Maneuverable Relays to Improve Energy Efficiency in Sensor Networks

Transcription

1 Maneuverable Relay to Improve Energy Efficiency in Senor Network Stephan Eidenbenz, Luka Kroc, Jame P. Smith CCS-5, MS M997; Lo Alamo National Laboratory; Lo Alamo, NM {eidenben, kroc, Abtract We propoe a hybrid model to alleviate the notoriou problem of premature battery depletion in enor network: in a firt tage, imple enor are deployed over an area of interet uing any traditional method, in a econd phae, more powerful relay are put in poition that allow them to off-load a much of the forwarding burden impoed on the imple enor a poible. We introduce thi model in detail, give a few theoretical reult with repect to the optimal placement of the powerful enor, propoe variou heuritic approache for their placement, and preent comparative imulation reult for thee heuritic.. Introduction It i well etablihed that while enor network promie unprecedented opportunitie for data collection in a great variety of cenario, their large-cale deployment i hindered by their thirt for energy. Coniderable reearch effort have gone into developing energy-efficient protocol on all tack layer for the enor network etting in which communication to a ingle bae tation happen in a multihop fahion with intermediate tranceiver enor being aked to forward data. While the multiple hop cheme i certainly an improvement in term of energy efficiency over older cheme that require each enor to emit a ignal trong enough to reach the bae tation in a ingle hop, it till fall hort of real-life energy efficiency requirement in many application, not to mention that the reliability of uch cheme uually decreae dratically a routing path get longer. We propoe a hybrid model that ha the potential to reduce energy requirement a claim that we upport by imulation evidence in the lat part of thi paper. In our model, there are two different type of tranceiver: Senor are equipped with a enor to meaure ome environmental variable (uch a temperature or radiation level) and with a low-cot, hort-range tranceiver that i able to receive data packet from other enor and to end data packet that it either generated itelf or received from other enor. Moreover, each enor i equipped with a GPS-like device allowing it to determine it poition relative to ome reference frame. Relay are more powerful tranceiver that are not necearily equipped with a enor. They receive data packet from enor and forward them directly to a fixed-infratructure bae tation uing their medium-range tranmiion capabilitie. Relay are alo equipped with a GPS-like capability. In the application cenario that we enviion, the enor are deployed in a firt tage, the relay are deployed in a econd tage, and actual data traffic tart being tranmitted only in a third phae. A key element of our model i that relay are maneuverable: they can be deployed to location pecified in coordinate; thi can be achieved in everal way depending on the application (e.g., by moving them manually to their poition or by equipping them with a motor and letting them drive to their poition). Figure illutrate the hierarchical architecture of the enor network. For eae of illutration, we aume a unit dik graph model (i.e., each enor ha the ame fixed tranmiion range) depite it deficiencie (generalization to more involved phyical model are feaible). In order to avoid the complication of colliion, we aume a TDMA model on the MAC layer with each tranceiver being aigned a unique time-lot. 2 A more precie meta-algorithm for the Additional energy aving may be poible by replacing tandard GPS device by a cheme where a mall number (at leat three) relay are placed on the boundary of the area in which the enor are ditributed. The relay can then end out ignal that are received by the enor; baed on the ignal trength from the different relay, the enor can then compute their poition (imilar to the way real GPS work). To eliminate the neceity for enor to be able to detect ignal trength, the relay can alo end out conecutive meage of increaing ignal trength; baed on the firt intercepted meage from each relay, a enor can compute it location fairly accurately. 2 Since not all enor are within each other tranmiion range, TDMA require global time ynchronization. Fortunately, a global clock i a feature of any GPS-like ytem, thu time ynchronization Authorized licened ue limited to: IEEE Xplore. Downloaded on February 2, 2009 at 0:35 from IEEE Xplore. Retriction apply.

2 Bae Station Relay Senor Figure. Schematic illutration of the hierarchical level of the enor network cenario i a follow:. Senor are deployed; each compute it own poition. 2. A ingle relay i placed into the center of the enor pread area. 3. The relay end out a beacon packet indicating that it i the relay by etting the hop-count field in the packet to zero. Each enor receive uch a packet, tore the ID of the ender of the packet, increae the hop count by one and forward the packet. At the end of thi flooding phae, each enor know it hop-count ditance to the relay and alo know to which neighbor it need to forward a packet when ending to the relay. 4. Each enor inform the fixed-infratructure bae tation about it poition by ending a packet with poition information along the computed hortet path through the relay. 5. From the enor poition, the bae tation compute the relay poition uing an algorithm or heuritic to find a good olution. 6. The relay are programmed with their final coordinate; they then move or are moved to their poition. 7. Each relay end out a beacon packet that i propagated by the enor a in Step 3. Each enor may receive everal of thee packet from different relay or intermediary enor, and chooe randomly among thoe on the hortet path. 8. Data traffic tart with data packet being forwarded along the computed hortet path to a relay who then end the data to the fixed bae tation. The computational work that the bae tation need to carry out in order to compute the target poition of the relay in Step 5 i key to the overall energy ue of the ytem. A i common, we aume that the bae tation ha unlimited tranmiion power and i equipped with a poweri not much of an additional burden. ful computer. Let S = {,...,n} denote the ID of the n enor; let the hop-count ditance between a enor node i and it aociated relay (i.e., it hop-count cloet relay) be d i ; finally, let f i (for i n) denote the average number of data packet that enor i generate in a time unit, and let E U denote the amount of energy that a enor need to pend to forward one data packet. With thi notation, the amount of energy E S ued by the enor in the ytem in a time unit (power) i n E S = f i d i E U, () i=0 ince each data packet that a enor node i end out need to travel d i hop before it reache it relay. Thu, we can formulate a formal optimization problem RELAY POSITION- ING:Givenn poition of enor in the plane and an integer k (and for a deciion verion, an energy threhold E T ), find k relay poition uch that the reulting energy uage E S i minimum. Alternatively, for the deciion verion, find k relay poition uch that the reulting energy uage E S i at mot E T. We will focu on thi apect of the propoed enor network, a other apect are fairly traight-forward. We tudy RELAY POSITIONING from both a theoretical point of view and from an applied point of view through imulation. We preent theoretical reult in Section 2, a few heuritic approache for olving the problem in Section 3, and imulation reult in Section 4. Pointer to related work and a brief concluion are given in Section Theoretical Reult In thi ection, we firt how that in order to find optimum olution for RELAY POSITIONING, we only need to conider a dicrete et of poition in the plane where relay can be placed. We then preent a proof that our RE- LAY POSITIONING i in fact NP-hard (depite it pecial tructure), thu forcing u to reort to approximation algorithm or heuritic to find good olution. Dicretization. We are auming a unit dik graph model among a finite et of enor node, o the et of enor node from which a relay can receive packet change only along a finite et of arc on the plane. Aume we are given the poition of the n enor node. If we draw a unit-radiu circle around each enor, we obtain a partitioning of the plane into cell whoe boundarie are circle egment. The et of enor that can reach a relay doe not change within a cell, o it doe not matter where in the interior of a cell we place a relay. A relay on the boundary of the cell i within reach of the ame et of enor a in the interior plu poible additional enor. By definition of the unit dik graph, the et of enor within reach of a relay change only along cell Authorized licened ue limited to: IEEE Xplore. Downloaded on February 2, 2009 at 0:35 from IEEE Xplore. Retriction apply.

3 boundarie, including the interection point of each pair of circle. When earching for optimum relay poition, we can limit ourelve to circle interection point becaue all point on each cell defining boundary are equivalent in thi ene, and thoe two point are guaranteed to repreent the more connected cell. Since each circle can interect each other circle at mot twice, the total number of interection point i O(n 2 ). Thu, we have: Lemma For any given intance of RELAY POSITION- ING, there exit an optimum olution in which each relay i poitioned at one of the O(n 2 ) unit circle interection point. With thi dicrete characterization, we can formulate our problem a a pecial cae of MAXIMUM k-facility LO- CATION [5] with the node et coniting of all enor poition and circle interection point, profit between enor node and potential relay poition defined a the negative of the hortet hop count ditance, other profit et to zero. A greedy heuritic achieve an approximation ratio of e e for MAXIMUM k-facility LOCATION and therefore alo for RELAY POSITIONING. However, the fact that MAXIMUM k-facility LOCATION i NP-hard doe not imply that RELAY POSITION- ING i NP-hard ince the latter i a pecial cae of the former. Hardne. We now how that the deciion verion of RELAY POSITIONING i NP-complete by propoing a polynomial-time reduction from DOMINATING SET ON PLANAR GRAPHS WITH MAXIMUM DEGREE 4, which i known to be NP-hard [6]. Thi reduction i inpired by a reduction for a imilar problem of [2]. We will alo need a graph drawing reult: Lemma 2 [7] A planar graph with maximum degree 4 can be embedded in the plane uing O( V ) area uch that it vertice V are at integer coordinate and it edge conit of (poible multiple) horizontal or vertical line egment each of which ha end point with integer coordinate. We are now ready to prove our reult: Theorem The deciion verion of RELAY POSITIONING i NP-complete. Proof: Lemma how that RELAY POSITIONING in it deciion verion i in NP: even an optimum olution can be decribed a a et of poition each of which i an interection point of two circle around input data point. Thu, a olution i of polynomial length in the input, and it validity can be verified in polynomial time. 3 3 Proving NP-memberhip i not a trivial for thi geometric problem a it i for mot combinatorial problem. We need to explicitly how that we can expre the coordinate of olution poition with a polynomial number of bit. To how that RELAY POSITIONING i NP-hard, we tranform an intance I of dominating et on planar graph with maximum degree 4. Intance I conit of a graph G(V,E) with n node V = {v,...,v n } and edge E V 2, and an integer k (for anwering the quetion whether a dominating et of at mot k node exit). We aume that we are given the input graph embedded in the plane according to Lemma 2 with node v i at integer coordinate (x i,y i ). Let l i,j denote the Euclidean length of the horizontal and vertical line egment that form edge (v i,v j ) in the embedding. By Lemma 2, l i,j i of polynomial length. We tranform intance I =(G, k) into a RELAY POSI- TIONING intance I =(S, k,e T ) that conit of a total of n = n+ (i,j) E (2l i,j 3) enor node S that are pread along the edge line in the embedding of I a follow: a enor node i i placed at the embedded poition of node v i ; on the line egment of length l i,j repreenting edge (i, j), an additional 2l i,j 3 enor S i,j = { i,j,...,i,j 2l i,j 3 } are placed conecutively at certain ditance. More preciely, enor i,j c for c 5 i placed at ditance c 0 from enor i ; imilarly, the five lat enor i,j 2l i,j 8+c for c 5 are placed at ditance c 0 from enor j. i placed at di- 2 (ditance defined a Euclidean ditance traveled when going along the line egment of the edge) from enor i for 0 c 2l i,j 8. With thi ditribution, each line egment end point of the edge i alo a enor A for the remaining enor, enor i,j 5+c tance 2 + c poition. Let i,j p,..., i,j p p be enor poition on line egment end point of edge (v i,v j ) (except for i and j ). We lightly refine the poition of enor i,j p t 2 and i,j p for t+2 t p in order to make the reduction work: i,j p i t 2 placed at ditance 2 + pt from enor i and enor i,j p t+2 i placed at ditance 2 + pt from enor i for t p. To complete the reduction, we et the unit radiu of all enor to 0, parameter k (the number of relay to be placed) of intance I to k + (i,j) E (4l i,j ) and the energy threhold E T = n. We need to how that I i a YES-intance if and only if I i a YES-intance. We firt how the if -direction: if a dominating et of cardinality k exit in graph G, there exit a olution for I with k relay and a total energy ue of exactly E T. Let the dominating et in I be S = {v,...,v k } w.l.o.g. Then the olution S for I place k relay at enor poition,..., k ; moreover, it place 4l i,j additional relay on enor poition for each edge (i, j) with i<j(to avoid double-counting on the bidirectional edge) a follow: if i S, then relay are poitioned at enor poition i,j 3c for c l i,j; if neither i nor j are in S, then the relay are poitioned at enor poition i,j 2+3c for 0 c 4l i,j 2. Thu, we have poitioned k relay in uch a way that each of the n enor can reach a relay in a ingle hop, reulting in an overall en- Authorized licened ue limited to: IEEE Xplore. Downloaded on February 2, 2009 at 0:35 from IEEE Xplore. Retriction apply.

4 j i,j j j i,j i,j i /0 /0 /0 /0 /0 /2 /2 /2 /2 /5 /0 /2 /2 i,j /0 Figure 2. Illutration of the reduction: for the only if -direction each cell need to be checked. Note that the two dahed circle do not interect. ergy ue of n, a required. In order to how the only if -direction, we aume that a olution S with total energy ue at mot E T i given a a et of relay poition. We modify the olution in uch a way that let u read off a olution S for I a follow: each relay in S that i not placed at a enor poition i moved to a enor poition from which it till hear all the enor (plu poible additional one) that it heard before the move. The contruction and the parameter choice make thi feaible. To ee thi, conider Figure 2, which how a mall part of the contruction. A cae analyi for each cell of Figure 2 how that relay can alway be moved without changing the et of enor that they hear and therefore alo without changing the total energy E S of the whole ytem, which i at mot E T = n. Obviouly each of the n enor mut ue at leat one hop to tranmit it packet to a relay (even if they are co-located), therefore no olution for I can exit with E S <n. Alo, if a enor require two or more hop to reach a relay in any olution, the olution mut ue more energy than n. Thu, our modified olution mut be a dominating et for the unit dik graph of I. Due to the way that enor poition are ditributed on the edge of the original graph G, an edge (i, j) of length l i,j will be covered by 4l i,j relay itting on internal enor poition. The contruction i uch that 4l i,j relay uffice to cover all internal enor poition i,j,...,i,j 2l but not i,j 3 i or j unle one of the two ha a relay a well. If i have a relayonthem,then4l i,j relay alway be placed uch that j i covered a well (and vice-vera). Thu, we can read off a olution for I by jut including in the dominating et S all node v i that have a relay on the correponding node i in S. j /5 /2 /0 /0 3. Heuritic Approache We conider four heuritic approache to olve the RE- LAY POSITIONING problem. Since the RELAY POSITION- ING problem can, in general, be viewed a a clutering problem, the main idea for each approach i taken from known clutering algorithm. The problem can be rendered a grouping the enor into cluter, and aigning each cluter one forwarding relay in uch a way a to minimize the cot of uch a olution. The cot function ued to meaure a quality of a olution i the um of hortet pathlength (meaured in hop-count) of enor to their correponding relay (in order to reduce parameter pace for our experiment, we aume that all enor need to deliver about the ame amount of data to the bae tation, which correpond to etting all weight f i =in Eq. ); thu, cot defined thi way correpond to the total energy ue of the network. The baic approache are decribed here, followed by detail about each algorithm. In the following, k i the number of relay we want to poition, and n i the number of enor. We remind the reader that we are only dicuing algorithm on how to compute the final relay poition; thu, when we ay that an algorithm place a relay and then update it poition, the relay will have to be phyically moved only once, namely when it final poition ha been computed (ee Step 6 of the meta-algorithm). a) k-mean: The k relay are initially placed in randomly elected POSITIONS and k cluter are created by aigning enor to the nearet (in hop-count) relay. The algorithm then iterate a follow until no change are made during an iteration: For each relay, find a poition which minimize it DIS- TANCE to the enor in it cluter. Recompute all cluter (for each enor, find the relay that i cloet in hop count). Thi may reult in ome node changing cluter they belong to. b) k-global: The k relay are again initially placed in randomly elected POSITIONS, and an iteration conit of the folowing tep that i repeated until the olution no longer change: For each relay (in random order), find the POSITION that minimize the cot of the overall olution given that all other relay poition remain unchanged (i.e. the um of length of the hortet path from all enor to their nearet relay i minimized). c) bottom-up: Thi algorithm tart by placing relay in the ame poition a the node, thu creating n relay and n one-enor cluter. It then run the following tep n k time: Authorized licened ue limited to: IEEE Xplore. Downloaded on February 2, 2009 at 0:35 from IEEE Xplore. Retriction apply.

5 Find two cluter with the mallet DISTANCE between the relay. Combine the two cluter by deleting one relay and placing the other one in a poition that minimize DIS- TANCES between the relay and enor in the combined cluter. Recompute all cluter d) greedy: Thi approach place relay one-by-one in k tep. In each tep, it find a POSITION for the new relay uch that the cot of the whole olution i minimized, given that poition of the relay already placed remain unchanged. We ue two different way to define POSITIONS and DIS- TANCE, creating ixteen implementation of the above approache. POSITIONS i a finite et generated from the location of the enor, and finding a POSITION mean earching through thi et. We ued two way to define PO- SITIONS: all poition of the enor (with a ize of n) and all poition of the enor plu all interection point of the enor radii (ize of O(n 2 )). The reaon for trying both et i that while the firt i relatively mall and widely ued by hierarchical enor network algorithm [3], uing the interection point may reult in better olution. In fact, there alway exit an optimal olution with relay placed in the econd POSITIONS et, a hown in Section 2. DISTANCE i a metric ued to compute ditance between relay and enor in certain part of the algorithm. We again ue two way to define it: a Euclidean ditance and a a hop-count ditance. In the k-mean algorithm, uing the Euclidean ditance metric reult in finding the average poition of the enor in the cluter, while the hopcount metric require a earch through a given POSITIONS et. The rationale behind trying both metric i again an apparent trade-off: while Euclidean metric i very imple to compute, it may not at all reflect the actual hop-count ditance of two enor. We have choen eight of the 6 algorithm are (the naming cheme i <approach>-<metric>-<whether radii interection point were conidered>) for experiment; we lit them including their theoretical running time, where n i the number of enor, k i the number of relay, and D i the average degree of the enor (i.e., a enor ha D other enor a neighbor on average): kmean-euk with a running time of O(kn) per iteration kmean-hop-no with a running time of O(n 2 D + knd) per iteration kmean-hop-ye with a running time of O(n 3 D + knd) per iteration kglobal- hop-no with a running time of O(kn 2 D) per iteration e e kglobal-hop-ye with a running time of O(kn 3 D) per iteration bottomup-euk with a running time of O((n 2 + nd)(n k)) greedy-hop-no with a running time of O(kn 2 D) greedy-hop-ye with a running time of O(kn 3 D) Note that greedy-hop-ye i guaranteed to find a olution that i at mot a factor =.58 off the optimum olution, thu we can only expect relatively mall improvement over thi algorithm. The running time are obtained by traight-forward analyi; for kmean and kglobal, we can give an upper bound of O(n 2 ) on the number of iteration, ince the wort poible olution will have at mot n path (one from each enor) of length O(n) and we only proceed to the next iteration if the algorithm find a better olution. Thee upper bound will clearly never be reached in reality, but they prove that our algorithm have polynomial running time. 4. Simulation Reult The cenario we ue to compare the eight algorithm in imulation all have 024 enor pread on a quare field. The tranmiion range are the ame for all enor and are et to value that reult in expected average degree of 6, 2, 8 and 24 in the connectivity network. The number of relay to be ued i, 2, 4, 8, 6, 32, 64 and 28. When the algorithm tart, the enor are placed uniformly at random on the field firt. Then a relay i placed in the middle of the field and only enor that are able to connect to the relay are conidered for the actual run of the algorithm (if le than 90% of the enor are connected, the enor are poitioned again). Thi correpond to Step through 4 of the meta-algorithm in ection. Conequently, the k-mean and k-global algorithm only place the remaining k relay randomly. For each cenario, we ran the algorithm and collected the cot of the reulting olution and running time of the algorithm. We ran each cenario multiple time with different random eed until the tandard deviation of the cot wa about 0% of it mean. The reult are hown in the following figure. Figure 3 how the reulting cot of a olution for different number of relay and average network degree of 6. The figure how that the cot found by the algorithm are remarkably imilar (the wort i within 5% of the bet). The difference decreae with increaing number of relay, and almot diappear when the number of relay get to 28, where nearoptimal olution i found by all algorithm (majority of enor are connected directly to relay). The bet algorithm i, nonethele, the kglobal-hop-ye. Authorized licened ue limited to: IEEE Xplore. Downloaded on February 2, 2009 at 0:35 from IEEE Xplore. Retriction apply.

6 Cot Average Degree = 6 bottomup euk greedy hop no greedy hop ye kglobal hop no kglobal hop ye kmean euk ye kmean hop no kmean hop ye Cot Algorithm kmean hop no Average Degree=6 Average Degree=2 Average Degree=8 Average Degree= Number of Relay Number of Relay Figure 3. Cot of a olution for variou number of relay (on log cale) and all algorithm for a topology with an average degree of 6. Figure 5. Cot of a olution for variou number of relay (on log cale) and different average degree for the kmean-hop-no algorithm. Time e+00 e+02 e+04 e+06 bottomup euk greedy hop no greedy hop ye kglobal hop no kglobal hop ye kmean euk ye kmean hop no kmean hop ye Average Degree = Number of Relay Figure 4. Running time (in [] on log cale) for variou number of relay (on log cale) and all algorithm for a topology with an average degree of 6. Figure 4 again how the cenario with average degree of 6 and all algorithm, but now the y-axi i the time taken for one run to be completed (notice the log cale of y-axi). Thi figure how two very different behavior clae with repect to running time of the algorithm. One cale a a power-law: for greedy and kglobal, thi finding i conitent with the theoretical running time for thee algorithm, which depend linearly on k. Similarly, kmean-euk-ye exhibit power-law behavior, which again i conitent with it theoretical runing time; relative to greedy and kglobal, the lope eem to be maller, which can be explained through the different number of iteration that thi algorithm mut make to converge. The running time of the econd cla of algorithm Time Algorithm greedy hop no and kmean hop no Average Degree=6 Average Degree=2 Average Degree=8 Average Degree=24 greedy hop no kmean hop no Number of Relay Figure 6. Running time (in [] on log cale) for variou number of relay (on log cale) and different average degree for the kmean-hop-no and greedy-hop-no algorithm. i inenitive to or even decline with the number of relay. In the cae of kmean-hop-ye and kmean-hop-no, it eem that the low-order term containing k in the theoretical running time i outweighed by the fewer iteration that the algorithm ha to go through with a larger number of relay, thu reulting in a mall time decreae for larger number of relay. Thu, kmean-hop eem to converge fater when we have relatively mall cluter. Finally, bottomup-euk running time alo very lightly decreae with an increaing number of relay, which again i conitent with it theoretical running time. The kglobal-hop-ye algorithm i Authorized licened ue limited to: IEEE Xplore. Downloaded on February 2, 2009 at 0:35 from IEEE Xplore. Retriction apply.

7 clearly the wort in running time. The kmean-hop-no, though till very competitive in the cot of olution found, ha a much maller running time. Figure 5 how how the cot of olution varie with average node degree of the connectivity network. The higher the connectivity, the lower the cot, a expected. The curve meet for 28 relay again, confirming that for 8 enor per relay on average, a near-optimal olution i found. The other algorithm behave very imilarly. Again, thee finding are conitent with the theoretical running time of all algorithm, where average degree D i a linear factor. Finally, Figure 6 how how the running time evolve with connectivity for elected repreentation of both clae (greedy-hop-no and kmean-hop-no). The key learning from the imulation can be ummarized a follow: uing more time-intene algorithm yield reult that are a few percentage point better than very fat algorithm. We believe that in mot application the olution quality improvement gained by uing more computational power i probably offet by the cot of uch additional computational power. In particular, allowing relay to be placed on interection point allow algorithm to find lightly better olution at coniderable additional computation time. [2] A.D. Ami, R. Prakah, T.H.P. Vuong, D.T. Hyunh; Max- Min D-Cluter Formation in Wirele Ad Hoc Network; Proceeding INFOCOM 2000 [3] Suman Banerjee and Samir Khuller; A Clutering Scheme for Hierarchical Routing in Wirele Network; INFOCOM 200 [4] Y. P. Chen, A. L. Leitman, and J. Liu; Clutering Algorithm for Ad Hoc Wirele Network; in Ad Hoc and Senor Network, Edited by Y. Xiao and Y. Pan, Nova Science Publiher, 2004 [5] Cornuejol, G., Fiher, M., and Nemhauer, G.; Location of bank account to optimize float: An analytic tudy of exact and approximate algorithm; Management Sci. 23, , 977 [6] Garey, M. R. and Johnon, D. S.; Computer and Intractability: A Guide to the Theory of NP-Completene; Freeman, San Francico, 979 [7] L. Valiant; Univerality Conideration in VLSI Circuit; IEEE Tranaction on Computer, Related Work and Concluion Hierarchical approache and related clutering approache for wirele network have been tudied intenely in the pat, ee [4] for a urvey. See [] for an introduction to baic concept in enor network. In contrat to previou work, our approach call for two different type of tranceiver, one of which can be moved to pecific location. Our cheme allow for truly imple enor that never need to erve a cluter-head with high emiion radii and computing power, uch a in the cheme of [3], in which it i not known a priori which enor may have to act a cluter-head and all enor mut therefore be trong enough to potentially act a cluter-head. We believe that our two-phaed approach ha potential for future reearch. We are working on a ytem where the relay find their poition in a elf-organizing manner by moving to high traffic volume location and changing their poition a the network load change. Other future work include a variation of our approach in which load i ditributed fairly and maximum energy ue per node i minimized intead of overall network energy ue. Reference [] Ian F. Akyildiz, Weilian Su, Yogeh Sankaraubramaniam, Erdal Cayirci; A Survey on Senor Network; IEEE Communication Magazine, Augut Authorized licened ue limited to: IEEE Xplore. Downloaded on February 2, 2009 at 0:35 from IEEE Xplore. Retriction apply.