Adaptive Distributed Topology Control for Wireless Ad-Hoc Sensor Networks

Transcription

1 Adaptve Dstrbuted Topology Control for Wreless Ad-Hoc Sensor Networks Ka-Tng Chu, Chh-Yu Wen, Yen-Cheh Ouyang, and Wllam A. Sethares Abstract Ths paper presents a decentralzed clusterng and gateway selecton algorthm for wreless ad-hoc sensor networks. Each sensor uses a random watng tmer and local crtera to determne whether to form a new cluster or to jon a current cluster and utlzes the messages transmtted durng herarchcal clusterng to choose dstrbuted gateways such that communcaton for adjacent clusters and adaptve dstrbuted topology control can be acheved. The algorthm operates wthout a centralzed controller, t operates asynchronously, and does not requre that the locaton of the sensors be known a pror. A performance analyss of the topology management and the energy requrements of the algorthm are used to study the behavors of the proposed algorthm. The performance of the algorthm s descrbed analytcally and va smulaton. I. INTRODUCTION Wthout a robust nfrastructure, sensors n an ad-hoc network may be requred to self-organze. Such sensor networks are self-confgurng dstrbuted systems and, for relablty, should also operate wthout centralzed control. In addton, because of the lmted energy source, energy-effcency s a crtcal consderaton. There has been extensve research on the desgn and development of energy effcent networkng technques. In [1], the Low-Energy Adaptve Clusterng Herarchy (LEACH) utlzes a randomzed perodcal rotaton of clusterheads to balance the energy load among the sensors. LEACH-C (Centralzed) [2] uses a centralzed controller to select clusterheads. The man drawbacks of ths algorthm are nonautomatc clusterhead selecton and the requrement that the poston of all sensors must be known. LEACH s stochastc algorthm s extended n [3] wth a determnstc clusterhead selecton. Smulaton results demonstrate that an ncrease of network lfetme can be acheved compared wth the orgnal LEACH protocol. The Ad hoc Network Desgn Algorthm (ANDA) [4] maxmzes the network lfetme by determnng the optmal cluster sze and the optmal assgnment of sensors to clusterheads but requres a pror knowledge of the number of clusterheads, number of sensors n the network, and the locaton of all sensors. The Weghted Clusterng Algorthm (WCA) [5] consders the number of neghbors, transmsson power, moblty, and battery usage n choosng clusters. It lmts the number of sensors n a cluster so that clusterheads can handle the load wthout degradaton n performance. These clusterng methods rely on The Department of Electrcal Engneerng, Graduate Insttute of Communcaton Engneerng, Natonal Chung Hsng Unversty, Ta-Chung, Tawan. (emal:cwen@dragon.nchu.edu.tw) The Department of Electrcal and Computer Engneerng, Unversty of Wsconsn-Madson, Madson, WI 5376, USA (emal:sethares@ece.wsc.edu) synchronous clockng for the exchange of nformaton among sensors wh typcally lmts these algorthms to smaller networks [6]. In [7], the dstrbuted topology control usng the cooperatve communcaton (DTCC) algorthm s proposed to provde a connected network topology wth mnmal total energy consumpton. In order to provde relable communcaton n wreless adhoc networks, mantanng network connectvty s crucal [8]- [15]. An mplementaton of the lnked cluster archtecture may consder the followng tasks: cluster formaton, cluster connectvty, and cluster reorganzaton. In order not to rely on a central controller, clusterng s carred out by adaptve dstrbuted control technques va random watng tmers. To ths end, the Adaptve Dstrbuted Topology Control Algorthm (ADTCA) forms clusters and lnks n three phases: (I) clusterhead selecton; (II) gateway selecton, and (III) cluster reformaton. In Phase I, clusterheads are selected and cluster members are assgned. A decentralzed algorthm [8] s used to organze the network nto clusters. Each sensor operates ndependently, montorng communcaton among ts neghbors. Based on the number of neghbors and a randomzed tmer, each sensor ether jons a nearby cluster, or else forms a new cluster wth tself as clusterhead. In Phase II, based on bdrectonal message exchanges and the cluster archtecture, sensors are selected as gateways n a fully dstrbuted way. Once the network topology s specfed (as a herarchcal collecton of clusters and dstrbuted gateways), mantenance of the lnked cluster archtecture becomes an ssue. In Phase III, localzed crterons governng cluster reformaton are descrbed and llustrated va smulatons. Ths proposed self-confguraton protocol s energy effcent, scalable, and may extend the lfetme of the network. Several aspects of ths cluster-based topology control (such as the tme synchronzaton problem and effcent network routng) are studed. A performance analyss and smplfed models of the algorthm are derved, and the results are compared to the behavor of the algorthm n a number of settngs. II. THE ADAPTIVE DISTRIBUTED TOPOLOGY CONTROL ALGORITHM (ADTCA) Ths secton descrbes a randomzed dstrbuted algorthm that forms clusters and reselects clusterheads effcently. The network setup s performed n three phases: clusterng, selectng gateways, and restructurng the clusters. The man assumptons on the network are that (a) the sensors are n fxed but unknown locatons, (b) all lnks between sensors are bdrectonal, and (c) all sensors have the same transmttng

2 Fg. 1. The connectvty of the network (top); clusters are formed n a random network of 1 sensors wth R/l =.17 (bottom). range. Observe that there s no base staton or centralzed control to coordnate or supervse actvtes among sensors. A. Phase I: Clusterhead Selecton When sensors of a network are frst deployed, they may apply the Clusterng Algorthm va Watng Tmer (CAWT) from [8] to partton the sensors nto clusters usng the watng tmer W T (k+1) = γ W T (k), (1) where W T (k) s the watng tme of sensor at tme step k and < γ < 1 s nversely proportonal to the number of neghbors. If the random watng tmer expres and none of the neghborng sensors are n a cluster, then sensor declares tself a clusterhead. It then broadcasts a message notfyng ts neghbors that they are assgned to jon the new cluster wth ID. After applyng the CAWT, there are three dfferent knds of sensors: (1) the clusterheads (2) sensors wth an assgned cluster ID (3) sensors wthout an assgned cluster ID, wh wll jon any nearby cluster after τ seconds and become 2-hop sensors, where τ s a constant chosen to be larger than all of the watng tmes. In ths phase, each sensor ntates 2 rounds of local floodng to ts 1-hop neghborng sensors, one for broadcastng sensor ID and the other for broadcastng cluster ID, to select clusterheads and form 2-hop clusters. Hence, the tme complexty s O(2) rounds. Fgure 1 shows the network connectvty and cluster formaton of a random network of 1 sensors wth R/l =.17, where R/l s the rato of transmttng range R to the sde length l of the square. Thus, the topology of the ad-hoc network s now represented by a herarchcal collecton of clusters. B. Phase II: Gateway Selecton Observe that Phase I nduces nonoverlappng clusters. Accordngly, to nterconnect two adjacent nonoverlappng clusters, one cluster member from each cluster must become a gateway. Ths subsecton presents a method of choosng dstrbuted gateways for adjacent nonoverlappng clusters. As n Phase I, random watng tmes and local nformaton are appled to select gateways and further acheve communcaton between clusters. The result of the phase II processng s that each cluster assgns a sngle member to communcate wth each nearby cluster j. The watng tmers help to ensure that the chosen member s one of the nearest members even though the topology of the system s unknown. If the clusters are too far apart (outsde the range of communcaton R), no gateway sensors wll be assgned. At the begnnng of the task, clusterheads broadcast messages to trgger the gateway selecton process. After applyng the procedure for determnng gateways, the gateway nodes broadcast messages to update the connectvty nformaton and actvate the lnked cluster archtecture. The procedure for choosng gateways s summarzed n Table I. Let n denote sensor n n cluster and m j denote sensor m n cluster j. G j wll denote the gateway sensor that connects cluster to cluster j. d n m j s the dstance between sensors n and m j, wh could be estmated by receved sgnal strength. The parameter β controls the rate at wh the tmers ncrease or decrease n response to the recepton of messages from nearby sensors. Note that n gateway selecton (n step d)(1)), a clusterhead may be able to communcate wth a nearby cluster drectly. Therefore, a larger counter (1β) s assgned to the clusterhead n order to be selected as a gateway n ths case. Otherwse, each cluster member follows a regular control rate β to ncrease the counter and decrease the watng tme. C. Phase III: Cluster Reformaton Ths subsecton presents two methods of choosng a new clusterhead for an exstng cluster. If the energy E of clusterhead s less than a threshold level η, then sensor broadcasts a message to ts cluster members to start the reselecton process. Only those sensors wth energy larger than η are elgble. The frst method s a centralzed technque that the current clusterhead, sensor, determnes a new clusterhead by aggregatng energy and neghbor nformaton from ts cluster members and solvng the optmzaton problem: arg max l (1 E(k) l El max ) N l (2) subject to : E l > η; l C, (3) where E (k) l s the energy at tme step k, El max s the ntal energy of sensor l, C s the ndex set of the cluster members of sensor, and N l s the number of neghbors of sensor l. That s, the current clusterhead pcks the new clusterhead, choosng a member wth large energy and many neghbors. The second method s a dstrbuted technque, wh operates much lke the CAWT n utlzng a random tmer. Once the energy n the current clusterhead s below the threshold,

3 TABLE I DESCRIPTION OF GATEWAY SELECTION. a) Based on the cluster formaton n Phase I, each sensor broadcasts ts cluster ID nformaton. b) Intalze a vector of random watng tmes W T (n,k) j, where W T (n,k) j s the watng tme of sensor n for cluster j at tme step k. c) Intalze a counter of sensor n, C (n ) j =, for gateway selecton n cluster to cluster j. d) If sensor n receves a message from sensor m j. (1) ncrease the counter f n s a clusterhead C (n ) j = C (n ) j + 1β. else C (n ) j = C (n ) j + β. end where C (n ) j s the counter of sensor n for cluster j, β = α(1 d n m j ) wth a postve nteger α, R d n m j s the dstance between sensors n and m j, and R s the transmsson range. (2) decrease the watng tme W T (n,k+1) j = W T (n,k) j C (n ) j. e) Gateway check: f W T (n,k) j = (1) assgn G j = n, and then G j broadcasts the gateway nformaton to ts neghbors. (2) set C (x ) j = and stop the watng tmer for all neghborng sensors x n cluster. else go to step d). end t transmts a message to start the reselecton process. Each cluster member then checks the energy constrant. As long as the cluster member satsfes the constrant, t generates a random watng tme: W T (k+1) = (1 E(k) E max ) N c W T (k), (4) wh depends on the number of neghborng cluster members N c and the remanng energy level. The motvaton for formng subclusters s to provde a way to do mult-hop communcaton wthn a cluster, wh may be needed because sensors are no more than 2 hops away from the ntal clusterhead and sensors may be up to 4 hops away from the new clusterhead. Hence, sensors n a cluster may be further classfed as: (1) subcluster member, (2) subclusterhead, or (3) clusterhead. Subclusters and subclusterheads are generated by applyng ths dstrbuted protocol to the cluster topology. For real applcatons, t s possble that the clusterhead may malfuncton before broadcastng the reselecton message. One soluton s that f a certan amount of tme has passed wth no messages from the clusterhead, then all sensors begn ther tmers and apply the algorthm. As a result, restructurng the cluster formaton of the network may be requred when the clusterhead malfunctons or when none of the cluster members satsfy the energy constrant. In ths case, t may necessary to re-ntalze the network nto new clusters to help balance the energy burden. Such reformaton may also be useful n the event that the network topology changes or the sensors move. III. PERFORMANCE ANALYSIS Because of the complexty of the ADTCA, t s dffcult to evaluate the algorthm drectly other than va smulaton. Snce the connectvty among sensors and the number of neghborng sensors play mportant roles n the ADTCA, t s reasonable to nvestgate the performance from the perspectve of these parameters. The performance analyss of cluster formaton (Phase I) s derved n [8]. In ths secton, we abstract the behavor of gateway selecton (Phase II) protocol usng two smplfed models wh approxmate the desred global behavor and serve to analyze ts performance. A. The Densty Model The frst smplfed model s the Densty Model wh s detaled n Table II. The basc dea of ths model s to suppose that the probablty of sensor n n cluster of beng a dstrbuted gateway to cluster j, p (n ) j, s proportonal to the number of the neghborng sensors wh belong to cluster j,. That s, N (n ) j p (n) j N (n) j, (5) M j where M j s the number of sensors n cluster j. If sensor n and ts neghborng sensors are not already chosen as a gateway to cluster j, then the sensor wth the largest p (n ) j s chosen to be a gateway and t assgns probablty to ts neghbors wh have not yet become a gateway to cluster j. Thus, a sensor becomes a gateway to cluster j f t has the hghest neghborng densty among all sensors wh have not yet become gateways. After updatng the probablty dstrbuton of sensors, the procedure repeats untl all gateways are chosen. The ratonale for ths choce s that, f the random watng tme of each sensor s long enough (n the sense that each sensor s able to collect suffcent neghborng nformaton), then the model s lkely to closely approxmate the behavor of Phase II n the ADTCA on any gven ad-hoc network. The close connecton between the model and the algorthm s explored va smulaton. B. The Dstrbuted Randomzed Model Snce a cluster s a small network, the behavor of the algorthms may be analyzed (followng our results n [8]) by the Averaged Model to nvestgate and descrbe the clusterng behavor. Moreover, gateway selecton s hghly related to the cluster formaton such that dstrbuted gateways can be appled to connect adjacent clusters, wh mples that the number of gateways n a network may be nduced by a probablstc model wth the number of clusterheads and cluster-based network topology. 1) Overvew of The Averaged Model: The CAWT can be modeled by a smplfed averagng procedure. Assume that a sngle clusterhead and an average number of neghborng sensors E (k) [N ] are removed durng each teraton k. Assume that each sensor wll be removed wth probablty p (k) rm = r k /m k, where r k s the number of sensors to be removed and m k s the number of sensors remanng at teraton k.

4 TABLE II DESCRIPTION OF THE DENSITY MODEL. a) Assgn a probablty to sensor n for beng a gateway to cluster j, p (n ) j, proportonal to the number of neghbors wh belong to cluster j, N (n ) j. That s, p (n ) j N (n ) j, where M M j s the number j of sensors n cluster j. b) Let S j denote the set of probablty measures {p (n ) j } n cluster for selectng a gateway to cluster j. c) Let B (n ) j be the set of neghborng sensors n cluster j wth respect to sensor n. d) Let P (k) be a set of probablty measures {S (k) j } at tme step k. e) Assgn k = and P () ={S () j }. whle (sum(p (k) ) > ) (1) Gateway selecton G j = arg max (k) S j (2) Update the probablty dstrbuton end {p (n ) j } p (m ) j =, m G j p (l j ) j = mn{2p (l j ) j, 1}, sensor l j B (n ) j. set k = k + 1. Denote the collecton of sensors at teraton k by V k. Snce a clusterhead and ts neghborng sensors are removed at each teraton, the collecton of sensors at the next teraton, V k+1, s smply a new and smaller network. The Lndeberg Theorem [16] can be appled to approxmate the dstrbuton of the number of clusterheads at teraton k by N (µ k, σk 2 ), where µ k = m k =1 p(k), σk 2 = m k =1 p(k) (1 p (k) ), m k s the number of sensors n V k, p (k) s the updated probablty dstrbuton of sensor at teraton k, wh s proportonal to the number of neghborng sensors, I k, and I k s the ndex set of sensors at teraton k. Once the procedure termnates, the number of teratons s an estmate of the number of clusterheads formed n the network. 2) The Predcton Formula: The operaton of the ADTCA wth the dstrbuted model s parttoned nto rounds, where each round ntalzes, clusters are formed, and gateways are selected. The Dstrbuted Randomzed Model s descrbed n Table III. To obtan the mean and varance of the number of clusterheads of each teraton, the probablty dstrbuton of these random varables must be updated. However, t s not smple to calculate p (k) at teraton k snce the process of selectng a clusterhead at each teraton s complex. The followng smplfed analyss restructures the connectvty of the network so that each sensor has the same average neghborng densty at each teraton. Therefore, we have E (k+1) [N ] = N (k) b r k E (k) [N ] m k+1. (6) Thus, the dstrbuton of the number of clusterheads can be approxmated by N (µ ch, σch 2 ), where N t N t m k µ ch = µ k = p (k), (7) k=1 k=1 =1 TABLE III DESCRIPTION OF THE DISTRIBUTED RANDOMIZED MODEL. a) Let N (k) b P be the sum of neghborng sensors of sensors at teraton k. N (k) m b = k =1 N (k). m k s the number of sensors remanng at teraton k. I k ; I k s the ndex set of sensors at teraton k. b) Let E (k) [N ] be the average number of neghbors at teraton k. E () [N ] = N () b. m c) Assgn the probablty p (k) to sensor, proportonal to the number of neghborng sensors, N k. That s, p(k) d) Assgn k =, m = n, r =. whle (m k r k ) > m k+1 = m k r k, E (k+1) [N ] = N (k) r b k E (k) [N ], m k+1 r k+1 = E (k+1) [N ] + 1, k = k + 1. N (k) N (k) b end s the celng functon. e) Gven the estmated number of clusterheads, N ch, generate a random network of N ch sensors wth transmsson range R 2 l 2 (ln(l)/n ch ) f) Approxmate the number of dstrbuted gateways n the network by the sum of the neghborng sensors of the N ch sensors P N N g = ch =1 N (g), where N (g) s the number of the neghborng sensors for sensor durng the procedure of gateway selecton. N t N t m k σch 2 = σk 2 = p (k) (1 p (k) ), (8) k=1 k=1 =1 where N t s the number of teratons. Moreover, suppose that the expectaton of the number of neghborng sensors of each sensor n the network s used to approxmate the number of neghborng sensors that wll be removed at each teraton (.e. the sensors wh wll eventually jon the new cluster). Thus, Then E (k) [N ] = E[N ] = 1 n. n N, for all k. =1 r k = E[N ] + 1, and a smple formula for predctng the number of clusterheads s n N ch = E[N ] + 1. (9) Based on the cluster formaton and gven the estmated number of clusterheads, N ch, a random network of N ch sensors wth transmsson range R 2 l 2 (ln(l)/n ch ) [17] s generated to abstract the behavor of gateway selecton and approxmate the number of dstrbuted gateways n the network. Ths s attrbuted to the close relatonshp between the cluster formaton and gateway selecton. Therefore, followng the analyss of the Averaged Model, the total number of gateways N g s gven by N ch N g = N (g), (1) =1

5 where N (g) s the number of the neghborng sensors for sensor durng the procedure of gateway selecton. Hence, the average number of gateways N g(avg) n a cluster s N g(avg) = N g N ch (11) = N g n ( E[N ] + 1). (12) The relatonshp between the behavor of gateway selecton (Phase II) of the ADTCA and that of the Dstrbuted Randomzed Model s shown expermentally n Secton V. IV. ENERGY CONSUMPTION ANALYSIS Ths secton analyzes the energy consumpton of the ADTCA when executng the three phases: clusterhead selecton, gateway selecton, and cluster reorganzaton. The total power requrements nclude both the power requred to transmt messages and the power requred to receve (or process) messages. A. Phase I The energy consumpton of clusterhead selecton assumng homogenous sensors s examned. In the ntalzaton phase, each sensor broadcasts a Hello message to ts neghborng sensors. Therefore, the number of transmssons N Tx s equal to the number of sensors n the network, n, and the number of receptons N Rx s the sum of the neghborng sensors of each sensor. That s, n N Tx = n and N Rx = N j. (13) j=1 As a sensor, say sensor, meets the condtons of beng a clusterhead, t broadcasts ths and assgns cluster ID to ts neghborng sensors. Its neghborng sensors then transmt a sgnal to ther neghbors to update cluster ID nformaton. Durng ths clusterng phase, (1+N ) transmssons and (N + j C N j ) receptons are executed, where C s the ndex set of neghborng sensors of sensor. Ths procedure s appled Suppose that the energy needed to transmt s E T, wh depends on the transmttng range R, and the energy needed to receve s E R. From (16) and (17), the total energy consumpton, E total, for cluster formaton n the wreless sensor network s E total = N T E T + N R E R. (18) Observe that the above analyss s sutable for any transmttng range. However, overly small transmsson ranges may result n solated clusters whereas overly large transmsson ranges may result n a sngle cluster. Therefore, n order to optmze energy consumpton and encourage lnkng between clusters, t s sensble to consder the mnmum transmsson power (or range R) wh wll result n a fully connected network. The performance of the total energy consumpton of Phase I wth dfferent selectons of R s examned va smulaton. B. Phase II The energy consumpton for determnng gateways s evaluated based on the descrpton of Table I. Fgure 2 shows The possble determnaton of a gateway n a cluster. In order to smplfy the presentaton, the man notatons are ntroduced as follows: let I denote the ndex set of clusterheads; let H denote the ndex set of 1-hop cluster members n the network; let H denote the ndex set of 1-hop cluster members of cluster (a subset of H); let M denote the ndex set of 2-hop cluster members n the network; let M denote the ndex set of 2- hop cluster members of cluster (a subset of M); smlarly, let S be the ndex set of sensors neghborng wth 2-hop cluster members; let S be the ndex set of sensors neghborng wth 2-hop cluster members of cluster (a subset of S); let G be the ndex set of gateway nodes Gateway Gateway to all clusterheads and ther cluster members. Now let NT c x and NR c x denote the number of transmssons and receptons for all clusters, respectvely. Hence, N c T x = I (1 + N ), (14) (a) Gateway (2 hop cluster member) Gateway (b) Gateway (1 hop cluster member) wth a 2 hop cluster member N c R x = ( N j + N ), (15) I j C where I s a ndex set of clusterheads. Therefore, the total number of transmssons N T and the number of receptons N R are N T = N Tx + NT c x = n + (1 + N ), (16) I n N R = N Rx + NR c x = j=1 N j + I ( j C N j + N ). (17) (c) Gateway (1 hop cluster member) Fg. 2. The possble determnaton of a gateway n a cluster: (a) a 2-hop cluster member, (b) a 1-hop cluster member wth a 2-hop member, and (3) a 1-hop cluster member. When clusterheads broadcast messages to trgger the gateway selecton procedure, the number of transmsson N T1 and recepton N R1 can be expressed by N T1 = N + N j (19) I I j S

6 N R1 = I N j + N j. (2) j H I j M After applyng the procedure for choosng gateways, the gateway nodes broadcast messages to update the connectvty nformaton and actvate the lnked cluster archtecture. For ths task, the number of transmsson N T2 and recepton N R2 s gven by N T2 = N + N + N (21) I S,/ G G N R2 = H N + M N + G(N Ñ), (22) where Ñ s the number of neghborng cluster members of the gateway. Thus, based on the energy needed to transmt and receve, the total energy consumpton for gateway selecton can be assessed. C. Phase III Ths subsecton consders energy consumpton of cluster reformaton usng both the centralzed and dstrbuted methods. The 1-hop and 2-hop cluster members depend on the ntal herarchy of clusters. A n-hop cluster member s a sensor wh s n hops away from ts ntal clusterhead. Let N be the number of neghborng sensors of sensor, N n hop be the number of n-hop cluster members of clusterhead sensor, and I s be the ndex set of the subclusterheads. 1) The Centralzed Method: For the present clusterhead to select a new clusterhead, t must gather nformaton from the sensors n the cluster. Thus the clusterhead requests data by sendng the nterest message usng 2 rounds of local floodng propagaton to ts 1-hop and 2-hop cluster members. The number of transmssons NT c 1 and receptons NR c 1 of ths desgn choce are approxmately gven by N c R 1 N c T N 1 hop, (23) N 1 hop + j C N j, (24) where C s the ndex set of the cluster members of sensor. Data from the cluster members s then sent towards the clusterhead. The number of transmssons NT c 2 and receptons are N c R 2 N c T 2 N 1 hop N c R 2 + N 2 hop, (25) j C N j. (26) When the clusterhead receves the desred nformaton for solvng the optmzaton problem of (2) and (3), t determnes the new clusterhead and notfes all members. The number of transmssons NT c 3 and receptons NR c 3 are thus NT c 3 = NT c 1 and NR c 3 = NR c 1. 2) The Dstrbuted Method: The energy consumpton of the dstrbuted method s examned n three steps. Step I of the method s to broadcast a message and group cluster members nto subclusters. In ths step, the cluster s consdered as a small network where the energy consumpton analyss of the CAWT [8] can be appled. Therefore, f the current clusterhead s sensor, the number of transmssons NT d 1 and receptons n an error-free channel are approxmately gven by N d R 1 N d T 1 2 (N 1 hop N d R N 2 hop ), (27) j C N j. (28) The msson of Step II s to collect suffcent nformaton from subcluster members. The subclusterhead frst broadcasts an nterest message to nform ts members about what knd of data t requres. Based on ths message, the subcluster members propogate the desred data back to the subclusterhead. Thus, the number of transmssons N d T 2 and receptons N d R 2 are approxmately N d T 2 N d R 2 j I s (1 + 2 N 1 hop j j I s (N 1 hop j N 2 hop j ), (29) k C j N k ). (3) In the fnal Step, subclusterheads exchange ID nformaton n order to determne the new clusterhead. The energy consumed n ths phase may depend on the number of subclusterheads, the related postons among subclusterheads, and how they communcate wth each other. Assume that there exsts n sch subclusterheads n a cluster. In ths case, each subclusterhead broadcasts an nterest message ncludng ts sensor ID to the whole cluster, wh allows subclusterheads to fgure out wh subclusterhead s the new clusterhead mmedately as they receve the ID nformaton and thereby complete the reselecton process. Therefore, we may approxmate the number of transmssons NT d 3 and receptons NR d 3 by N d T 3 n sch (N 1 hop N d R 3 n sch + N 2 hop ), (31) j C N j. (32) The analyss suggests that, compared wth the overall energy consumpton of the dstrbuted method, the centralzed method consumes less energy for reselectng a clusterhead whle the reselecton process may fal due to the malfuncton of the current clusterhead and the corrupted nformaton collecton. V. EXPERIMENTAL RESULTS The smulatons of ths secton study the performance of the ADTCA and valdate the smplfed models for wh analytcal results have been derved. Assume that n sensors are unformly dstrbuted over a square regon n two-dmensonal space. Parameters for the random watng tmer, number of

7 Dstrbuted Randomzed Model, these results provde evdence that the Dstrbuted Randomzed Model provdes a way to roughly predct the performance of the ADTCA n = 1, R = n = 15, R = n = 2, R = n = 1, R = n = 15, R = Densty Model Dstrbuted Randomzed Model Densty Model Dstrbuted Randomzed Model Densty Model Dstrbuted Randomzed Model ADTCA ADTCA ADTCA 5 5 n = 2, R = Fg. 4. The number of gateways formed n a random network usng the (1) ADTCA, (2) Densty Model, and (3) Dstrbuted Randomzed Model, respectvely, wth varyng R/l rato. The rght hand sde shows the standard devaton over 2 runs; the left hand sde shows the confdence ntervals at the 9% level. Fg. 3. Gateway selecton n a random network wth 1 sensors: Phase II of the ADTCA wth R/l =.17 (top) and the Densty Model wth R/l =.17 (bottom). sensors, and rato of transmttng range R to the sde length l of the square, R/l, are nvestgated to provde a smulatonbased study of the ADTCA. The frst set of experments n Fgure 3 evaluates the performance of the Densty Model, wh compares gateway selecton when usng the Densty Model and the operaton of Phase II. The outputs of the two methods are not dentcal due to the randomness of the watng tmer. Nonetheless, both clusterng structures are qualtatvely smlar gven the same network settngs, suggestng that the Densty Model provdes a good approxmaton to Phase II of the ADTCA. The second set of experments compares the estmates of the number of dstrbuted gateways when applyng the procedure of Phase II, the Densty Model, and the Dstrbuted Randomzed Model. In each method, the results of 2 typcal runs are merged. In order to compare the ADTCA and the smplfed models, Fgure 4 shows the standard devaton of the mean number of gateways. The plots vary the number of sensors n and the transmsson power R/l. Also shown n Fgure 4 are the confdence ntervals for the mean number of gateways at a 9% confdence level. The graphs suggest that the Densty Model approxmates the ADTCA somewhat better than the Dstrbuted Randomzed Model. Ths s reasonable because the Densty Model retans global connectvty nformaton whle the Dstrbuted Randomzed Model uses only the average densty nformaton. Though the Densty Model outperforms the The thrd set of experments consders the total energy consumpton of the ADTCA. Assume that the communcaton channel s error-free. Snce each sensor does not need to retransmt any data, two transmssons are executed for clusterhead selecton (Phase I), one for broadcastng the exstence and the other for assgnng a cluster ID to ts cluster members or updatng the cluster ID nformaton of ts neghbors. Hence, the total number of transmssons s 2n. Under these crcumstances, sensor wll receve 2N messages. Then, the total number of receptons s 2 n =1 N. Fgure 5 shows the average number of receptons of random networks after applyng Phase I of the proposed algorthm. Fgure 5 also shows that the number of receptons tends to ncrease as the raton R/l ncreases. Ths mples that energy consumpton s hgher for the network wth larger transmsson power. Ths can be attrbuted to the fact that larger transmsson power allows sensors to detect more neghbors, wh ncreases the number of receptons when assgnng cluster ID or updatng cluster ID nformaton. Therefore, n order to mnmze energy use and keep strong connectvty n the network, an approprate selecton of the transmsson range R s essental. Fgure 6 llustrates the average number of transmsson and recepton n a cluster for executng gateway selecton. Observe that the operaton of Phase II n the ADTCA may lead to a mnmal varaton of the energy consumpton wth ncreased network densty, wh may help to acheve balance the load among the clusters. For comparson, the same network topology and sensor energy level are used to study the performance of the two methods n Phase III durng the frst round. Let the threshold level η be E max /2. Samples from the dstrbutons, E max U(, 1) and E max /2 (1+U(, 1)) are assgned to clusterheads

8 Average Number of Receptons n = 25 n = 5 n = 75 n = Fg. 5. The number of receptons n random networks as a functon of the number of sensors and R/l rato n Phase I (Cluster Formaton) R/l Transmsson Recepton Fg. 7. Clusters are formed and clusterheads are reselected n a random network of 1 sensors wth R/l =.175; represents the ntal clusterhead (); represents a new clusterhead usng the centralzed protocol (); represents a new clusterhead usng the decentralzed protocol (). 16 The average number of Tx/Rx n a cluster The number of sensors Fg. 6. The average number of transmsson and recepton n a cluster for executng gateway selecton (Phase II) wth ncreased network densty. and cluster members as the remanng energy, respectvely. Fgure 7 demonstrates typcal runs of the operaton of Phase III. It shows that ths knd of local dynamc dstrbuton of clusterheads allow each cluster to adjust ts energy load among cluster members, wh allevates the problem that the battery of fxed clusterheads wll dran quckly. Therefore, when the reselecton operaton s completed, the energy usage s spread among the network and thereby the lfetme of the network s extended. VI. APPLICATIONS OF THE ADTCA A. Tme Synchronzaton The tme synchronzaton ssue s a typcal problem n wreless sensor networks because of the observaton and nteracton wth the physcal world. Due to random phase shfts and clock skews of oscllators, the tme readng of sensors mght start to loose synchronzaton wthout calbraton. The ADTCA technque may be a good way to keep the tme readngs of sensors as tghtly as possble n the herarchcal cluster-based network structure snce local par-wse synchronzaton [18] s achevable wthn a cluster usng two-way communcatons whle global calbraton can be acheved by (relatvely sparse) communcaton between clusterheads. B. Effcent Network Routng Herarchcal cluster-based network routng s a well-known protocol wth specal advantages related to scalablty and effcent communcaton for wreless sensor networks. In a herarchcal archtecture, clusterheads can be used to process and delver nformaton effcently whle gateways are responsble for forwardng nformaton between clusters. Ths mples that the creaton of clusters and gateways greatly contrbutes to system scalablty, network lfetme, and energy conservaton. Therefore, the proposed ADTCA approach may be an effcent way to lower energy consumpton snce the number of transmtted messages to the destnaton s decreased by performng data aggregaton and fuson n clusterheads and messages can be relayed wth relable broadcastng n dstrbuted gateways. VII. CONCLUSION Ths paper descrbes a decentralzed protocol for topology management n wreless sensor networks. The Adaptve Dstrbuted Topology Control Algorthm (ADTCA) performs cluster formaton and lnkage usng random watng tmers and local nformaton. On the bass of the cluster-based network topology, ths self-confgurng technque may be appled to acheve local and global tme synchronzaton and to provde effcent network routng. Ths work assumes that all sensors operate wth the same transmsson range. Future plans nvolve generalzng the method to consder power control strategy for mnmzng the total energy consumpton, to consder certan falure scenaros, and to desgn effcent topology control protocols for moble ad-hoc wreless networks.

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