An Adaptive Scheduling Algorithm for Set Cover Problem in Wireless Sensor Networks: A Cellular Learning Automata Approach

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1 2 3rd Internatonal Conference on Machne Learnng and Computng (ICMLC 2) n daptve chedulng lgorthm for et Cover Problem n Wreless ensor Networks: Cellular Learnng utomata pproach eza Ghader Computer Engneerng Department Islamc zad Unversty rak, Iran Ghader.re@gmal.com Mehd Esnaashar Computer Engneerng and Informaton Technology Department mrkabr Unversty of Technology Tehran, Iran Esnaashar@aut.ac.r Mohammad eza Meybod Computer Engneerng and Informaton Technology Department mrkabr Unversty of Technology Tehran, Iran mmeybod@aut.ac.r bstract edundant node deployment s a common strategy n wreless sensor networks. Ths redundancy can be due to varous reasons such as hgh probablty of falures, long lfetme expectaton, etc. One maor problem n wreless sensor networks s to use ths redundancy n order to extend the network lfetme whle keepng the entre area under the coverage of the network. In ths problem, whch s known as set cover problem, the man obectve s to select a subset of sensor nodes as actve nodes so that the set of actve nodes covers the entre area of the network. In ths paper, an schedulng algorthm s presented for solvng the set cover problem usng cellular learnng automata. In ths algorthm, each node s equpped wth a learnng automaton whch decdes for the node to be actve or not locally and based on the stuatons of ts neghbors. mulaton results n J-m smulator envronment specfy the effcency of the proposed schedulng algorthm over exstng algorthms such as PE and PEC. Keywords: Wreless ensor Networks, rea Coverage, chedulng lgorthm, Learnng utomata, Cellular Learnng utomata I. INTODUCTION One of the basc ssues n wreless sensor networks s the coverage problem whch specfes how the network s montored by sensor nodes []. The focus of ths paper s on a sub-problem of coverage problem, called the set cover problem. In set cover problem, by assumng redundancy n the number of deployed sensor nodes throughout the area of the network, the man obectve s to select a subset of sensor nodes as actve nodes so that the set of actve nodes covers the entre area of the network. electng a subset of sensor nodes as actve nodes s a sutable approach for prolongng the network lfetme. Ths s because n most scenaros of sensor networks, sensor nodes have lmted batteres, whch are not rechargeable, and hence deactvatng a number of sensor nodes and let them conservng ther batteres for later tmes, prolongs the lfetme of the network. Furthermore, deactvatng some of the sensor nodes decreases the probablty of collsons, whch n turn, decreases the need for retransmttng packets. In ths paper, we refer to any algorthm whch can select a subset of sensor nodes n such a way that the entre area of the network s covered as schedulng algorthm. In ths paper, a dstrbuted, adaptve schedulng algorthm based on cellular learnng automata for wreless sensor networks s proposed. The man purpose of ths algorthm s to mantan coverage n the network wth mnmum number of actve nodes, so that the total consumed energy of nodes s mnmzed. In the proposed algorthm, each node s equpped wth a learnng automaton whch decdes for the node to be actve or not accordng to the states (ether actve or not) of ts neghborng sensor nodes. We used J-m smulator to evaluate the performance of the proposed algorthm. mulaton results specfy the effcency of the proposed algorthm over exstng algorthms such as PE [2] and PEC [3] especally aganst hgh rato of unexpected falures. The rest of ths paper s organzed as follows. In secton II, a lterature overvew s presented. In secton III, learnng automata and cellular learnng automata are brefly revewed. The problem statement s gven n secton IV. The proposed schedulng algorthm s descrbed n secton V. mulaton results are gven n secton VI. ecton VII s the concluson. II. ELTED Work Coverage problem s one of the basc ssues n wreless sensor network about whch many dstrbuted and centralzed algorthms have been presented [2-7]. In [4], the problem of fndng the maxmal number of covers s pad attenton to n whch a cover s defned as a set of nodes that can completely cover the montored area. Ths s an NP-complete problem whch needs centralzed heurstc soluton. [5] pays attenton to coverage problem n wreless sensor networks wth a centralzed manner. In ths work, a genetc algorthm s used for coverage problem wth the mnmal number of nodes needed to cover entre area of the network. In [6, 7], authors solve the coverage problem n a dstrbuted manner. In ths work, each node decdes whether t can sleep or not based on the nformaton collected from neghborng nodes. In [2] a dstrbuted, probng-based schedulng algorthm named PE s presented. In PE, a subset of nodes remans n actve mode to mantan coverage and the rest of nodes go to sleep. Each sleepng node checks the exstence //$26. 2 IEEE V2-64

2 2 3rd Internatonal Conference on Machne Learnng and Computng (ICMLC 2) of ts workng neghbor nodes after awakenng. If no workng node s wthn ts probng range, t starts to operate n the actve mode; otherwse, t returns to sleep state. PEC algorthm [3] operates smlar to PE, but unlke PE, n PEC a node goes to sleep mode after a duraton beng n workng state and one of ts neghborng nodes replaces wth t. III. CELLUL LENING UTOMT In ths secton we brefly revew learnng automata and cellular learnng automata. Learnng utomata: Learnng utomata (L) s an abstract model whch randomly selects one acton out of ts fnte set of actons and performs t on a random envronment. Envronment then evaluates the selected acton and responses to the automata wth a renforcement sgnal. Based on the selected acton, and receved sgnal, the automata updates ts nternal state and selects ts next acton. class of L s called varable structure learnng automata and s represented by quadruple { α, β, p,t} n whch α = { α, α 2,..., α r } represents the acton set of the automata, β = { β, β 2,..., β r } represents the nput set, p = { p, p2,..., p r } represents the acton probablty set, and fnally p( n + ) = T[ α( n), β ( n), p( n)] represents the learnng algorthm. Let α be the acton chosen at tme n, then the recurrence equaton for updatng p s defned as p ( n + ) = p ( n) + a[ p ( n)] p ( n + ) = ( a) p ( n) for favorable responses, and p ( n + ) = ( b) p ( n) b p ( n + ) = + ( b) p ( n) r,, for unfavorable ones. In these equatons, a and b are reward and penalty parameters respectvely. If a = b, learnng algorthm s called L P, f b << a, t s called L 2 ε P, and f b =, t s called L 3 I. For more nformaton about learnng automata the reader may refer to [8, 9]. Cellular Learnng utomata: Cellular Learnng utomata (CL), whch s a combnaton of Cellular utomata (C) [] and learnng automata, s a powerful mathematcal model for many decentralzed problems and phenomena. The basc dea of CL, whch s a subclass of stochastc C, s to utlze L to adust the state transton probablty of stochastc C. CL s a C n whch a learnng automaton s assgned to every cell. The learnng Lnear eward-penalty 2 Lnear eward epslon Penalty () (2) automaton resdng n a partcular cell determnes ts acton (state) on the bass of ts acton probablty vector. Lke C, there s a rule that the CL operates under. The local rule of CL and the actons selected by the neghborng Ls of any partcular L determne the renforcement sgnal to the L resdng n a cell. CL has found many applcatons such as mage processng [], rumor dffuson [2], channel assgnment n cellular networks [3], and sensor networks [4, 5] to menton a few. For more nformaton about CL the reader may refer to [2, 6]. IV. POBLEM TTEMENT Consder a sensor network conssts of N sensor nodes s s N s,, 2..., wthn a feld ( Ω ). ensor nodes, whch are responsble for sensng and montorng the feld, are scattered randomly throughout the area of the network so that Ω s completely covered. ll sensor nodes have the same sensng range of and transmsson range of. s Each sensor node s has 4 dfferent modes of operaton [7] as follows: On-duty ( CPU C ): CPU, sensng and communcatng unts are swtched on referred to as actve mode. sensor node n the actve mode s referred to as an actve node. ensng Unt On-duty ( CPU C ): The CPU and the sensng unts are swtched on, but the communcatng unt s swtched off. Communcatng Unt On-duty ( CPU C ): The CPU and the communcatng unts are swtched on, but the sensng unt s swtched off. Off-duty ( CPU C ): CPU, sensng and communcatng unts are swtched off referred to as sleep mode. Note that n CPU C, CPU C, CPU C and CPU C, ndex stands for actve and ndex stands for sleep. t any nstance of tme, a sensor node can be only n one of the above 4 operaton modes. We assume that the number of sensors ( N ) s more than that requred to cover the entre area of the network. Thus, a schedulng algorthm can be adopted to use ths redundancy for prolongng the lfetme of the network. uch a controllng algorthm, selects a subset of sensor nodes as actve nodes so that the set of actve nodes fully covers Ω. Defnton : Network lfetme s defned as the tme elapsed from the network startup to the tme at whch the Ω s not further completely covered by the network due to node deaths. Consderng the above defntons and assumptons, the problem s to desgn a schedulng algorthm, whch tres to maxmze the lfetme of the network. t 3 Lnear eward Inacton V2-65

3 2 3rd Internatonal Conference on Machne Learnng and Computng (ICMLC 2) V. POPOED CHEDULING LGOITHM The proposed schedulng algorthm must provde two requrements;. complete coverage of the network area, and 2. the set of the selected actve nodes should consume as lttle power as possble so as to prolong the network lfetme. We consder the followng assumptons: The set of sensor nodes resdng throughout the network area covers the area completely. ensor nodes are aware of ther physcal locatons (usng some localzaton technques [8, 9]). N whch s the number of sensor nodes wthn the area of the network s known by all nodes. In what follows, we gve the detals of the proposed algorthm.. Detaled Descrpton of the Proposed chedulng lgorthm Intally, the network graph s mapped nto a cellular learnng automata. In ths mappng, each sensor node s n the network s mapped nto a cell n CL and two cells and are adacent n CL f ther correspondng sensor nodes are located wthn the sensng ranges of each other or n other words, two cells are adacent f the dstance between ther correspondng sensor nodes s not more than n gven by followng equaton: n = 2s ε 2s (3) We refer to n as neghborhood radus hereafter. The learnng automaton n each cell of CL, referred to as L uses lnear learnng algorthm gven by () and (2). ll learnng automata are L P. Each L has two actons α and α ; α s "plan to be n actve mode", and α s "plan to be n sleep mode". The probablty of selectng each of these actons s ntally computed accordng to (4). N I p = N (4) p = p In ths equaton, N I s a constant whch s greater than the mnmum number of actve nodes requred to cover the entre area of the network. p s selected ths way n order to have a sutable ntal dstrbuton (n terms of area coverage) of actve nodes throughout the network area. Neghborng nodes exchange HELLO packets wth each other perodcally to be aware of the states of each other. Detals on how to compute the tme nterval between two consecutve transmssons of HELLO packets n each sensor node wll be gven n secton V--. The HELLO packet of a node contans ts d and physcal locaton. Usng receved HELLO packets, each sensor node s stores for any of ts actve neghborng nodes, the locaton and the tme of the last receved HELLO packet. ensor nodes are ntally n INITIL state. In ths state, all nodes are n CPU C operaton mode. Each node s awakes after a random duraton whch s selected unformly from the range (, τ ). τ s the maxmum allowed tme nterval between two subsequent transmssons of HELLO packets. When a node s awakes, t uses ts learnng automaton to choose ts state. If L selects α whch s "plan to be n actve mode", sensor node s changes ts operaton mode from CPU C to CPU C and ts state from INITIL to WOK and then, broadcasts a HELLO packet n ts neghborhood. If L selects α whch s "plan to be n sleep mode", s changes ts operaton mode to CPU C and ts state to WIT_FO_LEEP, and then, wats to receve HELLO packets from ts neghbors whch are n WOK state. node whch s n WOK state (referred to as a workng node) montors ts surroundng area, and broadcasts HELLO packets to ts neghborng nodes perodcally. The renforcement sgnal s computed accordng to the followng two cases: If s s n WOK state and ts receved HELLO packets wthn τ duraton guarantee that the montored area of s s covered by ts neghbors, then t penalzes ts selected acton. Otherwse, t rewards ts selected acton. If s s n WIT_FO_LEEP state and ts receved HELLO packets wthn τ duraton, do not guarantee that the montored area of s s covered by ts neghbors, then t penalzes ts selected acton. Otherwse, s rewards ts selected acton. Each workng sensor node guarantees not to change ts state for a predetermned duraton T startng from the tme t dspatches ts HELLO packet. s a result, f a node, whch s n WIT_FO_LEEP state, s ensured (through receved HELLO packets) that ts montored area s covered completely by ts actve neghborng nodes wthn τ duraton, then t swtches to LEEP state. In LEEP state, all nodes are n CPU C operaton mode. leepng tme s determned by consderng the value of T and the recept tmes of the last HELLO packets from actve neghbors. Let t be the current tme of the network and t be the recept tme of the last HELLO packet from actve neghbor s at node s. The sleepng tme of the V2-66

4 2 3rd Internatonal Conference on Machne Learnng and Computng (ICMLC 2) node s ( T sleep followng equaton: sleep T ) s then computed accordng to the = mn s actve neghbors of s ( T ( t t )) When the sleepng tme of the node s s over, node s changes ts operaton mode to CPU C and ts state to WIT_FO_LEEP. Next tme for acton selecton of the learnng automaton of a node s s determned as follows: (5) If node s s n WIT_FO_LEEP state and acton α s penalzed, next acton selecton tme s mmedately after recevng the envronment response. If node s s n WOK state and acton α s penalzed, next acton selecton tme s at the dspatchng tme of the next HELLO packet. If the s enters selected acton of such a node s α, then WIT_FO_LEEP" state, but due to the assurance of ths node to ts neghbors, s must stay n actve mode and perform all of the tasks of a sensor node n WOK state, except for sendng HELLO packets, untl the end of the assurance tme. If the selected acton of node s s rewarded, then the next acton selecton tme s when ths acton s penalzed. In other words, the rewarded acton s performed repeatedly untl the tme t receves penalty. In Fgure, the transton dagram of operaton mode / state of the proposed schedulng algorthm n each sensor node has been shown. Fgure 2 shows the pseudo code of the proposed algorthm. Fgure. Operaton mode / tate transton dagram of the proposed schedulng algorthm n each sensor node. For each node s correspondng wth cell n CL do n parallel Intalze Wakeupfter(andom (, τ ) ) elect an acton accordng (4) If (the acton s α ) then ChangeOperaton_Mode/tateTo( CPU C / WOK ) else /* the acton s α */ ChangeOperaton_Mode/tateTo( CPU C / WIT_FO_LEEP ) End f Whle (Not ensordead) do Whle (the node s n WOK tate) do Broadcast HELLO Packet Update L s probablty vector End whle Whle (the node s n WIT_FO_LEEP tate) do If (NOT ssurancetoneghbors) then If (montored area of the node s covered by neghbors) then ChangeOperaton_Mode/tateTo( CPU C / LEEP ) End f End f Update L s probablty vector End whle If (the node s n LEEP tate) then Wakeupfter(leepngTme) ChangeOperaton_Mode/tateTo( CPU C / WIT_FO_LEEP ) End f End Whle End for Fgure 2. Pseudo code of the proposed algorthm ) Tme Interval for Transmsson of HELLO Packets s we stated before, sensor nodes whch are n WOK state, perodcally broadcast HELLO packets. Intally, the tme nterval between two consecutve transmssons of HELLO packets for each sensor node s s. Immedately after sendng the k th ( k > ) set to τ =τ HELLO packet, each node s updates τ accordng to (6). τ ; No = τ = No (6) τ ; Otherwse N I In the above equaton, No s the number of workng nodes from whch s receves at least one HELLO packet wthn the tme nterval [ t τ, t]. nce No s a measure of the traffc load n the neghborhood of s, (6) makes the tme nterval between two consecutve transmssons of HELLO packets n each sensor node adaptable to the local traffc load n the neghborhood of that node. V2-67

5 2 3rd Internatonal Conference on Machne Learnng and Computng (ICMLC 2) VI. PEFOMNCE EVLUTION. mulaton etup To evaluate the performance of the proposed schedulng algorthm, a number of experments are conducted and the results obtaned from the proposed algorthm are compared wth the results obtaned from PE [2] and PEC [3]. Experments are smulated usng J-m smulator [2]. We use a network area of 5 5m 2 through whch a number of sensor nodes are scattered unformly at random. Energy model gven n [7] s used n whch the energy consumpton ratos for transmsson, recepton (dle) and sleep modes are 2:4:. respectvely. The ntal energy level of each sensor node s chosen randomly from the range of 28 ~ 35 Jules. ensng and transmsson ranges of each sensor node are 7m and 3m, respectvely. Therefore, neghborhood radus accordng to (3) s 34m. Lke PE [2], each node has a raw wreless communcaton capacty of 2Kbps. mulaton tme for the frst two experments s assumed to be s. esults are averaged over 25 runs of smulatons. ) Parameters of the Proposed lgorthm We consder the value of parameter T as s and rate of reward and penalty parameters as.75 so that the sensor nodes have rapd reactons to topology changes of the network (due to unexpected falures, energy exhauston of sensor nodes,...). The values for the parameters n the proposed algorthm are lsted n Table I. TBLE I. PMETE VLUE UED IN THE POPOED LGOITHM ntal energy of channel s t N I each sensor node capacty T τ a, b 7m 3m ~ 35 Jules 2Kbps s.27s.75 2) Evaluaton Metrcs To evaluate the performance of the proposed algorthm, followng metrcs are used: () number of actve nodes; () percentage of area under the coverage of the network; () total consumed energy of sensor nodes; and (v) network lfetme. B. mulaton esults ) Experment Ths experment s conducted to study the performance of the proposed algorthm n terms of number of actve nodes, percentage of area under the coverage of the network, and total consumed energy of sensor nodes n comparson to PE and PEC algorthms. Experment s repeated for 5,, 2, 4, and 5 sensor nodes. Fgure 3 shows the results of the comparson for the number of actve nodes metrc. It can be seen from ths fgure that the number of actve nodes n the proposed algorthm, unlke PE and PEC algorthms, does not depend heavly on the number of sensor nodes n the network. Fgure 4 presents the results of the comparson between the proposed algorthm, PE, and PEC n terms of percentage of network area under coverage. s t can be seen from the fgure, the proposed algorthm fully covers the network area even n the networks of small szes (networks n whch the number of sensor nodes s below ). Fgure 5 compares the proposed algorthm wth PE and PEC algorthms n terms of the total energy consumpton of sensor nodes. It can be seen from ths fgure that the proposed algorthm consumes less than 7% and 45% of the energy consumed by PE and PEC, respectvely. 2) Experment 2 In ths experment, we study the tolerablty of the proposed algorthm aganst unexpected falures of sensor nodes n comparson to PE and PEC algorthms. To smulate unexpected falures of sensor nodes, n ths experment, 5% of the sensor nodes experence falures n random tmes durng the operaton of the network. mlar to Experment, networks wth 5,, 2, 4, and 5 sensor nodes are consdered for ths experment. Fgure 6, whch compares the proposed algorthm wth PE and PEC n terms of average number of actve nodes, ndcates that the presence of falures does not affect the performance of the proposed algorthm n terms of ths metrc sgnfcantly. Number of actve nodes n the proposed algorthm s less than 49% and 4% of the number of actve nodes n PE and PEC algorthms respectvely. ccordng to Fgure 7, whch gves the comparson of the mentoned algorthms n terms of percentage of network area under coverage, the proposed algorthm provdes full coverage of network area n all of mentoned network szes even n presence of unexpected node falures. Fnally, Fgure 8 gves the comparson of the mentoned algorthms n terms of the total energy consumpton of sensor nodes. Ths fgure shows that n the presence of unexpected falures, the energy consumpton of the proposed algorthm s less than 69% and 54% of the energy consumpton of PE and PEC, respectvely. V2-68

6 2 3rd Internatonal Conference on Machne Learnng and Computng (ICMLC 2) Fgure 3. Number of actve nodes versus number of sensor nodes Fgure 4. Percent of coverage versus number of sensor nodes Fgure 5. Total energy consumpton versus number of sensor nodes Fgure 6. Number of actve nodes versus number of sensor nodes wth falures Fgure 7. Percent of coverage versus number of sensor nodes wth falures Fgure 8. Total energy consumpton versus number of sensor nodes wth falures 3) Experment 3 Ths experment s conducted to study the performance of the proposed algorthm n terms of network lfetme. For ths experment, number of sensor nodes s assumed to be 25. The necton of unexpected falures of sensor nodes s performed wth a rate of 4.7 falures n every s. The results of smulatons show that the network lfetme for PE, PEC and the proposed algorthm s 9s, 2s and 22s, respectvely. Ths ndcates that the proposed algorthm better prolongs the lfetme of the network n comparson to exstng algorthms. VII. CONCLUION In ths paper, a novel schedulng algorthm based on cellular learnng automata for solvng the set cover problem n a wreless sensor network was presented. Ths algorthm tres to select a mnmum number of actve nodes, whch can fully cover the entre area of the network, so that the energy consumpton of sensor nodes on average s mnmzed, and consequently the network lfetme s maxmzed. The results of smulatons proved the superorty of the proposed algorthm over smlar exstng algorthms lke PE and PEC n terms of number of actve nodes, energy consumpton of sensor nodes, percentage of network area under coverage, and network lfetme. The results of experments also showed that the proposed algorthm outperforms PE and PEC n terms of the above mentoned metrcs even n the presence of unexpected falures n the sensor nodes of the network. EFEENCE [] C. F. Huang, and Y. C. Tseng, The coverage problem n a wreless sensor network, Moble Networks and pplcatons, vol., no. 4, pp , January 25. [2] F. Ye, G. Zhong,. Lu, and L. Zhang, PE: robust energy conservng protocol for long-lved sensor networks, In The 23nd Internatonal Conference on Dstrbuted Computng ystems (ICDC), 23. [3] Ch. Gu, and P. Mohapatra, Power conservaton and qualty of survellance n target trackng sensor networks, In Proc. of the th nnual Intl. Conf. on Moble Computng and Networkng (MOBICOM 24), Phladelpha, P, U, 24. [4]. lepcevc, and M. Potkonak, Power effcent organzaton of wreless sensor networks, In ICC 2, pp , June 2. [5] F. P. Quntao, F. G. Nakamura, and G.. Mateus, hybrd approach to solve the coverage and connectvty problem n wreless sensor networks, Unversty of Mnas Geras Belo Horzonte, MG. Brazl, 25. [6] X. Wang, G. Xng, Y. Zhang, C. Lu,. Pless, and C. Gll, Integrated coverage and connectvty confguraton n wreless sensor networks, In The Frst CM Conference on Embedded Networked ensor ystems, November 23. [7] H. Zhang, and J. C. Hou, Mantanng sensng coverage and connectvty n large sensor networks, d Hoc & ensor Wreless Networks, vol., pp , March 25. [8] M.. L. Thathachar, and P.. astry, Varetes of learnng automata: n overvew, IEEE Transacton on ystems, Man, and Cybernetcs-Part B: Cybernetcs, vol. 32, no. 6, pp , 22. V2-69

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