Impact of Mobility Prediction on the Temporal Stability of MANET Clustering Algorithms *

Transcription

1 Impact of Moblty Predcto o the Temporal Stablty of MANET Clusterg Algorthms * Aravdha Vekateswara, Vekatesh Saraga, Nataraa Gautam 1, Ra Acharya Departmet of Comp. Sc. & Egr. Pesylvaa State Uversty Uversty Park, PA, (814) {vekates, acharya}@cse.psu.edu Comp. Sc. Departmet Oklahoma State Uversty Stllwater, OK, (45) saraga@cs.okstate.edu Departmet of Id. Egr. Texas A&M Uversty College Stato, TX, (979) gautam@emal.tamu.edu ABSTRACT Scalablty ssues for routg moble ad hoc etworks (MANETs) have bee typcally addressed usg hybrd routg schemes operatg a herarchcal etwork archtecture. Several clusterg schemes have bee proposed to dyamcally detfy ad mata herarchy MANETs. To acheve sgfcat performace gas, t s mportat that the uderlyg clusterg scheme s able to detfy stable clusters such that the cost assocated wth matag the clustered archtecture s mmzed. I ths paper, we study the mpact of moblty predcto schemes o the temporal stablty of the clusters obtaed usg a moblty-aware clusterg framework. We vestgate the performace of the predcto schemes wth respect to Gauss-Markov, Radom Waypot, ad Referece Pot Group moblty models uder varyg etwork ad moblty codtos. Our results dcate that whle moblty predcto sgfcatly mproves temporal stablty of the clusters, a accurate moblty trackg algorthm eed ot always lead to a accurate moblty predcto scheme. Categores ad Subect Descrptors C..1 [Computer Commucato Networks]: Network Archtecture ad Desg wreless commucato; I.6.m [Smulato ad Modelg]: Mscellaeous. Geeral Terms Algorthms, Performace. Keywords Ad hoc etworks, clusterg, moblty predcto. 1. INTRODUCTION Advaces wreless commucato ad the wdespread use of moble ad hadheld devces has resulted a creasg popularty of moble ad hoc etworks (MANETs) etworks that Permsso to make dgtal or hard copes of all or part of ths work for persoal or classroom use s grated wthout fee provded that copes are ot made or dstrbuted for proft or commercal advatage ad that copes bear ths otce ad the full ctato o the frst page. To copy otherwse, or republsh, to post o servers or to redstrbute to lsts, requres pror specfc permsso ad/or a fee. PE-WASUN 5, October 1 13, 5, Motreal, Quebec, Caada. Copyrght 5 ACM /5/1...$5.. cosst of a collecto of geographcally dstrbuted odes that commucate wth each other over a wreless medum. MANETs do ot have a fxed frastructure place ad commucato takes place through wreless lks amog moble hosts. Moreover, lmted trasmsso rage of odes ofte results a mult-hop commucato scearo, where several hosts may eed to relay a packet before t reaches ts fal destato [1]. The moblty of odes coupled wth the traset ature of wreless meda ofte results a hghly dyamc etwork topology. Ths makes the task of routg a ad hoc etwork more dffcult whe compared to a wred etwork. Routg protocols ad hoc etworks ca be broadly classfed to two types: reactve ad proactve. However, a flat structure exclusvely based o proactve or reactve routg does ot perform well large dyamc MANETs []. Cosequetly, a herarchcal archtecture s essetal for ehacg the routg performace large-scale MANETs [6]. Ulke wred etworks, t s essetal to have a dyamc scheme to detfy ad mata a herarchy a ad hoc etwork. A clusterg scheme MANET orgazes the moble odes the etwork to vrtual groups kow as clusters, based o certa crtera. A cluster typcally cossts of a cluster head ad ts member odes. A clustered archtecture provdes a effectve meas for topology maagemet, sce topology chages local to a cluster eed ot be propagated across the whole etwork. Also, typcally oly the cluster heads are volved route dscovery whch sgfcatly reduces the cotrol overhead assocated wth the routg process. There are may papers the lterature whch focus o presetg a effectve ad effcet clusterg scheme for MANETs. A survey of such clusterg schemes s preseted [6]. A mportat argumet agast troducg a herarchy a ad hoc etwork s that, the overhead assocated wth matag the herarchy may outwegh ts potetal beefts. For stace, the membershp of a cluster ca frequetly chage as the odes move ad out of the rage of the cluster heads. Hece, the clusterg process may have to be ru frequetly creatg addtoal computatoal overhead. Thus, t s mportat for a clusterg scheme to detfy stable clusters by mmzg the frequecy of membershp chages. Sce t s ot possble to partto the etwork to clusters whch do ot chage at all, we eed to * Ths work s supported part by the NSF ITR grat Ths research was performed whe the author was at Pesylvaa State Uversty.

2 desg clusterg schemes that exhbt temporal stablty (.e., detfy clusters wth a log lfe-tme) order to effectvely apply herarchcal routg techques. Oe way to acheve ths s to use moblty predcto to detfy clusters cosstg of odes that show some temporal smlarty ther moblty patters. Such a approach ca also help troducg a oto of quasstablty a otherwse ustable etwork topology. Several schemes that utlze moblty predcto for clusterg MANETs have bee proposed [1], [13]. However, to the best of our kowledge, there s o work the lterature that aalyzes the mpact of dfferet moblty predcto schemes o the stablty of the clusters uder varyg etwork ad moblty codtos. Such a study ca provde a mpartal vew o the effcacy of moblty predcto schemes ad help researchers makg a formed selecto of predcto models approprate to ther etwork evromet. I ths paper, we compare the performace of two geerc moblty predcto algorthms: (1) Moblty Predcto usg the Lk Exprato Tme [7] ad () Moblty Predcto usg Lear Autoregressve Models [8]. We restrct our aalyss to these two predcto schemes as, ulke other schemes the lterature, oly these two schemes are depedet of the uderlyg model that defes the ode moblty. Further, these two schemes do ot requre the etwork to have ay well-kow vrtual cluster ceters [1] or waypots [1] ad hece are depedet of the etwork archtecture as well. I order to aalyze the performace of these predcto schemes, we propose a smple framework for a moblty predcto-based clusterg scheme that ams to provde temporal guaratees o lk avalablty betwee odes. Smulatos are performed to evaluate the temporal stablty of the clusters defed terms of the metrcs Cluster Survval Tme, Cluster Resdece Tme ad Number of Reafflatos. We compare the results wth a clusterg framework that s moblty sestve, but does ot utlze moblty predcto such as (Weghted Clusterg Algorthm [5]), order to better uderstad the effcacy of moblty predcto. The rest of the paper s orgazed as follows. I secto, we preset a summary of sgfcat cotrbutos the areas of clusterg ad moblty predcto algorthms for MANETs. The proposed predcto based clusterg framework s descrbed secto 3. I secto 4, we preset a detaled expermetal aalyss o the performace of the two predcto algorthms. Our coclusos are preseted secto 5.. RELATED WORK Several exstg approaches utlze moblty predcto schemes to desg effcet routg protocols for MANETs. I [7], Wllam et al. compute the Lk Exprato Tme () to predct the durato of a wreless lk betwee two odes the etwork. Ther approach assumes that the drecto ad speed of moto of the moble odes does ot chage durg the predcto terval. Ths smple mechasm s the appled to ehace the relablty of exstg ucast ad multcast ad hoc routg protocols. I [1], a offle algorthm s proposed to predct lk duratos the worst-case scearo for a urba MANET. The predcted lk duratos are the utlzed to desg a routg algorthm whch fds mmum cost paths wth requred durato guaratees. Dyamc clusterg ad hoc etworks has also bee extesvely studed the lterature. Several dstrbuted clusterg algorthms for MANETs have bee proposed. Whle some schemes try to balace the eergy cosumpto for moble odes, others am to mmze the clusterg-related mateace costs. Combed metrcs based clusterg schemes take a umber of metrcs to accout for cluster cofgurato. The Weghted Clusterg Algorthm () [7], s oe such scheme, where four parameters are cosdered the clusterhead electo procedure whch are represetatve of the degree, trasmsso power, moblty, ad battery power of the moble odes. Such a scheme ca flexbly tue the parameters to sut to dfferet scearos. Referece [6] presets a comprehesve survey of varous MANET clusterg schemes that exst the lterature. I ths paper, we cosder a clusterg framework that utlzes moblty predcto for detfyg temporally stable clusters. Oe of the earlest approaches to utlze moblty predcto clusterg was the Dstrbuted Dyamc Clusterg Algorthm proposed by McDoald et al. [13]. DDCA employs the (α, t)- clusterg scheme, where geerated clusters have the property that the path betwee ay two odes the cluster wll be avalable for tme t secods wth a probablty of at least α. Though ths predcto scheme gves such a strog characterzato, t s applcable oly for those scearos where the odes follow a radom walk moblty model. A (p,t,d)- clusterg model s proposed [1] whch s based o moblty predcto derved from data compresso techques. The clusterg s acheved by dvdg the etwork to crcular regos referred to as vrtual clusters. A vrtual cluster becomes a actual cluster wheever moble odes exst t. I [9], Zad et al. propose a two ter composte model of ode moblty that captures the group behavor a moble ad hoc etwork. They use a frst order autoregressve () moblty model, orgally proposed [8] to track the moblty state evoluto of a dvdual ode. Ther results dcate that wth approprate model parameters, model s capable of represetg a wde rage of moblty patters. A dyamc scheme to automatcally recogze group moblty behavor MANETs s also proposed [9]. Though ths could be cosdered as a clusterg scheme, there s o explct moblty predcto volved the approach. Group moblty s detfed by meas of a correlato dex test betwee the estmated moblty states of the dvdual odes. I ths paper, we buld a framework for a moblty-predcto based clusterg algorthm to aalyze the performace of two geerc moblty predcto schemes: (1) Moblty Predcto usg Lk Exprato Tme ad () Moblty Predcto usg Autoregressve Models. These moblty predcto schemes are evaluated through the clusterg framework uder three dfferet moblty models: (1) Gauss-Markov moblty model, () Radom Waypot moblty model ad (3) Referece Pot Group Moblty (RPGM) model. We also compare the results agast the whch s a moblty-aware clusterg framework that does ot utlze moblty predcto. 3. A PREDICTIVE CLUSTERING FRAMEWORK I ths secto, we descrbe a smple moblty predcto-based

3 clusterg scheme that ams to provde temporal guaratees o the avalablty of lks betwee moble odes. We assume that every ode the etwork has a uque d, whch could be the ode s IP address or a combato of oe or more ds. Every ode s also aware of ts geographcal locato ad moblty formato ether va GPS or usg mechasms such as [15] that use sgal stregth measuremets. 3.1 Termologes We model a moble ad hoc etwork as a udrected graph G = (V, E), where V s the set of all moble odes, ad E s the set of the udrected lks betwee them. A lk (u, v) s sad to exst betwee odes u ad v, f ad oly f both are the trasmsso rages of each other. Let N deote the set of all odes the oe hop eghborhood of ode. Cluster C s a set of odes C = u u N } for some V such that {. I addto, the members the set C satsfy certa costrats, whch wll be dscussed later o. Node s called as the seed or the clusterhead of the clusterc. Other odes the cluster are referred to as the member odes. We defe the resdece tme, τ of ode k, as the amout of tme k speds beg a part of k cluster, before gettg afflated to aother cluster. A ode ca get afflated to aother cluster f t moves outsde the rage of a clusterhead. 3. Algorthm Specfcato The proposed clusterg framework ams to partto the etwork to clusters cosstg of odes that exhbt temporal smlarty ther moblty patter. The desg of ths framework s motvated by the (α,t)-clusterg scheme orgally proposed [13]. Specfcally, order to o a clusterc, a ode must satsfy the followg codtos: 1. N k. τ T, where T s the admsso crtera assocated wth the clusterc. A clusterhead uses the moblty predcto scheme to check f a gve ode ca satsfy the admsso crtera, before admttg the ode ts cluster. The algorthm s desged to ru cotuously ad asychroously o each actve ode the etwork, avodg the eed for a cetralzed cotrol or perodc reclusterg. Every cluster head perodcally broadcasts HELLO messages to the odes ts eghborhood. The HELLO message cotas the clusterhead s admsso crtera, locato, ad moblty profle. Upo actvato, a ode rapdly seeks to o a feasble cluster based o the advertsemets from the eghborg clusterheads. If there are multple feasble clusters, the ode os the cluster wth maxmum umber of member odes. If o clusters are detected, the ode tself becomes a clusterhead ad starts broadcastg perodc HELLO messages. Adacet u-clustered odes are preveted from each formg a ew cluster by forcg odes wth hgher detfers to back off ad try aga as descrbed [13]. Cluster mateace s performed based o a soft-state approach. Each member ode matas tmers that are reset o recevg the perodc HELLO messages from ther cluster heads. If a member ode does ot receve the HELLO message from ts clusterhead wth a stpulated tme, the assocated tmer goes off to dcate oe of two possbltes: (1) the member ode has moved out of the clusterhead s trasmsso rage, or () the clusterhead has ded. I both these cases, the member ode tres to fd out f there are ay other feasble clusters ts eghborhood that t ca o. If oe s avalable, t becomes a clusterhead o ts ow ad starts broadcastg perodc HELLO messages. Smlar to the HELLO message, the member odes a cluster sed perodc MEMBER_UPDATE messages to the clusterhead. Every clusterhead proactvely matas the locato ad moblty formato of all the odes ts cluster. If a MEMBER_UPDATE message s ot receved wth the stpulated tme, t s assumed that the ode has moved out of the trasmsso rage of the clusterhead ad s o loger cosdered a part of the cluster. 3.3 Moblty Predcto Schemes I ths secto, we preset a overvew of the two moblty predcto schemes cosdered ths paper. The choce of these predcto schemes s due to the fact that ulke other schemes the lterature, both these schemes are depedet of the uderlyg model that defes the ode moblty ad of the etwork archtecture. Lk Exprato Tme: The Lk Exprato Tme () s a smple predcto scheme that determes the durato of a wreless lk betwee two moble odes by assumg that ther speed ad drecto of movemet remas costat. Let the locato of ode ad ode at tme t be gve by x, y ) ad ( x, y ). Also, let v r ad v r be the speeds, ad ( θ ad θ be the drectos of the odes ad respectvely. If the trasmsso rage of the odes s r, the the Lk Exprato Tme, D t, of the lk betwee the two odes, as defed [7], s gve by ( ab + cd) + ( a + c D t = a + c where a = v cosθ v cosθ b = x x c = v sθ v d = y y sθ ) r ( ad bc) K(1) The gves a upper boud o the estmate of the resdece tme of a ode a cluster. I the proposed clusterg framework, whe -based predcto s used, a ode s allowed to o a cluster oly f the predcted of the lk betwee the ode ad the clusterhead s greater tha the cluster s admsso crtera.

4 Lear Frst Order Autoregressve Model: The lear frst order autoregressve () model, as defed [8], has bee show to effectvely track the movemet of a moble ode rrespectve of the uderlyg moblty model. I a model, the moblty state of a ode at tme s defed by the colum vector s = where [ x, x&, y, y&, && x, & y ] x ad velocty, ad y specfy the posto, & ad x& x& ad y& specfy the & specfy the accelerato of the moble y& ode the x ad y drectos a two-dmesoal grd. The AR- 1 model for the moblty state s of a ode s gve by: s = As + w +1 () where A s a 6 x 6 trasformato matrx, the vector w s a 6 x 1 dscrete-tme zero mea whte Gaussa process, wth a covarace matrx Q. The matrces A ad Q are called the parameters of the model ad are estmated based o a trag data whch allows the model to accurately characterze a wde class of moblty patters. The parameters of the model are updated perodcally usg the actual observed values. If the state formato s at ay tme s avalable, t s possble to predct the moblty state s +m at ay tme +m the future usg the followg equato s = A s m + m (3) I our expermetal aalyss, we use the model to track the ode movemet ad to predct the resdece tme of a ode a cluster. A ode s allowed to o a cluster C oly f the estmated resdece tme s at least T (the admsso crtera of the cluster). 4. Expermetato Results I ths secto, we preset the results from detaled smulato expermets carred out usg the OPNET smulato software [16]. Before we dscuss the results, we frst descrbe the moblty models ad the performace metrcs used to evaluate the predcto schemes. 4.1 Moblty Models We model the movemet of odes the etwork usg three moblty models: (1) Gauss-Markov, () Radom Waypot ad (3) RPGM moblty models. Although radom ode moblty has bee wdely used, there are a umber of applcatos of ad hoc etworks tactcal commucatos such as emergecy respose teams, battlefelds, etc., where odes do ot exhbt complete radom moto. Therefore, order to effectvely study the performace of ay clusterg algorthm for a ad hoc etwork, we eed to have moblty models that smulate realstc movemet of moble odes. Hece, we selected the Gauss-Markov moblty model whch allows us to cotrol the radomess the movemet patter. We cosder the radom waypot moblty model as a worst case scearo for ay moblty predcto scheme. Whle good moblty predcto schemes should be successful detfyg explct group moblty the etwork, accurate moblty predcto the presece of absolute radom moblty s tough, f ot mpossble. The RPGM model troduces explct group moblty the etwork. A effectve moblty predcto scheme should be able to detfy the groups accurately. Therefore, order to evaluate the stregths of the predcto schemes, we also coduct smulatos cosstg of groups of odes, each movg depedet of each other a overlappg fasho. Referece [3] presets a comprehesve descrpto of the above metoed moblty models. 4. Performace Metrcs The prmary goal of usg a moblty predcto scheme s to eable the uderlyg clusterg framework to provde temporal guaratees o the avalablty of routes to all the odes wth a cluster. I order to aalyze the performace of the predcto schemes, we cosder the followg factors: (1) The clusters detfed through moblty predcto should exhbt temporal stablty,.e., there should be mmal chages the membershp of a cluster over a specfed durato of tme. () The overhead assocated wth cluster mateace should be mmzed. (3) The umber of clusters the etwork should be mmzed to acheve scalablty. Metrc for temporal stablty: Oe way to evaluate cluster stablty would be to observe the durato of tme for whch the membershp a cluster remas uchaged. However, the absece of explct group moblty, t s very ulkely that odes wll rema wth the same cluster for a log durato of tme. Nevertheless, the stablty of both ter- ad tra-cluster routes crtcally depeds o the frequecy of the odes leavg a cluster. Hece, we defe the cluster survval tme as the amout of tme betwee two cosecutve evets of odes leavg the cluster. We also record the cluster resdece tme whch s the average amout of tme spet by a ode a cluster. The cluster resdece tme s also a good measure of the stablty of a cluster [13]. It s smlar to cell resdece tme cellular systems, whch s a determat of the dstrbuto ad rate of hadoffs. Metrc for mateace overhead: The mateace overhead of the clusterg algorthm ca be evaluated usg the reafflato cout whch represets the umber of tmes moble odes chage ther cluster afflatos. A hgher reafflato cout meas hgher cotrol traffc overhead sce all actve routes to the ode eed to be updated. Metrc for scalablty: Fally, t s mportat to mmze the umber of clusters the etwork order to mprove scalablty. Nevertheless, a clusterg algorthm eed ot result a mmal umber of clusters, as log as the resultg clusters are relatvely stable. Measure for predcto accuracy: The performace of the clusterg scheme s heavly depedet o the accuracy of the predcto algorthm. The decso to allow odes to o a cluster s based o the future posto of the odes the etwork, as estmated by the moblty predcto algorthm. We defe the predcto error as the fracto of tmes a predcto turs out to be correct,.e., the fracto of tmes a ode leaves a cluster wthout satsfyg ts admsso crtera. It s mportat to ote that the above metoed metrcs are ot depedet of each other. However, they all dcate the

5 Predcto Error (%) Predcto Iterval (m) (a) Percetage Error Predcto performace of the predcto scheme from dfferet aspects. Clearly, there s a tradeoff betwee the sze of the clusters ad the stablty of the clusters. A small cluster mples hgher cluster survval tmes sce membershp chages wll be less frequet. However, t s desrable to have clusters wth multtude of odes to localze the effects of topologcal chages. A optmal clusterg scheme would be oe whch maxmzes the stablty of the clusters whle stll resultg hghly populated clusters. 4.3 Expermetal Setup We smulate a ad hoc etwork cosstg of 7 moble odes o a 1m x 1m grd. We used the OPNET smulator ad each of the smulato rus were carred out for a 5 hour tme perod. We compared three clusterg schemes, amely, -based predctve scheme, model-based predctve scheme ad. For each of the smulato rus, the model was tally traed o a data set cosstg of 6 data pots. Durg the course of the smulato perod, the parameters of the model were updated wth the observed values at tervals of 3 secods. 4.4 Results wth Gauss-Markov moblty model Gauss-Markov moblty model gves us the ablty to cotrol the radomess the movemet patters of the moble odes through a tug parameter α [3]. If α=1, the movemet of the odes s completely lear whereas a value of α =, results radom ode movemets. For our smulatos, α was set at.8. Sestvty to predcto terval: I our clusterg framework, a ode s allowed to o a exstg cluster the etwork oly f t satsfes the admsso crtera assocated wth the cluster. A clusterhead uses the moblty predcto scheme to check f a ode satsfes the admsso crtera. A strcter admsso crtero would requre the moblty predcto scheme to predct the movemet of the odes over a larger terval of tme. If the predctos were to be accurate, as the admsso crtera s creased, the resultg cluster wll exhbt greater temporal stablty wth hgh cluster survval ad resdece tmes. The graphs Fgure 1(a) dcate that both the schemes have a hgh predcto error over tervals greater tha mutes. We also observe that whle the frst order lear autoregressve model accurately tracks ode moblty, t has sgfcatly hgher predcto error, makg t usutable for mult-step predctos (predctos over large tervals). I our smulatos, we used the Resdece Tme (m) Survval Tme (m) Number of Clusters Reafflatos per ut tme Predcto Iterval (m) (b) Average cluster resdece tme Predcto Iterval (m) (c) Average cluster survval tme Predcto Iterval (m) (d) Average umber of clusters Predcto Iterval (m) (e) Reafflatos per ut tme Fgure 1. Effect of predcto terval uder Gauss-Markov moblty model

6 Number of Clusters Node Velocty (m/s) Resdece Tme (m) Node Velocty (m/s) (a) Average umber of clusters (b) Average cluster resdece tme Survval Tme(m) Node Velocty (m/s) Reafflatos per ut tme Node Velocty (m/s) (c) Average cluster survval tme (d) Reafflatos per ut tme Fgure. Effect of ode speed uder Gauss-Markov Moblty Model predcto scheme referred to as the plug- predctor whch s obtaed by repeatedly usg the ftted model wth ukow future values replaced by ther ow forecasts. Ths ofte results hgh predcto errors over large tervals especally f the model order has ot bee ftted well [14]. Erroeous predctos ofte lead to the cluso of some odes a cluster that realty, do ot satsfy the admsso crtera. As a result, hgh predcto errors the based scheme severely degrade ts performace as dcated by cluster survval ad resdece tmes fgure 1(b) ad 1(c). The -based scheme, o the other had, does result clusters wth creasg survval tmes as the admsso crtera of the clusters s creased. Ths s due to the fact that, the absece of total radom movemet, a lear approxmato of the movemet of the odes over a short terval of tme holds good. Nevertheless, both the moblty predcto-based schemes result better temporal stablty whe compared to whch s sestve to the admsso crtera. A predcto-based scheme also sgfcatly creases the cluster resdece tme ad hece the stablty of routes the etwork. Stable ad log-lved clusters also result sgfcatly less mateace overhead whch ca be verfed Fgure 1(e). Sestvty to ode speed: I the ext set of expermets, we vary the average speed of the moble odes from 1 m/s to 1 m/s. The admsso crtera of the clusters s fxed at mutes wth a uform trasmsso rage of 5 meters for all odes. As the average speed of the moble ode creases, they ted to move ad out of the clusters more frequetly resultg a hghly dyamc etwork topology. Cosequetly, matag the temporal stablty of the clusters becomes creasgly dffcult. Nevertheless, a good moblty predcto scheme should be able to accurately detfy odes that meet the admsso crtera of the clusters eve at hgher speeds. As a result, a clusterg scheme that uses moblty predcto should adapt the cluster sze to ode moblty whle matag the temporal stablty of the clusters. Specfcally, at low speeds, t results less umber of clusters wth larger cluster sze, whle the average umber of clusters the etwork gradually crease respose to hgher speeds. From our results, we observe that both the predcto schemes exhbt ths tred as ca be see fgure. For typcal walkg speeds (less tha m/s), the model-based scheme results hghly stable clusters comparso to the -based scheme as see fgures (b) ad (c). However, the -based scheme adapts well to creasg ode speeds makg t more sutable at hgher speeds. Whle the performace degradato of the model-based scheme could be offset partally by updatg the model parameters more frequetly, t wll sgfcatly crease the computatoal overhead. Nevertheless, we observe that both the predcto schemes do result clusters wth better temporal stablty whe compared to whch also has sgfcatly hgh umber of reafflatos as show fgure (d). 4.5 Results wth Radom Waypot moblty model The accuracy of a moblty predcto algorthm s drectly related to the movemet patters of the odes the etwork. I the presece of total radom movemet patters, t s almost

7 Number of Clusters Admsso Crtera (m) (a) Average umber of clusters Number of Clusters Referece Pot Separato (m) (a) Average umber of clusters Predcto Error (%) Admsso Crtera (m) ResdeceTme (m) Referece Pot Separato (m) (b) Percetage error predcto Fgure 3. Performace uder radom waypot moblty model mpossble for ay predcto algorthm to perform well. We cosder ths case as a worst case scearo for clusterg schemes that rely o moblty predcto. I fgure 4(a), we observe that the both the predcto schemes result a almost u-clustered etwork for hgh cluster admsso crtero. Ths s so because, every ode forms ts ow cluster sce the predcto scheme s uable to detfy ay feasble cluster. always yelds a wellclustered archtecture sce t does ot try to meet ay admsso costrat. Though the model has bee show to be successful accurately trackg radom ode movemet[9], mult-step predcto s worse tha sce t tres to model the moblty of the odes usg a lear model. Clearly, the presece of radom ode moblty, t s advsable to use a algorthm that does ot rely o moblty predcto. 4.6 Results wth RPGM model The Referece Pot Group Moblty (RPGM) model represets the radom moto of a group of odes as well as the dvdual odes wth the group. Each group the etwork s represeted by ts logcal ceter. Idvdual moble odes radomly move about ther ow pre-defed referece pots, whose movemets deped o the group movemet. Therefore, a accurate clusterg scheme should be able to detfy such explct group moblty the etwork. However, order to evaluate the stregths of the predcto schemes, we coducted smulatos cosstg of 1 groups of 7 odes each movg depedet of each other a overlappg fasho m x m grd. The referece pot Survval Tme (m) (b) Average cluster resdece tme Referece Pot Separato (m) (c) Average cluster survval tme Fgure 4. Performace uder RPGM model separato s creased across subsequet rus of the smulato to smulate groups whch are loosely coupled. The trasmsso rage of the odes s fxed at 5 meters ad the admsso crtero for the predcto schemes s set at 3 mutes. I fgure 5(a), we plot the umber of clusters detfed by the clusterg schemes wth respect to creasg referece pot separato. We observe that whe the odes wth a cluster are tghtly coupled together, all the three schemes are able to accurately detfy the groups the etwork. But as the separato betwee the referece pots s creased, eve the odes wth a group are far apart from each other makg t mpossble to detfy the groups usg a sgle hop clusterg scheme. As a result, the umber of clusters the etwork creases steadly. However, both the predcto schemes have smlar performace terms of all the performace metrcs. For ode separatos less tha 15

8 meters, there s o chage the clustered topology oce the actual groups are detfed. Thus, the cluster resdece tmes ad the cluster survval tmes equal the durato of the smulato. The performace of rapdly degrades comparso to the predctve schemes as llustrated fgures 5(b) ad 5(c). However, as the referece pot separato s creased, dvdual ode moblty (whch s smlar to radom waypot moblty model) starts to sgfcatly fluece the results. 5. CONCLUSIONS I ths paper, we studed the effect of moblty predcto o the temporal stablty of clusters MANETs. We used a smple moblty-aware clusterg framework to compare the performace of two geerc moblty predcto algorthms: (1) Moblty Predcto usg the Lk Exprato Tme ad () Moblty Predcto usg Lear Autoregressve Models. Based o our smulato results, we make the followg coclusos: 1. Whe the odes do ot exhbt total radom moto, a predctve clusterg scheme sgfcatly mproves the temporal stablty of the clusters whe compared to a moblty-aware o-predctve scheme. However, there s a tradeoff betwee the stablty ad the sze of the clusters.. I the presece of total radom ode moblty, t s advsable to use a algorthm that does ot rely o moblty predcto. 3. I the presece of explct group moblty, both predctve ad o-predctve clusterg schemes are successful accurately detfyg the groups. However, whe the separato wth the odes a group creases, moblty predcto helps mprovg the temporal stablty of the detfed clusters. However, the performace gas are restrcted due the oe-hop clusterg scheme used. 4. A predctve clusterg scheme s able to adapt to varyg etwork codtos by dyamcally adustg the cluster sze order to guaratee temporal stablty. 5. Whle the model has bee show to accurately track ode moblty [8], t does ot always result accurate moblty predctos. We make the followg coclusos about the comparatve study of the two predcto schemes. 1. The model wth the recursve plug- predctor results hgher mult-step predcto errors comparso to the -based scheme. However, for predctos over a small terval of tme, the based scheme results a optmal umber of clusters wth comparable survval tmes.. The model-based scheme performs well uder low moblty whereas the -based scheme s a more sutable choce at hgher speeds sce the performace of the model degrades faster tha the -based scheme wth creasg ode speeds. 3. I the presece of explct group moblty, both the predcto schemes perform equally well. I our smulatos, all the clusters the etwork have a fxed admsso crtero. We are curretly vestgatg varous approaches to arrve at better values for the admsso crtera of dvdual clusters based o parameters such as ode velocty ad trasmsso rage. 6. REFERENCES [1] Y.-C. Tseg, S.-L. Wu, W.-H. Lao, ad C.-M. Chao, Locato awareess ad hoc wreless moble etworks, IEEE Computer, 34(6), pp. 46-5, Jue 1. [] P. Guptar ad P. R. Kumar, The capacty of wreless etworks, IEEE Trasactos o Ifo. Theory, vol. IT-46., March, pp [3] T. Camp, J. Boleg, ad V. Daves, A survey of moblty models for adhoc etwork research, Wreless Comm. & Moble Comp. (WCMC), vol., o. 5, pp ,. [4] A.B. McDoald ad T.F. Zat, A moblty-based framework for adaptve clusterg wreless ad hoc etworks, IEEE Joural o Selected Areas Commucatos 17(8), pp , [5] M. Chatteree, S. K. Das, ad D. Turgut, : A weghted clusterg algorthm for moble ad hoc etworks, Joural of Cluster Computg, Specal ssue o Moble Ad hoc Networkg, No.5, pp ,. [6] J. Y. Yu ad P. H. J. Chog, A survey of clusterg schemes for moble ad hoc etworks, IEEE Commucatos Surveys, Vol 7, No. 1, Frst Quarter 5. [7] W Su, S-J Lee, ad M. Gerla, Moblty predcto ad routg ad hoc wreless etworks, Iteratoal Joural of Network Maagemet, Vol. 11, Ja-Feb 1, pp. 3-3 [8] Z. R. Zad ad B.L. Mark, Moblty estmato for wreless etworks based o a autoregressve model, Proceedgs of IEEE Globecom, Dec. 4. [9] Z. R. Zad, B.L. Mark, ad R. K. Thomas, A two-ter represetato of ode moblty ad hoc etworks, Proceedgs of IEEE SECON, October 4. [1] S. Svavakeesar, G. Pavlou, ad A. Lotta, Stable clusterg through moblty predcto for large-scale multhop tellget ad hoc etworks, IEEE Wreless Comm. ad Networkg Coferece, March 4 [11] S. Ja, D. He, ad J. Rao, A predcto-based lk avalablty estmato for moble ad hoc etworks, Proceedgs of IEEE INFOCOM, 1. [1] J. Tag, G. Xue, ad W. Zhag, Relable routg moble ad hoc etworks based o moblty predcto, IEEE Iteratoal Coferece o Moble Ad Hoc ad Sesor Systems, October 4. [13] A.B. McDoald ad T.F. Zat, Desg ad smulato of a dstrbuted dyamc clusterg algorthm for multmode routg wreless ad hoc etworks, Smulato, Vol. 78, No. 7, pp. 48-4, July. [14] C-K Ig, Selectg optmal multstep predctors for autoregressve processes of ukow order, The Aals of Statstcs, Vol. 3, No., pp , 4 [15] S. Capku, M. Hamd, J. P. Hubaux, "GPS-free postog moble da-hoc etworks," Proceedgs of HICSS, Hawa, Jauary 1, pp. 1 [16] OPNET smulator,