Modeling of IEEE in a Cluster of Synchronized Sensor Nodes

Transcription

1 Modeling of IEEE in a Cluser of Synchronized Sensor Nodes Kenji Leibniz, Naoki Wakamiya, and Masayuki Muraa Graduae School of Informaion Science and Technology, Osaka Universiy, 1-5 Yamadaoka, Suia, Osaka , Japan [leibniz,wakamiya,muraa]@is.osaka-u.ac.jp Absrac. In his paper we presen a model of he IEEE MAC proocol for a cluser of sensor nodes and discuss is performance. Our focus is on a special scenario where all nodes sar heir ransmission synchronously, which is he mos harmful case for CSMA/CA proocols. The influence of he cluser size and message lengh is invesigaed using a non-saionary analysis echnique. We characerize he delays for ransmiing/receiving daa from he cluser members, he success probabiliy, and discuss energy consumpion issues. Keywords: clusered sensor neworks, IEEE , CSMA/CA, energy consumpion. 1 Inroducion Wih he recen developmens in Micro Elecro Mechanical Sysem MEMS echnology, large-scale neworks of inegraed wireless sensor nodes have become available [1]. By deploying neworks of sensors, informaion abou behavior, condiions, and posiions of eniies in an environmen are gahered and forwarded o a sink for furher processing. The nodes are equipped wih a sensing device, radio ransmier, and are usually baery operaed. Since hey are designed o operae auonomously, hey mus be able o se up a communicaion nework in an ad-hoc manner and o adap o changes in he nework opology, when individual nodes may fail due o exhaused baeries. Conservaion of energy is, hus, a key issue in he deploymen of sensor neworks. Mos energy consumpion is caused by he communicaion over he radio link [2]. Recenly, several publicaions have shown he benefis of using clusering mehods in order o prolong he lifeime of he nework, e.g. [3, 4]. In clusered sensor neworks, he sensor nodes do no ransmi heir colleced daa o he sink, bu o designaed cluser heads which aggregae he daa packes and send hem direcly or via muli-hop communicaion o he sink. Thus, choosing he appropriae sizes and number of clusers is essenial for he performance of he nework lifeime. If he cluser s radius is oo large, i will hos many nodes and energy is wased due o iner-cluser collisions. On he oher hand, if he radius is oo small, a large number of clusers is needed o cover he observaion area, many of hem having a large disance o he sink.

2 In order o enforce sandardizaion among sensor devices, he ZigBee Alliance [5] was formed in 2002 as an associaion of companies o creae a low-cos and low-power ransmission sandard for wireless personal area neworks WPAN. The ZigBee specificaion defines he communicaion on he nework layer and above, while he IEEE sandard [6] is adoped for he physical and medium access conrol MAC layers. On MAC layer, access o he channel is conrolled wih a carrier sense muliple access wih collision avoidance CSMA/CA algorihm ha is especially designed for WPAN. Differen nework opologies, such as sar-shaped and peer-o-peer, are suppored. Recenly, here has been a growing number of publicaions dealing wih he performance of IEEE , e.g. [7 9]. However, mos papers use simulaion sudies or analyical evaluaion of CSMA/CA considering he sysem o operae under seady sae condiions. Our focus in his paper is on an applicaion in which he ransmission insans of each node are synchronized, i.e., all nodes simulaneously iniiae heir ransmission aemp. This specific scenario is highly non-saionary and very harmful for CSMA/CA as shown in [10] for IEEE Wireless LAN. In his paper we presen an analyic model of IEEE CSMA/CA in a cluser of sensor nodes. Our main ineres is on he ransmission delay and he resuling energy consumpion due o he MAC proocol. The purpose of his sudy is o provide a model for evaluaing cluser-based mehods. In some clusering models he unrealisic assumpion can be found ha a node operaes wih several differen MAC proocols. In our paper, a sensor node uses only he ZigBee proocol sack, which we will describe in Secion 2. This is followed in Secion 3 by he analyical model of he CSMA/CA proocol, from which we derive he delay disribuion depending on he number of nodes in a cluser and he message lengh. In Secion 4, we invesigae he effecs of he parameer seings on he energy consumpion. Finally, his work is concluded by a brief oulook on fuure work. 2 Sysem Descripion of he Sensor Nework The IEEE sandard aims a low rae wireless personal area neworks. Therefore, he requiremens on operaion and power consumpion differ from ha of oher CSMA/CA-based MAC proocols, e.g. IEEE for WLAN. 2.1 The IEEE MAC Proocol The MAC proocol can operae in wo modes: beacon-enabled or beacon-less mode. Boh modes use discree ime slos. In he beacon-enabled mode, superframes consising of 16 slos are used. The firs par of he superframe is he conenion access period in which CSMA/CA is employed. Up o 7 guaraneed ime slos a he end of he superframe may be used for he conenion free period ha are dedicaed o nodes requiring low laency. The acknowledgmen of packes is no sricly required and unlike WLAN an RTS/CTS mechanism is no used. In he following we will assume he beacon-less mode wih CSMA/CA operaing according o he algorihm given in Fig. 1. The ime axis is discreized ino backoff unis, each wih duraion of 20 symbol periods. We consider he nework o operae in he 2.4 GHz frequency band wih a symbol rae of 62.5 ksym/s, i.e., a backoff uni has a lengh of 80 bis. The variable BE denoes he backoff

3 NB NB = 0, 0, BE BE = BE BE min min delay for for random 2 BE BE --1 uni uni backoff periods perform CCA CCA channel free? no NB NB = NB+1 BE BE = minbe+1, BE BE max max yes no NB NB > M? M? yes failure success Fig. 1. Flow char of he CSMA/CA mechanism exponen ha is increased from BE min unil BE max. The variable NB characerizes he number of backoffs and is iniialized wih NB = 0 a he beginning of each round. Defaul values given in [6] are BE min = 3, BE max = 5 and he maximal number of backoffs is M = 4. If he ransmission aemp has no been successful unil he M-h backoff, i will be abored. Noe ha he 0-h backoff is always performed. The clear channel assessmen CCA is a physical layer primiive o check if he channel is busy. We incorporae he ime required by CCA in our model by assuming ha he ransmission can sar earlies a he nex ime slo afer he aemp. 2.2 Clusering in Sensor Neworks In order o simplify he elecronic circuiry of he sensor nodes, hey only gaher he informaion and forward he daa o he sink where he processing is done. If all nodes ransmi direcly o he sink, he sysem would no be scalable as he many-o-one ransmission can consis of hundreds or housands of nodes. Therefore, clusering mehods have been proposed, in which he nodes wihin a cluser send he daa o a designaed node, called cluser head. I collecs he daa locally from he oher cluser members and ransmis he aggregaed daa eiher direcly or via muli-hop ransmission o he sink, see Fig. 2. Furhermore, if he daa packes are locally correlaed, hey can be compressed o shorer messages [11] a he cluser heads. Since he cluser heads spend more energy han he oher cluser members, heir role is roaed among all nodes in order o equalize energy consumpion. 3 Analyical CSMA/CA Model In he following. we sudy he case where all sensors ransmi heir daa in a synchronized manner, which is regarded as he wors case scenario for CSMA/CA. Similarly o [10] our analysis consiss of wo seps: i he derivaion of he probabiliies ha each user

4 cluser members cluser members sink sink cluser head a 2-hop ransmission cluser head b muli-hop ransmission Fig. 2. Clusered sensor neworks aemps o access he channel, and ii he compuaion of he ransmission delay. Our focus lies on he impac of wo specific inpu parameers, he number of nodes N in a cluser and he message lengh L discreized in backoff unis. 3.1 Derivaion of he Aemp Probabiliies Le us assume an arbirary node in a cluser of N nodes in oal. The backoff duraion B k a he k-h backoff is chosen uniformly beween 0 and W k 1 and he oal number of backoffs is limied by M. W k = 2 minbe min+k,be max 0 k M 1 B k is a uniform random variable and is disribuion is given by Eqn. 2. The oal aemp duraion D k a he k-h backoff consiss of he sum of all B j, j k, given in Eqn. 3. b k = Pr[B k = ] = 1 W k 2 d k = Pr[B 0 + B B k = ] = b 0 b 1 b k 3 The probabiliies in Eqn. 2 and 3 are defined for 0 k = k j=0 W j and denoes he discree convoluion operaor. The number of backoffs prior o a successful ransmission is expressed by he random variable Q. Le ξ be he probabiliy ha he channel is found busy while aemping ransmission. Afer comparison wih simulaion resuls, we found ha approximaing q k as pmf of Q wih a binomial disribuion yielded beer resuls han a using a geomeric disribuion. The approximaion for ξ is given by he erm in Eqn. 4 where E[W ] is he average over all backoff window sizes. q k = M k ξ k 1 ξ M k { ξ = min 1, } L N 1 E[W ] The aemp probabiliy a for a node aemping a ransmission a ime slo is given by he sum over all d k. Furhermore, he probabiliy of aboring he ransmission aemp is defined as η = d M ξ. a = M d k 5 k=0 4

5 aemp probabiliy M= M=5 M= ime slo a Aemp probabiliy a node delay probabiliy N=5,L= analysis simulaion N=50,L= ime slo b Node delay disribuion τ node Fig. 3. Aemp probabiliy and node delay The aemp probabiliy for N = 10, L = 2 and differen values of M is shown in Fig. 3a. The curves all show he same disinc sawooh behavior repored in [10]. However, due o he limied number of M, all curves decrease o zero when approaches M. Obviously, he aemp probabiliy increases for large M. Noe ha he aemp probabiliy is closely relaed o he delay ha each cluser member encouners in a round when i ransmis is daa o he cluser head. To derive he disribuion of he random variable node delay T node we mus weigh he sum over he d k wih he backoff probabiliies q k. While he aemp probabiliies are simply a ime series of probabiliies, τ node represens a probabiliy disribuion where he sum mus be normalized o 1. I can be seen in Fig. 3b ha he analyical disribuion maches well wih he resuls from simulaion despie he rough approximaion of ξ. τ node = M d k q k k= Calculaion of he Toal Transmission Delay Afer having characerized he behavior of each individual sensor node, he nex sep consiss of aking he influence from he oher cluser members ino accoun. Each node sars is ransmission process a he synchronizaion ime insan = 0 and performs he backoff process as described in Secion 2.1. When he node has successfully ransmied he message o he cluser head, i remains silen unil he nex synchronizaion insan. We assume ha he iner-synchronizaion inerval is large enough o be negleced here. The oal ransmission delay T head is he ime ha he cluser head is required o sense he channel in a round unil all cluser members have successfully ransmied or abored heir aemp. The pmf of he random variable T head will be given by τ head. We assume he following sae space as illusraed in Fig. 4. I forms a pure deah process as no ransiions o higher saes are made. The saes and heir corresponding probabiliies x i,j are denoed by he number of nodes i ha have no ye compleed heir ransmission aemp and he number of slos j i is currenly ransmiing. Once he absorbing sae 0 is reached, he daa ransmission cycle is compleed.

6 f N N 2 f N... f N 1 1 N... f 2 N 1 N 2 f 2 1 f f N N 1 N f 2 f N,0 N-1,0 2,0 1, N-2,0 w N w N 1 w2 w f + f N N 1 + f 2 + f 1 s s N 1 s N s N 1 2 0,0 1 N,1 N,L N-1,1 N-1,L 2,1 2,L 1, ,L Fig. 4. Sae space wih ransiion probabiliies a ime All ransiion probabiliies are ime-dependen and are formulaed wih he help of he aemp probabiliy in Eqn. 5. A successful ransmission is described by s i when only a single of he remaining i nodes can successfully access he free channel a ime. The probabiliy for remaining in sae x i,0 is given in Eqn. 7 as w i when none of he i remaining nodes accesses he channel. Noe ha we define w 0 = 1 as a special case. The remaining probabiliy consiues he probabiliy of collision c i. Of all he nodes involved in a collision, some will abor heir ransmission due o reaching he maximum number of backoffs. As here can be muliple simulaneous failures, we model hese ransiions wih a binomial disribuion for 0 i k, see Eqn. 8. s i = i a 1 a i 1 w i = 1 a i 7 c i = 1 s i w i f k i i = c i η k 1 η i k 8 k The aemp probabiliies are ime-dependen, herefore, we mus perform a nonsaionary analysis echnique by using he simple power mehod. We sar wih an iniial probabiliy vecor x0 and ieraively muliply he sae vecor x = [x 0,0, x 1,L,..., x 1,1, x 1,0,... x N,L,..., x N,1, x N,0 ] wih he ime-dependen ransiion marix P unil = M is reached. x + 1 = x P 9 We use x0 = [0,..., 0, 1] as iniial probabiliy vecor, since a ime = 0 here will be N nodes in he sysem wih probabiliy 1. The resuling componen values x 0,0 of he vecor x consiue he cumulaive delay probabiliies of τ head. Examples of he disribuion are illusraed in Fig. 5a. The pale colored lines show he disribuions obained from simulaions. I can be seen ha he boldly colored resuls from he analysis mach well wih he simulaion values. 3.3 Probabiliy of Success We are ineresed in he probabiliy of a ransmission aemp being successful unil = M. Since our Markov model does no disinguish beween successful and abored

7 delay probabiliy N=2,L=10 N=5,L=5 N=50,L=1 successful nodes S N M=5 M=4 M= ime slo a Toal delay probabiliy τ head number of nodes N b Number of successful aemps Fig. 5. Toal ransmission delay and successful nodes aemps, we obain he number of successful nodes S N afer he round from a modified sae space of Fig. 4 where we only disinguish beween ransiions for successful and unsuccessful aemps. From he sae probabiliies x i,j M we hen derive he success probabiliy ϕ N. The average number of successful ransmissions and success probabiliy are given in Eqn. 10. S N = N [ L N i x i,j M ] i=0 j=0 ϕ N = S N N 10 The number of successful nodes is shown in Fig. 5b over he oal number of nodes. We varied he maximum backoff M in his experimen. I can be clearly seen ha increasing he number of nodes leads o a poin afer which he performance decreases due o collisions. Furher, he figure jusifies he use of clusering mehods from MAC viewpoin and shows ha he bes operaing range is up o approximaely 20 nodes. A large M increases he capaciy of he cluser, however, he value M = 10 used here is only a hypoheical value, as he sandard in [6] specifies a limiaion of M Approximaion of Number of Backoffs In Eqn. 4 we have used an approximaion for he las backoff unil success. For he evaluaion of he energy consumpion in he nex secion, he average number of backoff aemps is needed. Thus, when we have N nodes, he unsuccessful nodes experience he oal number of M backoffs, whereas for he successful S N he average number of backoffs is given by he expecaion of random variable Q. Thus, we have as approximaion of he average number of backoffs he erm C N in Eqn. 11. C N = M [1 ϕ N 1 ξ] Evaluaion of Energy Consumpion For he evaluaion of he energy consumpion we consider he disribuion of node posiions according o a homogeneous spaial Poisson process. The disribuion is charac-

8 erized by he densiy λ which describes he average number of nodes in a uni area size. 4.1 Basic Energy Consumpion Model We adop he energy consumpion model given in [3] for ransmiing and receiving daa wih lengh l bis for a ransmier and receiver separaion of x. E T x l, x = l E elec + ε fs x 2 E Rx l = l E elec 12 The elecronics energy E elec is 50 nj/bi and ε fs = 10 pj/bi/m 2 is he energy for he ransmier amplificaion in free space. Aggregaing daa messages consumes E fuse = 5 nj/bi/signal/bi and he energy for sensing requires E sense = E elec. 4.2 Energy Consumpion per Cluser The oal energy consumpion per round in a sensor node cluser usually consiss of four pars: i he ransmission energy of he daa from he cluser members o he cluser head, ii he recepion energy of hese daa messages a he cluser head, iii he energy for fusing and aggregaing he received daa, and finally iv he ransmission energy of he aggregaed daa from he cluser head o he sink/nex hop. In his paper we only focus on he effecs wihin a single generic cluser and only roughly ake ino accoun he seps iii and iv as hey depend on he specific applicaion and he mehod of how he clusers are generaed. However, i should be remarked ha his par grealy influences he overall performance and he model in his paper can be regarded as a ool o analyze each individual case when dealing wih a specific clusering mehod. In a cluser wih N nodes, we sor he nodes by heir disance R n o he cluser head which is given by he Erlang probabiliy densiy funcion and is average E[R n ] is expressed wih he Euler gamma funcion in Eqn. 13. r n x = 2λπx2 n x n 1! e λπx2 E[R n ] = Γ n λπ Γ n 13 The average energy for he n-h node successfully ransmiing a message of lengh l bis o he cluser head is E node. For evaluaion of he ransmission/recepion energy, we consider he success probabiliy given by ϕ N, he energy consumpion for he unsuccessful nodes only consiss of he energy wased while sensing. E node n = C N E sense + l ϕ N Eelec + ε fs E[R n ] 2 14 The cluser heads mus sense he channel unil all nodes have eiher successfully compleed he round or abored heir aemp. They receive S N messages, which are aggregaed o a single message and hen ransmied o he sink. We assume ha he cluser head is locaed a disance x from he sink and ha no compression akes place, i.e., he aggregaed message has a lengh of l S N. The average energy expended a a cluser head

9 normalized energy consumpion 2.5e-5 2.0e-5 1.5e-5 L=1 1.0e-5 L=2 L=5 0.5e-5 L= number of nodes N a Energy consumpion per node oal energy consumpion 1.2e-3 1.0e-3 L=10 8.0e-4 L=5 6.0e-4 L=2 4.0e-4 L=1 2.0e success probabiliy b Tradeoff: success vs. energy Fig. 6. Toal energy consumpion per round per round is denoed as E head and he oal energy consumpion in he cluser is given by E cluser in Eqn. 16. E head N, x = E[T head ] E sense + l S N + 1 [ E fuse + ε fs x 2] + 2 S N + 1 E elec 15 N E cluser N, x = E head N, x + E node n 16 n=1 The energy consumpion normalized per node and packe lengh is depiced in Fig. 6a for he values λ = 0.01, M = 4, and x = 50. I seems ha increasing he number of nodes or he message lengh reduces he energy consumpion. However, from Fig. 5b we could see ha large N or L end o have a small number of successful nodes. The monoonous decrease in Fig. 6a is caused by many node failures and few acual ransmissions, so energy is only consumed by sensing. In Fig. 6b we mapped he success probabiliy o he dissipaed energy. Energy consumpion is minimal, when he success probabiliy is high, however, his only occurs for small N. The mos energy is consumed in he mid-region where we have he highes absolue number of successful nodes. The opimal operaing poin of he sensor nework should herefore lie somewhere o he righ of he maximum poin, depending on he desired success probabiliy. 5 Conclusion and Oulook In his paper we modeled he CSMA/CA algorihm in IEEE and performed a non-saionary analysis for synchronized ransmission aemps. We showed ha using he defaul values given in [6] provides oo shor backoff window sizes causing many collisions when he number of nodes is large. Wih our model we derived he disribuion of he oal delay for a cluser wih N nodes and he ime each individual node needs for is ransmission aemp. Based on hese disribuions, we esimaed he average energy consumpion for performing a single round of daa gahering in one cluser. The resuls showed ha i is indeed very hard o deermine a mos energy-efficien cluser size by rading off success probabiliy and energy consumpion.

10 However, o give deailed resuls abou he energy consumpion of a whole sensor nework, a specific clusering mehod and he coss of is energy overhead [12] need o be analyzed in conjuncion wih he MAC proocol. In he fuure we wish o invesigae hese effecs and deermine he opimal cluser size when he cluser heads employ direc or muli-hop ransmission o he sink. Wih his paper a framework o faciliae he analysis of clusered sensor neworks operaing wih IEEE CSMA/CA is provided. Acknowledgmens The firs auhor would like o hank Michael Menh for he discussions on he model in [10]. This research was suppored by The 21s Cenury COE Program: New Informaion Technologies for Building a Neworked Symbiosis Environmen and a Gran-in-Aid for Scienific Research A of he Minisry of Educaion, Culure, Spors, Science and Technology in Japan. References 1. Akyildiz, I., Su, W., Sankarasubramaniam, Y., Cayirci, E.: A survey on sensor neworks. IEEE Communicaions Magazine Ye, W., Heidemann, J., Esrin, D.: An energy-efficien MAC proocol for wireless sensor neworks. In: IEEE INFOCOM, New York, NY Heinzelman, W., Chandrakasan, A., Balakrishnan, H.: An applicaion-specific proocol archiecure for wireless microsensor neworks. IEEE Transacions on Wireless Communicaions Kamimura, J., Wakamiya, N., Muraa, M.: Energy-efficien clusering mehod for daa gahering in sensor neworks. In: Firs Workshop on Broadband Advanced Sensor Neworks BaseNes, San Jose, CA ZigBee Alliance. hp:// 6. IEEE : Wireless Medium Access Conrol MAC and Physical Layer PHY Specificaions for Low-Rae Wireless Personal Area Neworks LR-WPANs Achir, M., Ouvry, L.: Power consumpion predicion in wireless sensor neworks. In: ITC Specialis Seminar on Performance Evaluaion of Wireless and Mobile Sysems, Anwerp, Belgium Lu, G., Krishnamachari, B., Raghavendra, C.: Performance evaluaion of he IEEE MAC for low-rae low-power wireless neworks. In: Energy-Efficien Wireless Communicaions and Neworks EWCN 04, Phoenix, AZ Misic, J., Shafi, S., Misic, V.: Performance of beacon enabled PAN in sauraion mode. In: Symposium on Performance Evaluaion of Compuer and Telecommunicaion Sysems SPECTS, San Diego, CA Foh, C., Zukerman, M.: Performance evaluaion of IEEE In: IEEE Vehicular Technology Conference VTC Fall, Alanic Ciy, NJ Krishnamachari, B., Esrin, D., Wicker, S.: The impac of daa aggregaion in wireless sensor neworks. In: Proc. of DEBS 02, Vienna, Ausria Leibniz, K., Wakamiya, N., Muraa, M., Remiche, M.A.: Analysis of energy consumpion for a biological clusering mehod in sensor neworks. In: Third Inernaional Workshop on Measuremen, Modelling, and Performance Analysis of Wireless Sensor Neworks SenMerics, San Diego, CA 2005