International Conferene on Wireless Algoritms, Systems and Appliations Capaity Analysis for Flat and Clustered Wireless Sensor etworks Min Song, Bei He Department of Eletrial and Computer Engineering Old Dominion University orfolk, VA 359 {msong, bexx1}@odu.edu Abstrat Wireless sensor networks are often divided into lusters to gain ig-performane and prolong network lifetime. In tis paper we analyze te network apaity of two different aritetures, named flat sensor network and lustered sensor network. For ea network, we first define te network model and ten analyze te network apaity and te fators tat affet te apaity. umerial results suggest tat lustering an signifiantly improve te network apaity. We also found tat te apaity of a lustered network is saturated after te number of lusters is above a ertain value. For lustered network ariteture, we furter study te apaity differene wit or witout te distributed oordination funtion. It is found tat tere is a ritial value of te number of luster eads beyond wi te network apaity of two lustered models approaes te same. esults from tis resear will provide guidane in deploying igperformane wireless sensor networks. 1. Introdution eent advanes in miro-eletro-meanial systems tenology, wireless ommuniations, and digital eletronis ave put wireless sensor networks into a wide range of appliations [1]. A wireless sensor network is omposed of a large number of sensor nodes wit a sort-range radio and on-board proessing apability, wi are densely deployed eiter inside or lose to te penomenon to sense ertain pysial penomena. At te same time tese sensor nodes must organize temselves to form a multi-op ommuniation network, sine teir main task is to report te raw or partially proessed data to a entral unit, alled sink. Te sink is te ultimate destination of data from all sensor nodes. Terefore, te basi ommuniation model of wireless sensor networks is many-to-one type. We use te same definition in [] to desribe te transport apaity of su many-to-one type: wen all or many of te soures are transmitting to a single sink, te trougput apaity is te per soure data trougput. Ariteturally, sensor nodes an be organized as a flat network or a lustered network. In te flat ariteture, all sensor nodes transmit teir own data and relay data for oter nodes to te sink. In te lustered ariteture, adaent nodes are organized as a luster; a ead is eleted for ea luster. Sensor nodes tat belong to te same luster an only send or relay data to teir luster ead. Te luster ead ten relays te data to te sink via a long-aul ommuniation link. Clustering brings many advantages, for example, it allows for salability of MAC and routing, and it solves energy unbalaning penomena [3]. Cluster eads an also serve as fusion points to aggregate and proess data, to redue te transmitted data to te sink. Te standardized MAC tenique of 8.11 protools is alled distributed oordination funtion (DCF) [4]. DCF desribes a four-way andsaking tenique, known as TS/CTS/DATA/ACK meanism, to redue ollisions aused by idden terminals. In te flat network ariteture, DCF is applied to detet and notify te interferene. But wen DCF is applied to te lustered network ariteture, it may redue te network apaity. In tis paper our onern is te apaity analysis of flat sensor networks and lustered sensor networks. Te unique ontribution of our work is te definition of an operational lustered network model. Unlike ideal lustered model, our network model does not assume ea node witin te lusters spontaneously knows wen te interferene ours and ow to avoid it. We analyze ow te ombination of DCF and lustering affets te network apaity. To make te analysis simple, sensor nodes and luster eads are stationary ere. Te rest of tis paper is organized as follows. Setion presents some related work. Setion 3 gives te flat network model and analyzes its apaity. In -7695-981-X/7 $5. 7 IEEE DOI 1.119/WASA.7.3 49
Setion 4 we define te representative lustered network model and perform te apaity analysis. In Setion 5 numerial apaity omparison between flat and lustered aritetures is presented. Setion 6 onludes te paper.. elated work Gupta and Kumar [5] studied te trougput apaity of a wireless network. Wen a wireless network as n randomly loated nodes, ea apable of transmitting at W bits per seond and using a fixed radio range, te aievable per node trougput is Θ ( W nlogn). As a diret result te trougput at ea node dereases wit inreasing nodes, beause ea node gives up some of its available trougput to forward pakets from neigboring nodes. So it an be expeted tat if te soure nodes only link wit te nearest relay, and forwarding is limited to te relays, te trougput will inrease. However, Gupta and Kumar indiated tat te addition of dediated relays would not ange te saling properties if te relays use te same wireless annel. If mobility is used to redue te number of ops needed to rea te destination, te apaity obtained in [5] an be inreased. Paper [6] introdued a very partiular traffi pattern, named relay traffi pattern, to study te apaity of ad o networks. Aording to te relay traffi pattern, tere is only one ative soure/destination pair; all oter nodes (exept te sender and reeiver nodes) at as relays. It is possible to derive tat te upper bounds for te apaity in tis ase, wit te number of nodes n inreasing to infinity, is of O(logn) bits per seond. Paper [7] gave te performane analysis in a largesale lustered sensor network, in wi luster eads use multi-op ommuniations to transmit data to te sink. Analytial study was onduted to investigate ow parameters, su as te ommuniation distane of a luster ead, affet te network trougput. Te onlusion is tat te network trougput an be approximately doubled by not unneessarily relaying data in te neigborood of te sink. Duarte-Mel and Liu [] analytially evaluated te apaity of wireless sensor networks. Tey introdued an overall upper trougput bound as W/n per node. Tey studied under wat onditions tis bound an be aieved and under wat onditions it an not. Wen te bound is not met, tey dedued ow O(W/n) an be aieved wit a ig probability as te number of sensor nodes goes to infinity. By employing te lustering tenique, it is proved tat te apaity of te lustered network ould easily rea W/n wen ertain onditions, su as te number of luster eads and te radio range of sensor nodes, are satisfied. 3. Flat network model and apaity Te flat network model is defined as following: 1) Te sensing area is a irle of radius ; te sink is loated at te enter of te irle. ) Totally sensor nodes are uniformly distributed over te sensing area; all nodes sare a ommon wireless annel; te fixed transmitting range of ea node is r. 3) ode X i transmits data to node X suessfully only te following two onditions old: X i r and X k X i +, ere represents te guard zone to prevent a neigboring node X k from transmitting on te same annel at te same time. It also allows for impreision in te aieved range of transmissions. 4) Ea node as a single ommuniation annel, so no node an transmit and reeive data simultaneously; ea sensor node ommuniates wit te sink via a single-op or multi-op ommuniation. Apparently, transmitting interferene exists among nodes. Take node A in Figure 1 as an example. ode A an suessfully transmit data to oter nodes witout interferene unless tere are also transmissions from oter nodes witin te irle of radius r + entering on node A. To see te reason let us onsider te ase tat nodes A and C are transmitting data simultaneity. Te intended reeiver of A is B. If A and C are witin r + range, and B is loated witin te overlapping area between te irle of radius r around node A and te irle of radius r + around node C, C s transmission interferes wit te transmission from A to B. So te area of interferene of one transmitting node is a irle of radius r +. Figure 1. Commonly Interferene Model To study te apaity of su a flat network, we assume tat all sensor nodes sare te resoure by following a transmission sedule tat onsists of time slots. Tis sedule determines wi subset of nodes an transmit simultaneously, wit a onstraint tat every node as a ane to transmit. Sine te sink is a 5
bottlenek beause all pakets tend to onentrate in its reeiving annel, te trougput apaity of per node an be defined as te reiproal of te above sedule lengt. Let te number of nodes tat an transmit simultaneously be Sim. We ave π Sim π ( r (r + Wit te assumption tat ea node as te same traffi load, te sedule lengt, denoted by s, is determined as follows: s Sim ( r eall tat only te nodes tat are one op away from te sink transmit data to te sink. Te number of one-op nodes an be approximated as following: πr r one op π Let λ denote te per node apaity. In order to get maximized per node apaity, ea one-op node as to get an equal sare of te total traffi load. We derived te per node apaity as following: λ one op W s ) 3) Cluster eads annot send and reeive data simultaneously. 4) DCF is te MAC protool to notify interferene. Figure sows te lustered network ariteture. Ea luster overs an area of te same size, toug not neessarily te same sape, wi means te lusters essentially form a Voronoi tessellation [8] of te field. Witin ea luster, sensor nodes ommuniate wit teir luster ead via a single-op or multi-op ommuniation. Te luster ead ten ommuniates wit te sink. Here te lustered model is eterogeneous [9]. Te interferene area of su a lustered sensor network is analyzed by using Figure 3. Figure. Clustered etwork Ariteture We ave te per node apaityλ, W r λ (1) (r It is interesting to notie tat λ is independent wit. 4. Clustered network model and apaity As indiated in Eq. (1), λ an be inreased by reduing te number of sensor nodes. Tis inspires te idea of introduing some pure relay nodes serving exlusively as forwarders. Te lustered network model is defined as follows: 1) Totally sensor nodes are uniformly distributed over te sensing area; among of tem, nodes are luster eads; te number of sensor nodes in ea luster is tus. ) Two frequeny annels are used, one for te ommuniation between sensor nodes and luster eads and te oter one for te ommuniation between luster eads and te sink; te transmission apaity of ea annel is same as te one in flat network (W). Figure 3. Interferene model wen DCF is introdued In Figure 3, node D is transmitting data. odes B, C, E, and F ten an not transmit data, beause all of tem are loated in te irle of radius r + entering on node D. Furtermore, node A, toug apart te distane of 3r from node D, an not transmit data simultaneously. Atually node A an send orret TS to node B, but node D s transmissions prevent B from sending te orresponding CTS bak. So te area 51
of interferene of one transmitting node is a irle of radius3 r +. Te luster ead splits its time into two parts: reeiving data from sensor nodes and transmitting data to te sink. Let λ denote te per node apaity. So λ sould be te per node apaity aieved during te portion of time tat te luster ead is reeiving data. Ea luster ould be onsidered as a flat ariteture, and te luster ead is te sink. eall te interferene area is a irle of radius3 r + beause of DCF. Aording to Eq. (1), we get: W r W r λ () ( 3r ( ) (3r Comparing Eqs. (1) wit (), λ as one more fator, and is on te numerator position. At te same time, on te denominator position te interferene area is enlarged by te introdution of DCF. Tus it is not immediately lear weter λ is greater tanλ. In order to aieve te maximum apaity, te sink as to be busy all te time, wi means tat at any moment tere sould be one transmission between te sink and one of te luster eads. We assume tat all luster eads diretly ommuniate wit te sink and all luster eads transmit te same amount of data. So te sink splits its time period into time slots and assigns one slot to ea luster ead. Terefore, ea luster ead transmits 1 fration of te time, and uses ( 1 1 ) fration of te time to reeive data. Here luster eads serve only as simple relays by wi all sensed data are sent to te sink. If te total trougput aieved witin lusters is greater tan W, sensor nodes ave sent more to te luster eads tan tey an delivery to te sink. In tis ase, te sink as to drop some reeived data. Terefore, λ must satisfy te following inequality: λ (1 1 ) W After some algebra, we ave: W λ (3) ( 1) Sine te apaity λ must satisfy bot () and (3) simultaneously, it is as flowing: min( W r W λ, ) (4) (3r ( 1) 5. Comparative results In tis setion, te trougput apaity of different network aritetures is ompared. First, te lustered network model wit DCF is ompared wit te flat network model. Ten it is ompared wit te ideal lustered network witout DCF used in []. 5.1 Compare wit te flat network model In te ase of, wi means tere is no guard zone between two neigbor nodes, te omparative ratio K is te funtion of te number of luster eads as sown in Figure 4. Capaity atio K 5 4.5 4 3.5 3.5 1.5 1.5 K vs wen guard zone apaity ratio K referene value 1 5 1 15 5 3 35 4 45 5 umber of Cluster Heads Figure 4. Capaity ratio between lustered network wit DCF and flat network in te ase of In Figure 4, wen 3, te urve is always above te line wose value is 1, wi means te apaity of lustering network model wit DCF is greater tan tat of a flat network model. It is observed tat K ontinues inreasing wit te inreasing of, until it reaes te maximum value beause of te ontribution of lustering. Ten K dereases and eventually onverges to a ertain value wit te inreasing of to te infinity, wi results from te total trougput limitation indiated in formula (3). Similar urves were obtained wen. Tis proves tat te introdution of lustering is te maor fator to improve network apaity. 5. Compare wit te ideal lustered network eall tat DCF is not used in te ideal lustered network. Figure 5 sows te apaity ratio between 5
lustered network model wit DCF and te ideal lustered network model in te ase of. Capaity ation K K vs wen guard zone 1.8.6.4. 6. Conlusions In tis paper we studied te ommuniation apaity in many-to-one sensor networks. We defined a lustered network model tat uses DCF to andle te interferene. Comparing our model wit te flat network, te onlusion is tat lustering is te maor fator to improve network apaity. Witout enoug luster eads, te introdution of DCF into lustered network dereases te network apaity ompared wit te ideal lustered network. However, te two lustered models ave te same upper bound. We also found tat wen te number of luster eads reaes a ertain value, DCF does not affet te network apaity. 4 6 8 1 1 14 16 18 umber of Cluster Heads Figure 5. Capaity ratio between lustered network wit DCF and ideal lustered in te ase of As an be seen from Figure 5, before bot models rea teir apaity upper bounds, te introdution of DCF redues te network apaity. Wit te inreasing of te number of luster eads, te apaity differene beomes negligible. From Figure 5 we find tat tere is a ritial value of te number of luster eads beyond wi te network apaity of two lustered models approaes te same. We plot tis ritial value in Figure 6 for different guard zone size. From Figure 6 we find tat tis ritial value is independent wit te network size, but related wit te size of guard zone. If we enlarge guard zone between two neigboring nodes, we must add more luster eads to guarantee te network apaity. Critial value of luster eads 3 5 15 1 5..4.6.8 1 1. 1.4 1.6 1.8 atio between guard zone range and transmitted range /r Figure 6. Critial value of luster eads vs. guard zone size Aknowledgement Te resear of Min Song is supported by te ational Siene Foundation Career award. eferenes [1] I.F. Akyildiz, W. Su, Y. Sankarasubramaniam and E. Cayiri, Wireless sensor networks: a survey, IEEE Computer, vol. 38, no. 4, pp. 393-4, Mar. [] E. J. Duarte-Melo and M. Liu, Data-gatering wireless sensor networks: organization and apaity, Computer etworks, vol. 43, no. 4, pp. 519-537, 3. [3] Jing Ai, Damla Turgut, and Ladislau B ol oni, A luster-based energy balaning seme in eterogeneous wireless sensor networks, Pro. of te 4t International Conferene on etworking, pp. 467-474, April 5. [4] G. Biani, Performane analysis of te IEEE 8.11 distributed oordination funtion, IEEE Journal on Seleted Areas in Communiation, vol.18, pp.535-547, Mar,. [5] P. Gupta, and P.. Kumar, Te apaity of wireless networks, IEEE Trans. on Information Teory, vol. 46, no., pp. 388-44,. [6] M. Gastpar, and M. Vetterli, On te apaity of wireless networks: te relay ase, Pro. of IEEE IFOCOM,. [7] Masasi Sugano, Yuii Kiri, and Masayuki Murata, Performane analysis of large-sale wireless sensor network ariteture wit multi-luster onfiguration, Pro. of IASTED International Conferene on etworks and Communiation Systems, pp. 188-193, Mar 6. [8] A. Okabe, B. Boots, and K. Sugiara, Spatial Tessellation Conepts and Appliations of Voronoi Diagrams, Wiley, ew York, 199. [9] V. Matre and C. osenberg, Homogeneous vs eterogeneous lustered sensor networks: a omparative study, Pro. of IEEE ICC, vol. 6, pp. 3646-3651, June 4. 53