebottlene ks.

7.2.3 Hybrid networks

In a se ond time, the apa ity with the max-min obje tive and the link-oriented fairness sharing in hybrid networks is studied (g. 8). In an hybrid network, the A ess Point onstitutes either the sour e or the destination of ea h ow. Thus, in a network with

n

nodes, exa tly

n

ows exist. More pre isely, sin e ea h ow reatesabidire tionaltra ,

2n

routesare omputed. Consequently,the apa ityperowismu hhigher thaninaMANET(g. 8and9). OLSRoersanhigher apa itythansomomandWu&Li: theA essPoint representsthebottlene k ofthehybridnetwork,but theatroutingproto ol distributese ientlytheroute. The ba kboneof Wu &Li presents an higher throughputthan somom: the rst one seemsmore e ient in hybridnetworkstodistributetheloadamongtheba kbonenodes.

Finally, we an remark that the fairness model does not present any impa t in an hybrid network: the apa itywiththenode-orientedfairnessresour esharing(g. 9)remainsun hanged.

In hybrid networks, a self-organization proto ol seems to oer a degraded apa ity ompared to a at routingproto ol. Thus,ane ientba kbone onstru tionproto oloptimizingtheloaddistributionamongthe neighborsoftheAPmustbeproposed.

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0

0.002

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0.008

0.01

0.012

20

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60 Capacity per flow

Number of nodes

Lower bound - OLSR

Upper bound - OLSR

Lower bound - VSR

Upper bound - VSR

Lower bound - Wu and Li via cds

Upper bound - Wu and Li via cds

Figure9: Capa ityofanhybridnetworkwiththemax-minobje tive(node-orientedfairness)

8 Con lusion and future work

Thispaperfo usesongeneri methodsforevaluatingthe apa ityofMANets. Ourapproa h onsistsinmodeling radio resour esharingprin iples of 802.11-likeMACproto ols asaset oflinear onstraints. Wepropose two MAClayerfairnessmodels. Oneassumesthattheprobabilitytoa esstheradio hannelisuniformlydistributed among thenodes,while theother oneassumesthat forthe radio links. Forea hof these fairnessmodels, we proposeapessimisti andanoptimisti s enarioofthespatial-reutilizationofthemedium.

These models are notintegrated with aparti ular routings heme. Theyjust need asinput theoverhead and routes for a given routingproto ol. This work onstitutes thereforea relevant framework forevaluating and omparingthe apa ityofdierentroutingproto ols.

We apply this framework to a hieve a omparative analysis of at and self-organized stru tured routing proto ols. Wehaveshownthat the apa ityprovidedbyVSR andaatroutingproto ol(OLSR)aresimilar. Self-organization s hemes seem therefore to be arelevant hoi e for routing in MANets, sin e they ombine robustness,s alabilityande ien y. However,thestrategyproposedbyWu&Li,whi h onsistsinsendingall thetra throughtheba kbone,hasatoostrongimpa tonthe apa itytobepra ti al.

When onsideringhybridnetworks,bothself-organizedstru turesfollowtheWu&Listrategy, onsequently providing amu h lower apa ity than the atrouting proto ol. Self-organizations hemes must therefore be improved for be oming an eligible solution. A relevant strategy seems to try to distribute the tra in the neighborhoodofthea esspoint,while urrents hemes on entrateitonafewradiolinks.

In the lose future, weplan to pursue our omparison ampaign by in luding theother main at routing proto ols (AODV, DSR, DSDV...), eventhoughwe onje turethat there performan esshould theoreti ally besimilar to those ofOLSR. Weare alsointerested in evaluating multi-path routingproto ols [2℄,sin e they havebeenproposedforimprovingthethroughputofthenetwork.

This work yields also an appealing question. Given an estimation of the apa ity of a network, how to designadistributedroutingproto oloraself-organizations hemeinordertoprovidethemaximalthroughput ? Besides, we arelooking for morerealisti models for the(un-)fairness of 802.11MAC layer,and willing to investigateitsimpa tontheoverall apa ityofMANets.

Referen es

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[2℄ JonathanL.Bredin, ErikD. Demaine, MohammadTaghiHajiaghayi, andDanielaRus. Deployingsensor networks with guaranteed apa ity and fault toleran e. In International Symposium on Mobile Ad Ho Networking &Computing(MOBIHOC),pages309319,Urbana-Champaign,USA,May2005.ACM. [3℄ RaaeleBruno,Mar oConti,andEnri oGregori.Meshnetworks: Commoditymultihopadho networks.

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[4℄ JeanCarleandDavidSimplot-Ryl. Energye ientareamonitoringbysensornetworks. IEEE Computer Magazine, 37(2):4046,February2004.

[5℄ ThomasClausenandPhilippeJa quet. Optimizedlink stateroutingproto ol(OLSR). RFC3626,IETF, O tober2003.

[6℄ Douglas S. J. De Couto, Daniel Aguayo, Benjamin A. Chambers, and Robert Morris. Performan e of multihop wireless networks: shortest path is not enough. ACM SIGCOMM Computer Communi ation Review, 33(1):8388,january2003.

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[9℄ Hung-YunHsieh andRaghupathySivakumar. Performan e omparisonof ellularandmulti-hopwireless networks: aquantitativestudy. InSIGMETRICS,pages113122,Cambridge,USA,June2001.ACM. [10℄ ILOGCPLEX. http://www.ilog. om/produ ts/ plex/index. fm(v7.5).

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About the Capacity of Flat and Self-Organized Ad Hoc and Hybrid Networks

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and Hybrid Networks

Hervé Rivano, Fabrice Theoleyre, Fabrice Valois

To cite this version:

Hervé Rivano, Fabrice Theoleyre, Fabrice Valois. About the Capacity of Flat and Self-Organized Ad

Hoc and Hybrid Networks. [Research Report] RR-5977, INRIA. 2006, pp.23. �inria-00095216v2�

inria-00095216, version 2 - 18 Sep 2006

a p p o r t

d e r e c h e r c h e

Thème COM

About the Capacity of Flat and Self-Organized Ad

Hoc and Hybrid Networks

Hervé Rivano — Fabrice Theoleyre — Fabrice Valois

N° 5977

Unité de recherche INRIA Rhône-Alpes

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