An Energy-Efficient MAC Protocol for WSNs: Game-Theoretic Constraint Optimization with Multiple Objectives

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1 Wreless Sensor Network, 2009, 1, do: /wsn Publshed Onlne November 2009 ( An Energy-Effcent MAC Protocol for s: Game-Theoretc Constrant Optmzaton wth Multple Obectves Abstract Lqang ZHAO, Le GUO, L CONG, Haln ZHANG State Key Laboratory of Integrated Servces Networks, Xdan Unversty, X an, Chna Emal: lqzhao@mal.xdan.edu.cn Receved March 23, 2009; revsed June 2, 2009; accepted June 10, 2009 In s, energy conservaton s the prmary goal, whle throughput and delay are less mportant. Ths results n a tradeoff between performance (e.g., throughput, delay, tter, and packet-loss-rate) and energy consumpton. In ths paper, the problem of energy-effcent MAC protocols n s s modeled as a game-theoretc constrant optmzaton wth multple obectves. After ntroducng ncompletely cooperatve game theory, based on the estmated game state (e.g., the number of competng nodes), each node ndependently mplements the optmal equlbrum strategy under the gven constrants (e.g., the used energy and QoS requrements). Moreover, a smplfed game-theoretc constrant optmzaton scheme () s presented n ths paper, whch s easy to be mplemented n current s. Smulaton results show that can ncrease system performance whle stll mantanng reasonable energy consumpton. Keywords: Wreless Sensor Network, MAC, Energy Effcency, Game Theory, Constrant Optmzaton 1. Introducton As an emergng technology, Wreless Sensor Networks (s) have a wde range of potental applcatons ncludng envronment montorng, smart spaces, medcal systems and robotc exploraton. Performance analyss and optmzaton of s, especally ts Medum Access Control (MAC) protocols, have attracted much research nterests. Tradtonal MAC protocols for wreless ad hoc networks are desgned to mze throughput and mnmze delay. As sensor nodes are generally battery-operated, to desgn a good MAC protocol for s, the frst attrbute that has to be consdered s energy consumpton [1]. Other mportant attrbutes (such as throughput and delay) are generally the prmary concerns n tradtonal wreless ad hoc networks, but n s they are secondary. IEEE Dstrbuted Coordnaton Functon (DCF), the basc MAC protocol n Wreless LANs (WLANs), s based on Carrer Sense Multple Access wth Collson Avodance (), one of typcal contenton-based MAC protocols. uses an acknowledgment (ACK) mechansm for verfyng successful transmssons and optonally, an RTS/CTS handshakng mechansm for decreasng collsons overhead. In both cases an exponental backoff mechansm s used. Before transmttng, a node generates a random slotted backoff nterval, and the number of the backoff slots s unformly chosen n the range [0, CW-1]. At the frst transmsson attempt, the contenton wndow, CW, s set equal to a value CW mn called the mnmum contenton wndow. After each unsuccessful transmsson, CW s doubled up to the mum value CW. Once CW reaches CW, t wll reman at the value untl the packet s transmtted successfully or the retransmsson tme reaches retry lmt. Whle the lmt s reached, retransmsson attempts wll cease and the packet wll be dscarded. Currently, has been the de facto MAC standard for wreless ad hoc networks, wdely used n almost all of the testbeds. Moreover, low-power, low-rate Wreless PANs (WPANs) such as IEEE utlzes too. However, the energy consumpton usng s very hgh when nodes are n an dle mode. It s manly called problem of dle lstenng. -based s explctly desgned for s to solve ths problem [2]. The basc dea of s that used energy s traded for throughput and delay by ntroducng an actve/sleep duty perod. Some researchers are attemptng to mprove the performance of [3 6]. To handle load varatons n tme and locaton, ntroduces an adaptve duty cycle by dynamcally endng ts actve part. Ths reduces Copyrght 2009 ScRes.

2 L. Q. ZHAO ET AL. 359 the amount of energy wasted on dle lstenng, n whch nodes wat for potentally ncomng messages, whle stll mantanng a reasonable throughput [7]. Recently, game theory [8] becomes a very good tool to analyze and mprove the performance of contenton-based protocols. Game-theoretc approaches were proposed to solve the problem of securty, query routng, and power control respectvely n dstrbuted sensor networks [9 12]. When usng game theory n s rather than mathematcs or economcs, much attenton should be pad to the context of s. For example, explct cooperaton among nodes s clearly mpractcal n s as t causes addtonal energy and bandwdth consumpton. We presented a novel concept of ncompletely cooperatve game theory to mprove the performance of MAC protocols n s wthout any explct cooperaton among nodes [13 14]. In ths paper, the prelmnary results presented n [13 14] wll be substantally extended. The problem of energy-effcent MAC protocols for s s modeled as game-theoretc constrant optmzaton wth multple obectves, e.g., energy consumpton and QoS metrcs. 2. Game-Theoretc Constrant Optmzaton A node starts a game process when a new packet arrves at the node s transmsson buffer and ends t when the packet s moved out of the buffer (.e., transmtted successfully or dscarded). Each game process ncludes many tme slots and each tme slot corresponds to one game state. In each tme slot, each player (.e., node) estmates the current game state based on ts hstory. After estmatng the game state, the player adusts ts own equlbrum strategy by tunng ts local contenton parameters. Then all the nodes take actons smultaneously,.e., transmttng, lstenng, or sleepng. Although the player does not know whch acton the other nodes (.e., ts opponents) are takng now, t can predct ts opponents actons accordng to ts hstory. In the game, each player takes a dstrbuted approach of detectng and estmatng the current game state, and tunng ts local contenton parameters to the estmated game state. In economcs, normally, the optmal target of the player s to mum ts own profts. However, n s, the target of each player s to mum the system performance under certan lmts, e.g., energy consumpton and QoS requrements. In the game for s, the utlty functon of the player (.e., node ) s represented by μ μ s, s. The parameters of the vector, μ, correspond to ts energy consumpton and QoS requrements, e.g., bandwdth, delay, tter, and packet-loss-rate. Obvously, there are some lmts on ts utlty functon, called μ, e.g., the mum energy consumpton, the tolerant mnmum bandwdth, mum delay, tter, or packet-loss-rate. If we do not consder ts opponents, the strategy of the player, s, ncludes three possble actons: transmttng, lstenng or sleepng. The strategy profle of ts opponents (.e., all the other n neghbors) s defned as s s1, s2,..., s 1, s 1,..., sn. Smlarly, we can get the utlty functon of ts opponents that μ s, s. Also, there are some lmts on the above utlty functon, called μ. In many game-theoretc models, a player s a node contendng for the channel. As there may be many nodes n a and each node may contend for the channel repeatedly, a very complcated method s needed to determne the strategy. Hence, n the game, a player s not always a node. If we analyze the equlbrum strategy of node, Player 1 s node, and Player 2 (.e., ts opponents) s all the other n-1 nodes. In fact, t s possble for Player 1 to estmate Player 2 s state, and dffcult for Player 1 to estmate the states of each node n Player 2. In a formal descrpton, we are lookng for s s,, arg mn μ μ s,,, arg mn μ μ s, Obvously, Player 1 adusts ts strategy s not to obtan ts own optmal utlty ( ), but to help Player 2 get the μ optmal utlty ( μ ); vce verse. Hence, t ndcates that all the nodes play the cooperatve game based on the estmated game states. On the other hand, the two players help each other get the optmal utlty under ther own lmts respectvely. It ndcates that all the nodes play the constraned game. As Player 2 ncludes all the other n-1 competng nodes except Player 1, collsons may happen among the n-1 competng nodes even not consderng Player 1. So Player 2 ncludes four possble actons: successful transmsson, faled transmsson, lstenng or sleepng, even f we do not consder Player 1. Table 1 s the strategy table wth 2 players (.e., n nodes). Wth regard to the payoff of Play 1 n a gven tme slot, there are four possbltes when consderng the two players. Frstly, Player 1 sleeps wth the probablty of w, whose payoff s c w,, where corresponds to the -th parameter of the utlty functon. Secondly, Player 1 lstens to the channel wth the probablty of 1w1, whose payoff s c. Here, s the condtonal transmsson probablty of Player 1. Thrdly, Player 1 fals to transmt ts packets due to the collson between the two players wth the probablty of (1) Copyrght 2009 ScRes.

3 360 L. Q. ZHAO ET AL. Table 1. Strategy model wth n+1 nodes. Player 1 (node ) Transmttng Lstenng Sleepng Successful Transmsson c, c, c s c, Player 2/Opponent (all the other n nodes) Faled Lstenng Transmsson f c f c f c s, c c, c c, c, w c f w c Sleepng c f, c w c, c w c, c w w 1w 1w w, whose payoff s c. Here w f, and are the sleepng probablty and the condtonal transmsson probablty of Player 2 respectvely. Fnally, Player 1 transmts successfully wth the probablty of 1w 1w1, whose payoff s c. s, Wth regard to the payoff of Player 2 n a gven tme slot, there are four possbltes too after consderng the two players. Frstly, Player 2 sleeps wth the probablty of w, whose payoff s c. Secondly, Player 2 lstens to w, the channel wth the probablty of 1w1, whose payoff s c. Thrdly, Player 2 fals to transmt ts pack-, ets due to the collsons between the two players or among the n-1 nodes wthn Player 2 wth the probablty of 1w 1w p1w1w, whose payoff s c. Fnally, Player 2 transmts successfully f, wth the probablty of 1 w 1 p1w1, whose payoff s c. Here, s, p s the condtonal collson probablty of Player 2, whch s the functon of the probablty [14]. Hence, the optmal strateges of the two players under the gven constrants are expressed as w c p w c w p w w c wc s s, s, f, w, arg mn 1 μ μ w,, 1w 1w 1 c 1 c 1w w c wc s,, f, w, arg mn 1 μ μ w,, (2) In general, the contenton-based MAC protocol n s s modelled as a game-theoretc constrant optmzaton wth multple obectves. Based on the estmated game state, each node acheves the global optma by adustng ts transmsson and sleepng probablty smultaneously. 3. A Smplfed Game-Theoretc Constrant Optmzaton Scheme for s Unfortunately, the above problem has been proven to be NP-hard [15], so we cannot hope an algorthm that can fnd the theoretcal optmum and runs n polynomal tme. Hence, we present a smplfed game-theoretc constrant optmzaton scheme () n ths secton. In, we optmze the performance (e.g., the system throughput, delay, tter, and packet-loss-rate) under the lmted energy consumpton. In, tme s dvded nto super-frames and every super-frame has two parts: an actve part and a sleepng part. Durng the actve part, each node contends for the channel n the ncompletely cooperatve game. Durng the sleepng part, each node turns off ts rado to preserve energy. The tme length of the actve and sleepng part s adusted accordng to the estmated game state too. In the game, frstly, a node estmates the current state of the game, e.g., the number of ts opponents n-1. When the node s transmttng ts frame, f any other node transmts at the same tme slot, the frame wll be collded. So the frame collson probablty of the node p s obtaned as follows: n 1 p 1 1 (3) where τ s the frame transmsson probablty of the node. If solvng the above equaton wth respect to n, we obtan: log 1 p n 1 log 1 (4) Copyrght 2009 ScRes.

4 Secondly, the node adusts ts e qulbrum strategy, e.g., the mnmum contenton wndow (CW mn), to the est- number of ts opponents ( ˆn ), as follows mated [14]: CW ˆ mn n rand 7,8 where rand (x, y) returns a rando m value between x and y, and [z] returns the floor functon of z. However, Vercauteren et al [16] showed that (4) s accurate only under saturated condtons (.e., each node always has a packet watng for transmsson), and far from beng accurate under unsaturated condtons f not CW L. Q. ZHAO ET AL. 361 (5) fltered, e.g., for burst traffc. Banch and Tnnrello [17] presented two run-tme estmaton mechansms,.e., auto regressve movng average (ARMA) and Kalman Flters. The two mechansms are very accurate even n unsaturated condtons. However, they are too complex to mplement n sensor nodes. We provded an auto degressve backoff mechansm to mplement the game n current WLANs [14], whch can be mplemented easly n sensor nodes. In the actve part, after transmttng or dscardng a packet,.e., at the end of each game process, to mantan the current contenton level, the player adusts CW mn as CWmn, CW / 2 The prevous packet s transmtted successfully mn CW The prevous packet s dscarded (6) The parameter CW mn, CW, and CW at the rght of (6) are the values of the nomnal CW mn, CW and the fnal contenton wndow used n the prevous game process respectvely. The parameter CW mn at the left of (6) s used n the current game process to transmt a new packet. In, a node starts a contenton process always wth the nomnal CW mn, e.g., n IEEE b CW mn =32. So has one man drawback: n a hgh load network the ncrease of the value of CW s obtaned at the cost of contnuous collson. In, after transmttng a packet, no matter t s transmtted successfully or not, the player does not start the next game process wth the nomnal CW mn, as shown n Fgure 1. Gven that the prevous packet s transmtted successfully, the fnal value of CW s the optmal one. The best strategy for the player s to set CW mn =CW/2, to make use of the channel effectvely. On the contrary, gven that the prevous packet s dscarded, the best strategy for the player s to set CW mn =CW, to decrease collsons. Fgure 1. Auto degressve backoff mechansm. Copyrght 2009 ScRes.

5 362 L. Q. ZHAO ET AL. Obvously, compared wth the game, the most attrac- ergy consumpton. tve feature of s that t s smple to mplement. Moreover, at the end of the actve part, the node Frstly, no estmaton mechansm s needed. Secondly, t changes the length of the actve part (T actve ) and the next s not needed to compute the optmal value of CW mn. perod (T next ), accordng to the estmated game state, as That s to say, would not cause any more en- follows: next current current current current Tactve Tactve, Tactve, Tnext 0. 5 T nˆ n, Tactve / T 0.5 next current current current current T mn, ˆ actve Tactve Tactve,mn Tnext 2 T nn, Tactve / T 0.1 next current next current Tactve Tactve Tsleep Tsleep else (7) where (x, y) and mn(x, y) return the larger value and the smaller value between x and y respectvely. The pa- that n the last current rameters T actve and T current are the tme length of the actve part and the perod n the current perod. T actve, and T actve, mn, are the m axmum and mnmum length of the actve part. T next actve and T next are used n the next perod. α s a predetermned nteger, n s the last estmated number of competng n odes, and ˆn s the current estmated number of competng nodes. At the end of the current actve part, f the estmated number of competng nodes s larger than actve part, t ndcates many nodes stll have packets to send. So the tme length of the next actve part equals to that of the current actve part plus α but not longer than the mum actve part sze. The tme length of the next perod s half that of the current perod; thereby the nodes can wake up more frequently to reduce the delay of communcaton. On the other hand, f the estmated number of competng nodes s smaller than that n the last perod, the tme length of the next actve part equals to that of the current actve part mnus α but not shorter than the mnmum actve part sze. The tme length of the next perod s twce that of the current perod, so the nodes need not wake up frequently. 4. Smulaton Results To evaluate the proposed protocol, the fol- smulatons are made n an deal channel. The lowng values of the parameters used to obtan numercal results for smulatons are specfed n IEEE b protocol, as shown n Table 2. Table 2. Smulaton parameters. channel rate aslot Tme retry lmt MAC header PHY header 1Mb/s 20μs 7 144μs 192μs ACK SIFS DIFS 112μs 10μs 50μs T ransmt Recevng Lsten Power Sleepng Power Power CW mn Power 27.45mW 13.5mW 13.5mW 0.015mW CW The packets wll be dscarded only due to the retransmsson tme reaches the retry lmt, and do not consder the delay lmt. We set a st ar topology wth one coordnator and 50 devces, where each devce generates n ew fxed sze packets under a Posson process and transmt them to the coordnator. The packet arrval rate s ntally set to be lower than the saturaton case, and t s subsequently ncreased so that, at the end of the smulaton tme, all nodes are almost n saturaton condtons [18]. s consdered as the worst case: t has no energy savng features at all. The rado of each node does not go nto the sleep mode. It s ether n the lstenng/recevng mode or transmttng mode. s consdered as the basc contenton-based MAC protocol n s. It ncludes the perodc actve and sleepng tme to acheve energy savngs. For smplcty, the length of the actve and sleepng part are fxed at 500ms n the followng smulatons. Compared wth, can adapt to the load varatons n tme and locaton, and can end the actve part accordng to the traffc loads. Fgure 2 shows that the four protocols have almost the same system throughput under lght traffc loads, and under heavy traffc loads, the system throughput of s a lttle hgher than that of, whch s about 2 tmes that of and a lttle hgher than. put System through Smulaton tme(sec) Fgure 2. System throughput. Copyrght 2009 ScRes.

6 L. Q. ZHAO ET AL. 363 Fgure 3 shows that delay n, and are much lower than that n. Under lght traffc loads, delay n s a lttle larger than that n, whch s due to the perodc actve/ sleepng perod n. Under heavy traffc loads, delay n s lower than that n and, whch s due to the game n. Fgure 4 shows that tter n s much hgher than that n the other 3 protocols. Fgure 5 shows that packet-loss-rate n almost keeps zero, whch s much lower than that n S- MAC and. Meanwhle, packet-loss-rate n G- ConOpt s a lttle lower than that n, whch s due to the game n. Fgure 6 shows that the energy consumpton n s near to one half that n, whch s due to the perodc actve/sleepng scheme. Energy consumpton n s a lttle lower than that n under lght traffc loads, for nodes n sleep longer than that n. However, energy consumpton n s larger than that n under heavy traffc loads, snce nodes n sleep shorter than that n. The energy consumpton n s the lowest one n the four protocols, whch s due to the dynamc duty cycle strategy and the game n. As an energy-effcent MAC protocol, consders not only energy consumpton but also energy effcency (.e., the rato of the successfully transmtted bt rate to energy consumpton). Fgure 7 shows that energy effcency n s much hgher than that n and and. As an energy-aware MAC protocol, has hgher energy effcency than under lght traffc loads. However, the advantage of over decreases wth the ncreasng of traffc loads. Under heavy traffc loads, energy effcency n s almost equal to that n. Energy effcency n s always larger than that n and Delay(sec) ec) Jtter(s Smulaton tme(sec) Fgure 3. Delay. 0 Smulaton tme(sec) Fgure 4. Jtter. Packet-loss-rate Energ y co nsumpton(m) Smulaton tme(sec) Fgure 5. Packet-loss-rate. 0 Smulaton tme(sec) Fgure 6. Energy consumpton. Copyrght 2009 ScRes.

7 364 L. Q. ZHAO ET AL. Energy effcency(kb/s/m) Conclusons Smulaton tme(sec) Fgure 7. Energy effcency. In ths paper, frstly, the ncompletely cooperatve game s used to model the MAC protocol of s. Secondly, after consderng the context of s, e.g., the requrements on energy consumpton, the problem of the MAC protocols of s s modeled as a game-theoretc constrant optmzaton problem. Moreover, one smple for- each nodes can acheve ndependently the optmal per- mulaton s presented for the problem. Fnally, a smplfed protocol, s proposed, whch can be easly mplemented n current s. Based on, formance under lmted energy consumpton. The smu- laton results show that s an approprate tool to mprove the performance of s under certan con- strants. In ths paper we only provde a smplfed method to address the sleepng probablty. We are developng an analytcal model to obtan the optmal equlbrum of the sleepng probablty. Acknowledgement: Ths work s supported by the 111 Proect (B08038), State Key Laboratory of Integrated Servces Networks (ISN090105), Program for New Century Excellent Talents n Unversty (NCET ), Natonal Natural Scence Foundaton of Chna (No ), and UK-Chna Scence Brdges: R&D on 4G Wreless Moble Communcatons. 6. References [1] I. F. Akyldz, W. Su, Y. Sankarasubramanam, et al., Wreless sensor networks: a survey, Computer Networks, Vol. 38, No. 4, pp , March [2] W. Ye, J. Hedemann, and D. Estrn, An energy-effcent MAC protocol for wreless sensor networks, INFOCOM, New York, Vol. 3, pp , June [3] T. Dam and K. Langendoen, An adaptve energy- effcent MAC protocol for wreless sensor networks, ACM SenSys, Los Angeles CA, November [4] J. Polastre, J. Hll, and D. Celler, Versatle low power meda access for wreless sensor networks, ACM SenSys, USA, pp , November [5] A. El-Hoyd and J. D. Decotgne, WseMAC: An ultra low power MAC protocol for the downlnk of nfrastructure wreless sensor networks, ISCC, Egypt. pp , June [6] P. Ln, C. Qao, and X. Wang, Medum access control wth dynamc duty cycle for sensor networks, WCNC, Atlanta, Georga, March [7] T. van Dam, K. Langendoen, A adaptve energy-effcent MAC protocol for wreless sensor networks, ACM SenSys, USA, pp , November [8] P. D. Straffn, Game theory and strategy, The Mathematcal Assocaton of Amerca, [9] A. Agah, S. K. Das, and K. A. Basu, Game theory based approach for securty n wreless sensor networks, IPCCC, USA, pp , Aprl [10] R. Kannan, S. Sarang, and S. S. Lyengar, Sensor-centrc energy-constraned relable query routng for wreless sensor networks, Journal of Parallel and Dstrbuted Computng, Vol. 64, No. 7, pp , July [11] S. Sengupta and M. Chatteree, Dstrbuted power control n sensor networks: A game theoretc approach, IWDC, Inda, pp , December [12] X. Zhang, Y. Ca, and H. Zhang, A game-theoretc dynamc power management polcy on wreless sensor network, ICCT, Chna, pp. 1 4, November [ 13] L. Zhao, L. Guo, K. Yang, and H. Zhang, An Energyeffcent MAC Protocol for s: Game-theoretc constrant optmzaton, IEEE Internatonal Conference on Communcaton Systems, Chna, pp , November [14] L. Zhao, L. Guo, J. Zhang, and H. Zhang, A Gametheoretc MAC protocol for wreless sensor network, Journal of IET Communcatons, Vol. 3, No. 8, pp , August [15] M. S. Garey and D. S. Johnson, Computers and Intractablty: Gude to the theory of NP-completeness, W. H. Freeman, New York, [16] T. Vercauteren, A. L. Toledo, and X. Wang, Batch and sequental bayesan estmators of the number of actve termnals n an IEEE network, IEEE Trans. on Sgnal Processng, Vol. 55, No. 2, pp , January [17] G. Banch and I. Tnnrello, Kalman flter estmaton of the number of competng termnals n an IEEE network, IEEE INFOCOM, Vol. 2, San Francsco, pp , March [18] G. Banch, Performance Analyss of the IEEE dstrbuted coordnaton functon, IEEE JSAC, Vol. 18, No. 3, pp , March Copyrght 2009 ScRes.