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- 1. 1836 IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, VOL. 21, NO. 12, DECEMBER 2010 Energy-Balanced Dispatch of Mobile Sensors in a Hybrid Wireless Sensor Network You-Chiun Wang, Member, IEEE, Wen-Chih Peng, Member, IEEE, and Yu-Chee Tseng, Senior Member, IEEE Abstract—We consider a hybrid wireless sensor network with static and mobile nodes. Static sensors monitor the environment and report events occurring in the sensing field. Mobile sensors are then dispatched to visit these event locations to conduct more advanced analysis. A big challenge is how to schedule these mobile sensors’ traveling paths in an energy-balanced way so that their overall lifetime is maximized. We formulate this problem as a multiround sensor dispatch problem and show it to be NP-complete. Then, we propose a centralized and a distributed heuristics to schedule mobile sensors’ traveling paths. Our heuristics allow arbitrary numbers of mobile sensors and event locations in each round and have an energy-balanced concept in mind. The centralized heuristic tries to minimize mobile sensors’ moving energy while keeping their energy consumption balanced. The distributed heuristic utilizes a grid structure for event locations to bid for mobile sensors. Through simulations, we show the effectiveness of our schemes. This paper contributes in defining a more general multiround sensor dispatch problem and proposing energy-efficient solutions to it. Index Terms—Energy saving, load balance, mobile sensor, robot, wireless sensor network. Ç1 INTRODUCTIONH YBRID sensor networks with static and mobile nodes open a new frontier of research in wireless sensornetworks (WSNs). Static sensors support environmental sensors exhaust their energy too early, the remaining mobile sensors may need to travel longer distances to serve some event locations, thus further shortening the systemsensing and network communication. Mobile sensors are lifetime. On the contrary, if there are more mobile sensors,more resource-rich in sensing and computing capabilities each mobile sensor may need to visit only local eventand can move to particular locations to conduct more locations. Such an example is [8], which targets at greedilycomplicated missions such as repairing the network or minimizing the overall energy consumption of mobileproviding in-depth analysis [1], [2]. Introducing mobility to a sensors in each round without considering energy balanceWSN not only reduces its deployment and maintenance costs among mobile sensors. Take an example in Fig. 1. Initially,but also enhances its capability. Applications of hybrid mobile sensors s1 and s2 are located at l1 and l2 ,WSNs have been studied in [3], [4], [5]. respectively, each with energy of 600 units. The energy In this paper, we focus on the problem of dispatching cost to move between any two locations is given in Fig. 1a.mobile sensors to the locations of events appearing in the Suppose that in each odd round, events appear at l3 and l4 ,sensing field. Static sensors serve as the backbone to identify and in each even round, events appear at l1 and l2 . Fig. 1bwhere suspicious events may appear and report such events shows that with the above greedy strategy, s1 and s2 moveto mobile sensors so as to conduct more in-depth analysis. between ðl3 ; l1 Þ and ðl4 ; l2 Þ, respectively. The system lifetimeAssuming that events may appear anytime and anywhere, it is nine rounds. Fig. 1c shows that by balancing their energyis inefficient to dispatch one mobile sensor right after an event consumption, s1 and s2 move between ðl4 ; l1 Þ and ðl3 ; l2 Þ,appears. We thus propose dividing time into multiple rounds respectively, and can survive 10 rounds, although in eachand schedule mobile sensors’ traveling paths in a round by round they consume more energy.round manner. The objective is to emphasize both path In this paper, we prove that even if all event locations in theefficiency and balance of mobile sensors’ energy consump- future rounds are known in advance, the sensor dispatchtion because moving energy is critical for mobile sensors [6], problem is NP-complete. We then propose a centralized and a[7]. Then, we measure the system lifetime, which is defined as distributed heuristics to extend the system lifetime. The ideathe number of rounds until some event locations cannot be is to minimize the moving energy of mobile sensors whilereached by any mobile sensor due to lack of energy. balancing their energy consumption in each round. Our Balancing energy consumption is important in the case of centralized heuristic allows arbitrary numbers of eventmultiple mobile sensors. For example, when some mobile locations and mobile sensors in each round. When mobile sensors are more than event locations, we translate the dispatch problem to a maximum matching problem in a. The authors are with the Department of Computer Science, National Chiao- Tung University, 1001 University Road, Hsinchu, Taiwan 300, R.O.C. weighted complete bipartite graph [9], where the vertex set E-mail: {wangyc, wcpeng, yctseng}@cs.nctu.edu.tw. contains mobile sensors and event locations and the edge setManuscript received 12 Mar. 2009; revised 30 Oct. 2009; accepted 4 Feb. contains each edge from every mobile sensor to every event2010; published online 23 Mar. 2010. location. In addition, when matching two vertices, we adopt aRecommended for acceptance by S. Das. bound concept to avoid choosing edges with too large weights,For information on obtaining reprints of this article, please send e-mail to:tpds@computer.org, and reference IEEECS Log Number TPDS-2009-03-0112. so the energy-balanced goal can be achieved. On the otherDigital Object Identifier no. 10.1109/TPDS.2010.56. hand, when mobile sensors are fewer than event locations, we 1045-9219/10/$26.00 ß 2010 IEEE Published by the IEEE Computer Society
- 2. WANG ET AL.: ENERGY-BALANCED DISPATCH OF MOBILE SENSORS IN A HYBRID WIRELESS SENSOR NETWORK 1837 The rest of the paper is organized as follows: Section 2 reviews related work. Section 3 defines the sensor dispatch problem and shows it to be NP-complete. Sections 4 and 5 propose our centralized and distributed heuristics. Simula- tion results are presented in Section 6. Conclusions and future research topics are drawn in Section 7. 2 RELATED WORK Mobility management has received considerable attention in mobile ad hoc networks (MANETs). Most studies focus on the communication issue [12], [13] or topology control [14], [15] due to frequent node mobility. They consider that nodes move in an arbitrary manner or follow some mobility models [16]. Unlike MANETs, node mobility in hybrid WSNs is controllable and can even be coordinated. A multirobot system (MRS), one topic in the field of robots, uses multiple cooperative robots to accomplish a task in an uncertain environment [17], [18]. Multiagent reinforcement learning [19], [20], [21] is proposed to train robots to learn mappings from their statuses to their actions. However, these studies have different objectives from our work. Multirobot task allocation [22] determines which robot should execute which task to cooperatively achieve the overall goal, where a task is viewed as an independent subgoal that is necessary for achieving the overall goal. However, [22]Fig. 1. Comparison of dispatch solutions: (a) the network configuration, does not aim at the energy issue of robots.(b) the greedy approach, and (c) the energy-balanced approach. Mobile sensors have been intensively researched to improve a WSN’s topology. Moving sensors to approximategroup event locations into clusters where the number of the event distribution, while maintaining complete coverageclusters is equal to that of the mobile sensors. Then, we adopt of the sensing field, is studied in [23]. The work in [24] movesthe above matching approach combined with the traveling- nodes to keep a WSN biconnected. With a grid structure, thesalesman approximation algorithm (TSP) [10]. Designed with a work in [25] moves sensors from high-density grids to low-similar philosophy, we also propose a distributed heuristic density ones to generate a uniform topology. The works [26],using a grid structure. Specifically, each grid with event [27] use virtual forces to drive sensors’ moving directions,locations adopts grid-quorum [11] to obtain the information while the work in [28] discusses moving sensors to fillof mobile sensors. Then, the grids bid for mobile sensors with uncovered holes. The studies [29], [30] also address the sensoreach other by using the bound concept in the centralized dispatch problem, but they do not consider energy balanceheuristic. After determining the winning grids, each mobile and only optimize energy consumption in one round.sensor visits these grids by the proposed two-level TSP scheme. Some studies deploy mobile sensors to track movingIn particular, the mobile sensor first calculates the shortest targets. The purser-evader game is studied in [31], where apath to visit the winning grids and then moves to the event pursuer needs to intercept an evader by the assistance oflocations inside each of these grids. static sensors. The work in [32] discusses the problem of Although sharing the same bound concept, the centralized maneuvering mobile sensors for the optimal data acquisitionand distributed heuristics have two differences in essence. from moving targets. Target tracking with the assistance ofFirst, the centralized heuristic clusters event locations, from a mobile sensors is discussed in [33] with concerns of energyglobal view, when there are fewer mobile sensors, while the consumption, network connectivity, and sensing coverage.distributed heuristic always clusters event locations into They assume that the future trajectory of the moving targetfixed grids. Second, the centralized heuristic requires a may be predicted, whereas our work allows events tocentral node (e.g., the sink) to calculate the dispatch arbitrarily appear.schedules, which incurs network flooding to gather/dis-seminate global information. In contrast, the distributed Several variations of the sensor dispatch problem haveheuristic adopts grid-quorum to reduce the message com- been studied in the literature. In [34], static sensors detectingplexity but lets event locations compete for mobile sensors events will ask mobile sensors to move to their locations tousing partial information. Our simulation results reflect that conduct more in-depth analysis. The mobile sensor that has awhen there are more mobile sensors, the grid structure helps shorter moving distance and more energy, and whoseextend the system lifetime. On the other hand, when there are leaving will generate a smaller uncovered hole, is invited.fewer mobile sensors, the centralized heuristic has a longer The work in [35] dispatches mobile sensors to improve thesystem lifetime due to its efficient clustering and global sensing coverage of a hybrid WSN. Static sensors estimate theknowledge. Nevertheless, both heuristics result in a longer uncovered holes close to them and use the hole sizes tosystem lifetime compared to the greedy scheme. Also, compete for mobile sensors. The concept of energy balance insimulation results show that the distributed heuristic is more dispatching mobile sensors is exploited in [36]. Once a mobilemessage efficient. sensor si identifies a destination lj , si tries to form a sequence
- 3. 1838 IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, VOL. 21, NO. 12, DECEMBER 2010 TABLE 1 Summary of Notations Fig. 2. Reduction of the partition problem to the sensor dispatch decision problem.of si ! sk1 ! sk2 ! Á Á Á ! skm ! lj , such that cascaded move-ments si ! sk1 , sk1 ! sk2 ; . . . , and skm ! lj will happen. How the current energy of si is expressed by ei . Consequently, theevent locations can find mobile sensors in a message-efficient energy required to complete si ’s dispatch schedule ismanner is discussed in [37]. Compared with prior studies, formulated asthis paper considers a more general dispatch problem, whereevents may appear in arbitrary locations, event locations inthe future rounds are unpredictable, and the relationship fðDSi Þ ¼ emove Â dðsi ; DSi ½1Þbetween the number of event locations and the number of !mobile sensors is arbitrary. We will develop centralized and jDSi jÀ1 Xdistributed algorithms with energy-balanced property to þ dðDSi ½j; DSi ½j þ 1Þ ; j¼1prolong the system lifetime. where emove is the energy cost for a mobile sensor to move one3 PROBLEM STATEMENT unit distance, jDSi j is the number of event locations in DSi , and dðÁ; ÁÞ is the distance between two locations. Clearly, anyWe consider a hybrid WSN with both static and mobile dispatch schedule of a mobile sensor should satisfysensors. Sensors are aware of their own locations, which can ei ! fðDSi Þ. Also, we are given the initial energy einit of each ibe achieved by global positioning system (GPS) or other si , i ¼ 1::n, in round 0. Assuming that mobile sensors are notlocalization techniques [38]. Static sensors are dense enough rechargeable, the objective is to schedule their travelingto form a connected network that fully covers the sensing paths such that the system lifetime is maximized. Table 1field. They can cooperate to identify events that may appear summarizes the notations used in this paper.in arbitrary locations in the sensing field (refer to [34] for Next, we show that the above sensor dispatch problem ispossible solutions). We make no assumption on the event NP-complete even if the event locations are known indistribution, and the occurrence of any two events is advance in each round. We first formulate the sensorindependent. Mobile sensors are more resource-rich andcan be dispatched to event locations to conduct more in- dispatch problem as a decision problem.depth analysis. Both the moving speed of a mobile sensor Definition 1. Given a set of mobile sensors S and a sequence of kand its energy consumption to move a unit distance are event location sets L1 ; L2 ; . . . ; Lk , the sensor dispatch decisionassumed to be constants. Also, we assume that the sensing problem is to determine whether there is a feasible schedule forfield is obstacle-free, so mobile sensors can directly move to S to visit L1 ; L2 ; . . . ; Lk in that order.their destinations using the shortest distances. The time is divided into rounds. Each round is led by a Theorem 1. The sensor dispatch decision problem is NP-collecting phase followed by a dispatching phase. Static sensors complete.report those events that have been detected but not yet Proof. We first show that this problem belongs to NP. Given aprocessed in the collecting phase. Mobile sensors then visit problem instance and a solution containing the dispatchthese event locations in the dispatching phase. In each round, schedules in k rounds, it can be verified whether thean event only needs to be visited by one mobile sensor. Our solution is valid in polynomial time. So, this part is proved.discussion focuses on the dispatch problem in one round. We then reduce the partition problem [39], which isTherefore, given a set of m event locations L ¼ fl1 ; l2 ; . . . ; lm g known to be NP-complete, to our problem. Given a finiteand a set of n mobile sensors S ¼ fs1 ; s2 ; . . . ; sn g in a round, set X in which each element xi 2 X is associated with aour objective is to assign each si a dispatch schedule DSi , number ðxi Þ, the partition problem is to determinei ¼ 1::n, which contains a sequence of event locations. The whether we can partition X into two subsets such thatunion of locations in all dispatch schedules should be equal to the sums of their associated numbers are equal.L. In case that DSi is too long for si to complete in the current Let X ¼ fx1 ; x2 ; . . . ; xk g be an instance of the partitionround, the remaining unvisited locations are deleted from problem. We construct an instance of the sensor dispatchDSi and will be put into the next round for scheduling (thus, decision problem as shown in Fig. 2. Initially, mobilethese deleted locations may be visited by other mobile sensors sa and sb are located at la and lb , respectively, each Psensors). The jth location of DSi is denoted by DSi ½j and with initial energy of k ðxi Þ. For each xi , i ¼ 1::k, we i¼1
- 4. WANG ET AL.: ENERGY-BALANCED DISPATCH OF MOBILE SENSORS IN A HYBRID WIRELESS SENSOR NETWORK 1839 construct a location li such that the energy required to Below, we propose a heuristic to find M: move from both la and lb to li is ðxi Þ. Now, consider a 2k- round problem such that in the ð2i À 1Þth round, an event 1. For each location lj 2 L, we associate with it a appears at li , and in the ð2iÞth round, two events appear at preference list P j , which contains all mobile sensors la and lb , i ¼ 1::k. We show that X has a solution if and ranked by their weights in correspondence with li in only if the dispatch problem has a solution. an ascending order. In case of tie, sensors’ IDs are Suppose that we have a solution to the sensor used to break the tie. dispatch decision problem. The solution must dispatch 2. Construct a queue Q containing all locations in L.1 one mobile sensor to one event location in each odd 3. To achieve objective 3, we create a bound Bj for each round and then dispatch the same mobile sensor back to location lj 2 L to restrict the mobile sensors that lj its original location in the subsequent even round. That can match with. Initially, we set Bj ¼ wðsi ; lj Þ such is, either sa or sb will move to li and move back in the that si is the
- 5. th element in lj ’s preference list P j , ð2i À 1Þth and the ð2iÞth rounds, respectively. The total where
- 6. is a system parameter. P 4. Dequeue an event location, say, lj from Q. energy consumption of sa and sb is thus 2 Á k ðxi Þ. Pk i¼1 Since the initial energy of sa and sb is i¼1 ðxi Þ, both sa 5. To achieve objective 2, we select the first candidate and sb exhaust their energy after 2k rounds. This implies mobile sensor, say, si from P j , and try to match si that sa and sb have moved the same distance. Therefore, with lj . If si is also unmatched, we add the match the sets of locations visited by sa and sb all constitute a ðsi ; lj Þ into M and remove si from P j . Otherwise, si solution to the partition problem. This proves the if part. must have matched with another location, say, lo . Conversely, suppose that subsets X a and X b are a Then, lj and lo will compete by their bounds Bj and solution to the partition problem. Then, in the ð2i À 1Þth Bo . Location lj wins the competition if one of these round, i ¼ 1::k, we can dispatch sa (respectively, sb ) to conditions is true: visit li if X a (respectively, X b ) has an element associated a. Bj Bo : Since lj has raised to a higher bound, with a number ðxi Þ, and move it back in the ð2iÞth we match si with lj . round. Clearly, both sa and sb P move the same distance b. Bj ¼ Bo and wðsi ; lj Þ wðsi ; lo Þ: Since moving si and exhaust their energy (i.e., k ðxi Þ) in the ð2kÞth i¼1 to lj is more energy efficient, we match si with lj . round. This constitutes a solution to the sensor dispatch c. Bj ¼ Bo , si is the only candidate of lj , and lo has decision problem, thus, proving the only if part. u t more than one candidate: In this case, if si is not matched with lj , lj has to increase its bound Bj .4 A CENTRALIZED DISPATCH ALGORITHM However, lo may not increase its bound Bo if si is not matched with lo . Thus, we match si with lj .In this section, we propose a centralized algorithm todispatch mobile sensors. The idea is to minimize their If lj wins the competition, we replace the pair ðsi ; lo Þmoving energy while keeping their energy consumption in M by ðsi ; lj Þ, remove si from P j , enqueue lo into Q,balanced after each round. Without loss of generality, we and go to step 7. Otherwise, we remove si from P jdelete those mobile sensors that do not have sufficient (since lj will not consider si any more) and go to step 6.energy to reach any location in L from S. Considering the 6. If lj still has candidates in P j (under bound Bj ), go tovalues of jSj and jLj, there are two cases to be discussed. step 5 directly. Otherwise, we increase lj ’s bound toWhen jSj ! jLj, we translate the dispatch problem to a Bj ¼ wðsk ; lj Þ such that sk is the
- 7. th element in themaximum matching problem in a weighted complete current P j and then go to step 5. (Note that since P j isbipartite graph. On the other hand, when jSj jLj, we sorted in an ascending order and the first mobilepartition L into jSj clusters so that each mobile sensor only sensor si is always removed from P j after step 5, weneeds to visit one cluster of event locations. Then, the will obtain a new larger bound Bj ¼ wðsk ; lj Þ maximum matching approach is applied again. wðsi ; lj Þ.) 7. If Q is empty, the algorithm terminates; otherwise,4.1 Case of jSj ! jLj go to step 4.We first construct a weighted complete bipartite graph Since jSj ! jLj, each event location will eventually find aG ¼ ðS [ L; S Â LÞ. Each mobile sensor and event location is mobile sensor to match with. Thus, the above algorithm mustconverted into a vertex. Edges only connect vertices terminate and return a maximum matching. Here, the boundbetween S and L. For each si 2 S and each lj 2 L, its of an event location implicitly indicates that if the currentweight is defined as wðsi ; lj Þ ¼ emove Â dðsi ; lj Þ. Then, the candidate mobile sensor cannot match with the eventsensor dispatch problem is formulated as the problem of location, the event location may possibly match with anotherfinding a matching M in G such that mobile sensor of a distance equal to that bound. Since we 1. The number of matches is maximum. want to balance the energy consumption among mobile 2. The sum of the weights associated with all matches sensors by preventing some mobile sensors from moving too is as small as possible. long distances, we should avoid raising the bounds of event 3. The standard deviation of the weights associated locations. The system parameter
- 8. determines the number of with all matches is as small as possible. candidate mobile sensors and the bound. We suggest setting
- 9. 1 and will discuss the effect of
- 10. in Section 6.6.Note that objective 1 is a necessary condition in our algorithm.However, minimum values for both objectives 2 and 3 may 1. It can be verified that any order of the locations in Q can lead to thenot always be achieved, but keeping them small is our goal. same result in our scheme. So, we do not specify the order in this step.
- 11. 1840 IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, VOL. 21, NO. 12, DECEMBER 2010Fig. 3. An example of finding M: (a) the energy consumption to move each mobile sensor to each event location and (b) the running iterations. Fig. 3 gives an example, where
- 12. ¼ 2. The energy cost to ^ ^ ~ ðsi ; Lj Þ such that si 2 S and Lj 2 L. The weight of ðsi ; Lj ) is ^move each mobile sensor to each event location is given in defined as wðsi ; L ^ j Þ ¼ emove Â ðdðsi ; Lj Þ þ ðLj ÞÞ, where ^ ^Fig. 3a. Let Q ¼ fl1 ; l2 ; l3 g. Fig. 3b shows the running ^ dðsi ; Lj Þ is the distance from si to the nearest event locationiterations. In iteration 1, l1 has two candidates s1 and s2 in in L^ j and ðLj Þ is the moving distance for si to visit all event ^its P 1 and sets bound B1 ¼ wðs2 ; l1 Þ ¼ 99. Since s1 is l1 ’s first ^ ^ locations in Lj (below, we call ðLj Þ the cluster cost). Then,candidate and s1 is also unmatched, we match s1 with l1 . we adopt the algorithm in Section 4.1 to find a maximumSimilarly, s2 is matched with l2 . In iteration 2, l3 finds that its ^ matching M on G0 . For each ðsi ; Lj Þ 2 M, we dispatch si tofirst candidate s1 has already matched with l1 , it thus the nearest event location in L ^ j and then apply any TSPcompetes with l1 by their bounds. Since B3 ¼ 111 B1 ¼ 99, solution for si to visit other event locations in Lj . ^we thus replace the pair ðs1 ; l1 Þ by ðs1 ; l3 Þ in M. In iteration 3, There are two remaining issues in the above algorithm:l1 checks its remaining candidates and competes with l2 for 1) how to estimate cluster costs and 2) how to cluster events2 . However, because B1 ¼ 99 B2 ¼ 127, l1 loses the locations. For issue 1, since the TSP problem is NP-completecompetition. Therefore, in iteration 4, l1 expands its bound and it is not yet known which mobile sensor will visit whichas B1 ¼ wðs4 ; l1 Þ ¼ 231 and matches with its first candidate cluster (different mobile sensors may land at different initials3 . The final result is M ¼ fðs3 ; l1 Þ; ðs2 ; l2 Þ; ðs1 ; l3 Þg. locations of a cluster), we need to estimate a value for each We then analyze the time complexity of the above ^ ðLj Þ. Since some TSP heuristics [10] are based onalgorithm. Recall that jLj ¼ m and jSj ¼ n. Calculating the constructing a minimum spanning tree from the nodes topreference lists of all event locations takes Oðmn lg nÞ time. ^ be visited, we propose letting ðLj Þ be the sum of all edgeThe worst case to match an event location with a mobile 2 weights in the minimum spanning tree of Lj . Fig. 4a shows ^sensor is OðnÞ because the event location has to go through an example, where ðAÞ ¼ 50, ðBÞ ¼ 12, ðCÞ ¼ 15, andits whole preference list. Thus, computing the maximum ðDÞ ¼ 68. For issue 2, we introduce three schemes below.matching M takes OðmnÞ time. Therefore, the total time K-means clustering scheme [40]. This scheme groupscomplexity is Oðmn lg n þ mnÞ ¼ Oðmn lg nÞ. event locations based on their relative distances in the sensing field such that those locations close to each other4.2 Case of jSj jLj are grouped together. Initially, L is randomly partitionedWhen mobile sensors are fewer than event locations, we into jSj nonempty clusters. Then, an iterative process is ^ ^ ^divide L into nð¼ jSjÞ clusters L1 ; L2 ; . . . ; Ln and dispatch conducted. In each iteration, the central point of each clusterone mobile sensor to visit one cluster of event locations. The is computed. Explicitly, given a cluster of locations ~ ^ ^ ^algorithm is outlined as follows: Let L ¼ fL1 ; L2 ; . . . ; Ln g. fðx1 ; y1 Þ; ðx2 ; y2 Þ; . . . ; ðxp ; yp Þg, its central point is calculatedWe construct a weighted complete bipartite graph G0 ¼ P P as ð1 p xi ; 1 p yi Þ. Then, L is repartitioned such that p i¼1 p i¼1 ~ ~ðS [ L; S Â LÞ such that the vertex set contains S (all mobile ~sensors) and L (all clusters), and the edge set contains all 2. The weight of an edge ðli ; lj Þ is the distance between li and lj .
- 13. WANG ET AL.: ENERGY-BALANCED DISPATCH OF MOBILE SENSORS IN A HYBRID WIRELESS SENSOR NETWORK 1841Fig. 4. Examples of clustering results: (a) the K-means clustering scheme, (b) the MaxMin clustering scheme, and (c) the balanced clusteringscheme.locations closest to the same central point are put into the clusters, we merge two clusters with distance winter . The minsame cluster. The process is repeated until no cluster is above operation is repeated until wintra winter . This scheme max minchanged. Fig. 4a shows an example by assuming jSj ¼ 4. can avoid clusters containing very long edges, thereby The time complexity of the K-means clustering scheme is reducing the energy costs for mobile sensors to visitOðjSj Á jLj Á Þ ¼ OðmnÞ, where is the number of iterations clusters. Figs. 4a and 4b give an example. In Fig. 4a, wintra ¼ maxto perform K-means for clustering. According to [40], 50 (in cluster D) and winter ¼ 15 (between clusters A and B). minusually ranges from tens to hundreds. We thus split cluster D into two clusters D1 and D2 , and MaxMin clustering scheme. The K-means clustering then merge clusters A and B, as shown in Fig. 4b. Now, wescheme could be inefficient when the distribution of event have wintra ¼ 40 and winter ¼ 20, enforcing us to further split max minlocations is irregular or sparse. For example, l1 and l10 in A0 and then to merge C and D1 . After this operation, weFig. 4a are far away from other locations, and thus, have wintra ¼ 20 and winter ¼ 40. Thus, the scheme termi- max minconsidered sparse. Therefore, we propose a MaxMin cluster- nates and the final result is shown in Fig. 4b.ing scheme that is based on the result of K-means and then The time complexity of the MaxMin clustering scheme isiteratively split and merge some clusters to obtain better analyzed as follows: Since there are jLj ¼ m event locations,clustering. Intuitively, clusters with sparse locations should we need mðmÀ1Þ edges to connect each pair of locations (in a 2be split. In each iteration, we first construct the minimum complete graph). The worst case occurs when one half ofspanning tree of each cluster. Let wintra be the maximum of max these mðmÀ1Þ edges belong to intracluster edges (after 2the maximum edge weight in each cluster among all executing K-means) and the other half of them belong toclusters and winter be the minimum of the distances between min intercluster edges. We then build a maximum binary heapall cluster pairs, where the distance between two clusters is Émax and a minimum binary heap Émin to maintain allthe distance between the two closest locations in the two intracluster and intercluster edges, respectively. Building aclusters. We split the cluster which contains the edge with heap requires OðmðmÀ1ÞÞ ¼ Oðm2 Þ time. Recall that in each 4weight wintra by removing that edge. Then, among all jSj þ 1 max iteration of MaxMin, we find the edges with weights wintra max
- 14. 1842 IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, VOL. 21, NO. 12, DECEMBER 2010and winter and then exchange them (i.e., let the edge with min 1. Delete the maximum in ÉC to find the cluster with maxweight wintra become an intercluster edge and the edge with max the maximum cost, which takes Oðlg nÞ time.weight winter become an intracluster edge) if wintra winter . min max min 2. Split that cluster into two balanced clusters. TheThus, one iteration involves four operations in the two worst case occurs when we have to search all treeheaps: deletion of the maximum in Émax , deletion of the edges in the cluster with ðm À n þ 1Þ locations. Thisminimum in Émin , insertion of wintra into Émin , and insertion max takes Oðm À nÞ time.of winter into Émax . Each of these four operations takes min 3. Merge two clusters such that the cost of the newOðlg m2 Þ ¼ Oð2 lg mÞ time. Thus, the total time to complete cluster derived by merging these two clusters isone iteration in MaxMin is 4 Á Oð2 lg mÞ ¼ Oð8 lg mÞ. Now, minimized. Since there are ðn þ 1Þ clusters, this nþ1we calculate how many iterations are executed in MaxMin. operation takes OðC2 Þ ¼ Oðn2 Þ time.The worst case occurs when Émax contains the edges with 4. Insert the two new clusters into ÉC , which takes maxthe smallest mðmÀ1Þ weights and Émin contains the edges 2Oðlg nÞ time. 4with the largest mðmÀ1Þ weights. In this case, MaxMin is 4 Thus, an iteration takes Oðlg nÞ þ Oðm À nÞ þ Oðn2 Þ þexecuted until Émax and Émin exchange all of their edges. So, 2Oðlg nÞ ¼ Oðn2 Þ time. Since the balanced clustering schemethere are totally mðmÀ1Þ iterations in the worst case. Thus, the 4 stops when the total cluster cost is no longer reduced, thetotal time complexity of MaxMin is number of iterations should be no more than that of MaxMin. Therefore, the time complexity of the balanced clustering ðtime to execute K-meansÞ þ ðtime to build Émax and Émin Þ scheme is OðmnÞ þ Oððm À n þ 1Þ2 Þ þ mðmÀ1Þ Oðn2 Þ ¼ 4 mðm À 1Þ Oðmn þ m2 n2 Þ. þ time to execute iterations We then analyze the total time complexity when jSj jLj. 4 Recall that it spends Oððm À n þ 1Þ2 Þ time to calculate the mðm À 1Þ ~ ¼ OðmnÞ þ 2Oðm2 Þ þ Á Oð8 lg mÞ costs of all clusters. Since jLj ¼ n and jSj ¼ n, it takes 4 Oðn2 lg nÞ time to execute the algorithm in Section 4.1. ¼ Oðmn þ m2 lg mÞ: Therefore, if the K-means clustering scheme is adopted, Balanced clustering scheme. The MaxMin clustering the total time complexity is OðmnÞ þ Oððm À n þ 1Þ2 Þ þscheme can minimize the total cost of clusters, but it may Oðn2 lg nÞ ¼ Oðmn þ ðm À n þ 1Þ2 þ n2 lg nÞ. If the MaxMinlead to unbalanced clusters. Thus, we should try to reduce clustering scheme is adopted, the total time complexity isboth the total cost of clusters and the standard deviation ofclusters’ costs. To do so, we first cluster event locations by K- Oðmn þ m2 lg mÞ þ Oððm À n þ 1Þ2 Þ þ Oðn2 lg nÞmeans. Then, we iteratively split and merge some clusters. In ¼ Oðmn þ m2 lg mÞ:each iteration, we split the cluster with the maximum costinto two new clusters, say, ci and cj , such that jð^i Þ À ð^j Þj is ^ ^ c c Finally, since the balanced clustering scheme has alreadyminimized. Then, among all jSj þ 1 clusters, we merge the calculated the cost of each cluster, the total time complexitytwo clusters into one new cluster, say, ck , such that ð^k Þ is ^ c is Oðmn þ m2 n2 Þ þ Oðn2 lg nÞ ¼ Oðmn þ m2 n2 Þ.minimized. This operation is repeated until the total clustercost is no longer reduced. Figs. 4a and 4c show an example. In 5 A DISTRIBUTED DISPATCH ALGORITHMFig. 4a, D has the maximum cost of ðDÞ ¼ 68, so we split it.There are two ways to split D. One is to split D into D1 ¼ In this section, we propose a distributed heuristic based on afl8 ; l9 g and D2 ¼ fl10 g. The other way is to split D into D3 ¼ grid structure. There are three challenges. First, how can wefl8 g a n d D4 ¼ fl9 ; l10 g. S i n c e jðD1 Þ À ðD2 Þj ¼ 18 efficiently exchange the messages between event locationsjðD3 Þ À ðD4 Þj ¼ 50, we split D into D1 and D2 , as shown and mobile sensors so that they can know each other? Second,in Fig. 4c. Then, we merge C and D1 such that the new cluster how can one event location compete for a mobile sensor whenC 0 has the minimum cost of 53. In the next iteration, since C 0 the event location is not aware of other event locations? Third, 0 since it is difficult to cluster event locations, how can wehas the maximum cost, we split it into C1 ¼ fl6 ; l7 g and 0 0 0 handle the case when jSj jLj? To address the aboveC2 ¼ fl8 ; l9 g. However, among the five clusters A; B; C1 ; C2 , 0 0 challenges, we propose a distributed algorithm outlined asand D2 , we have to merge C1 and C2 because the cost of themerged cluster is the smallest. Since the total cluster cost is follows: We partition the sensing field into grids and elect onestill 115, the balanced clustering scheme terminates. The final static sensor as the grid head in each grid. Mobile sensorsresult is shown in Fig. 4c. report their locations and remaining energy to their grid The time complexity of the balanced clustering scheme is heads. On detecting events, static sensors notify their gridanalyzed as follows: Clustering event locations (by K- heads of the events. A grid with events is called an event grid.means) takes OðmnÞ time. Calculating the cost of each We assume that all sensors are roughly time-synchronizedcluster by constructing its minimum spanning tree can be (how to do so is beyond the scope of this work). The time isdone by the Prime’s algorithm [41]. The worst case occurs divided into multiple rounds and each round is furtherwhen one cluster contains ðm À n þ 1Þ locations and each of divided into three phases (refer to Fig. 5). In the disseminationother ðn À 1Þ clusters only contains one location. In this phase, each grid head collects the locations of events andcase, constructing the minimum spanning tree in the largest mobile sensors in that grid. Then, the existence of mobilecluster takes Oððm À n þ 1Þ2 Þ time. Then, we build a sensors is advertised (respectively, queried) by grids withmaximum heap ÉC to maintain these n clusters, which max mobile sensors (respectively, event grids). In the competitiontakes OðnÞ time. An iteration of the balanced clustering phase, event grids bid for mobile sensors by sending invitationscheme involves the following four operations: messages. Then, mobile sensors determine their target grids
- 15. WANG ET AL.: ENERGY-BALANCED DISPATCH OF MOBILE SENSORS IN A HYBRID WIRELESS SENSOR NETWORK 1843Fig. 5. Phases of a round in the distributed dispatch algorithm.and compute their dispatch schedules. Finally, in the dispatchphase, mobile sensors travel according to their dispatchschedules and visit all event locations in these grids. Lengthsof these phases depend on situations. Note that strict timesynchronization of these phases is not necessary. Fig. 6. An example of the grid-quorum scheme. To balance the energy consumption among mobilesensors, event grids adopt the bound concept in Section 4.1 (RPY) message containing the mobile sensors in the ADV isto bid for mobile sensors. Specifically, each event grid sent back to the REQ-initiating grid. Also, an RPY containingmaintains a preference list that ranks all mobile sensors by the event locations in the REQ is sent back to the ADV-their energy costs. For competition purpose, it also maintains initiating grid. In this way, both ADV-initiating and REQ-a bound. Then, event grids send invitation (INV) messages initiating grids can obtain each other’s information. Notecontaining their bounds to bid for mobile sensors. On the that when some grids are empty, the intersection property ofother hand, each mobile sensor si maintains a dispatch the grid-quorum scheme may not exist. In this case, someschedule DSi to record its target grids. Each si limits the size recovery mechanism may be applied [11].of its DSi to dme, where m is the number of event grids and n We then analyze the message complexity of the above nis the number of mobile sensors (how to obtain m and n will scheme. Assume that the sensing field is partitioned into ^ ^ ^ M Â N grids. For each event grid, it takes ðM À 1Þ REQs tobe discussed later). On receiving an INV, si does notimmediately reply its decision but will continuously collect make other grids in the same row to obtain its information.more INVs for a small duration Át (it can be a few of average Similarly, for each grid containing mobile sensors, it takes ^ ðN À 1Þ ADVs to make other grids in the same column topacket round-trip time). Then, si determines the winners(based on event grids’ bounds), inserts them into its DSi , and obtain its information. Suppose that there are m event gridsreplies a confirmation (CFM) message to each of them. For and n mobile sensors. The worst case occurs when n gridseach nonwinning grid, si replies a reject (RJT) message contain mobile sensors. Since a grid that hears both ADVcontaining the remaining number of free entries in its DSi . and REQ has to send RYPs to the ADV-initiating and REQ-An event grid removes those mobile sensors with no initiating grids, the message complexity of this scheme is ^ ^ ^ Oð2ðmðM À 1Þ þ nðN À 1ÞÞÞ ¼ OðmM þ nNÞ. ^remaining capacity from its preference list and tries to inviteother mobile sensors until a CFM is received or all mobile To deal with issue 2, event grids bid for mobile sensorssensors run out of their capacities in this round. Note that a as follows:mobile sensor may scan its preference list more than once 1. Each event grid gj calculates the energy cost for each(explained later). mobile sensor si to visit its grid. The cost is There are four remaining issues in the above discussion: formulated by wðsi ; gj Þ ¼ emove Â ðdðsi ; j Þ þ ðLj ÞÞ, 1. How event grids collect locations of mobile sensors where j is the center of all events in gj and Lj is in a message-efficient way? the set of event locations in gj . Then, gj sorts all 2. How event grids bid for mobile sensors? available mobile sensors into a preference list P j 3. How mobile sensors accept bids and determine their according to their costs in an ascending order. Note dispatch schedules? that if the remaining energy of a mobile sensor cannot 4. How mobile sensors visit event locations in an afford to visit gj , it is removed from P j . If P j is empty, energy-efficient way? gj does not participate in this round but may participate in future rounds.Fig. 5 relates these issues to our three phases. To address issue 1, we adopt the grid-quorum scheme in 2. Each event grid gj maintains an iteration counter j[11]. Each grid with mobile sensors periodically sends an and a bound Bj . Initially, j ¼ 1 and Bj ¼ wðsi ; gj Þ,advertisement (ADV) message containing the locations and where si is the
- 16. th mobile sensor in P j . Also, eachremaining energy of the mobile sensors inside its grid to mobile sensor in P j is marked as unsolicited. It isother grids in the same column. On the other hand, each changed to solicited if gj has ever sent an INV to theevent grid sends a request (REQ) message to other grids in mobile sensor in the current iteration. A mobile sensorthe same row. This behavior ensures that each ADV and si in P j is called a candidate for gj if it is unsolicited andeach REQ will intersect. Fig. 6 gives an example. Grid ð0; 1Þ wðsi ; gj Þ Bj .with two mobile sensors sends an ADV along its column, 3. Each event grid gj selects the first candidate mobilewhile event grid ð2; 3Þ sends an REQ along its row to search sensor, say, si from P j , and sends si an INVðgj ;for mobile sensors. When an REQ meets an ADV, a reply j ; wðsi ; gj Þ; Bj ; cj ; nÞ, where cj is the remaining
- 17. 1844 IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, VOL. 21, NO. 12, DECEMBER 2010 number of candidates in P j under bound Bj and n is the worst case as follows: Suppose that there are m event the number of mobile sensors that gj learns in the grids fg1 ; g2 ; . . . ; gm g and n mobile sensors fs1 ; s2 ; . . . ; sn g, dissemination phase. Then, gj waits for si ’s response. where m n. Then, DSi of each si has a capacity of m (for n If gj receives a CFM from si , this algorithm simplicity, we assume that m is divisible by n). In the first terminates. Otherwise, gj should receive an RJT iteration, m event grids compete for one mobile sensor, say, containing si ’s remaining capacity. If gj finds that s1 , and then only one event grid, say, g1 , wins. In this case, m si ’s remaining capacity is zero, it removes si from its event grids send m INVs and s1 replies 1 CFM and ðm À 1Þ P j ; otherwise, gj marks si as solicited and one of RJTs. Thus, the total number of messages is 2m. In the three cases will happen: second iteration, ðm À 1Þ event grids fg2 ; g3 ; . . . ; gm g com- pete for one mobile sensor, say, s2 , and then only one event a. If gj still has candidates under bound Bj , it grid, say, g2 , wins. Thus, the total number of messages is repeats step 3 again. 2ðm À 1Þ (because ðm À 1Þ event grids send ðm À 1Þ INVs b. If gj has no candidate under bound Bj and there and s2 replies 1 CFM and ðm À 2Þ RJTs). Similarly, in the ith still exist unsolicited mobile sensors in P j , gj iteration, ðm À i þ 1Þ event grids compete for one mobile increases its bound to Bj ¼ wðsk ; gj Þ such that sk sensor, say, si , by sending ðm À i þ 1Þ INVs, and then si is the
- 18. th unsolicited mobile sensor in the replies 1 CFM and ðm À iÞ RJTs. So, the total number of current P j and repeats step 3 again. messages is 2ðm À i þ 1Þ. Since there are at most m c. Otherwise, gj has reached the end of its P j . If P j iterations, the overall number of messagesP the competi- in is empty, the algorithm terminates; otherwise, gj tion phase is 2m þ 2ðm À 1Þ þ Á Á Á þ 2 ¼ 2 Á m i ¼ mðm þ i¼1 clears all entries in P j as unsolicited, increases 1Þ. In the dispatch phase, mobile sensors move to event its iteration counter j by 1, resets its bound as locations to conduct event analysis. However, there is no Bj ¼ wðsi ; gj Þ such that si is the
- 19. th unsolicited need to exchange messages for determining the dispatch mobile sensor in P j , and repeats step 3 again. schedules of mobile sensors. Therefore, the total message The above case c occurs when gj fails to invite any complexity of our distributed algorithm is OðmM þ nNÞ þ ^ ^ mobile sensor after examining all elements in its P j . ^ ^ Oðmðm þ 1Þ Á hÞ ¼ OðmM þ nN þ m2 hÞ, where the sensing In this case, gj enters the next iteration and ^ ^ field is partitioned into M Â N grids and h is the network reexamines its P j to check those mobile sensors still diameter (i.e., the average hop count between sources and with remaining capacities. As will be seen later, the destinations). counter j may help gj win a mobile sensor. Remark 1. The length of the dissemination phase depends To deal with issue 3, each mobile sensor si maintains a on the applications. Specifically, when events occurdispatch schedule DSi to record event girds that it has to frequently, a shorter dissemination phase should bevisit. The capacity of DSi is set to dme (m can be learned n used. Otherwise, a longer dissemination phase canfrom the dissemination phase and n can be obtained from be adopted. One possible way to determine the lengthINVs). It may happen that the received values of n from of the dissemination phase is to measure the frequency ofINVs are inconsistent (the differences should be minor). If events from historical statistics. For the competitionso, the largest value is taken. INVs are processed in a batch phase, the worst case occurs when one event grid has tomode after every Át interval. Multiple INVs may be query all mobile sensors, each with dme times, where m is naccepted. For all INVs with the same iteration counter, the number of event grids and n is the number of mobileonly one event grid is accepted and the others are rejected. sensors. Let RT T be the round-trip time for an event gridThe following rules are enforced: If si has no remaining to query and get a response from a mobile sensor. Thecapability, an RJT indicating that it has no capability is sent. length of the competition phase can be set asOtherwise, all requesting event grids with the same dme Á n Á RT T ð% m Á RT T Þ. Finally, for the dispatch phase, niteration counter will compete for one position. Specifically, its length depends on the longest traveling path for afor two INVðgj ; j ; wðsi ; gj Þ; Bj ; cj ; nÞ and INVðgk ; k ¼ j ; mobile sensor to visit all event grids in its dispatchwðsi ; gk Þ; Bk ; ck ; nÞ, gj wins if one of the following conditions schedule. We can initially allocate a longer dispatchis true: 1) Bj Bk , 2) Bj ¼ Bk and wðsi ; gj Þ wðsi ; gk Þ, and phase and then calculate the average time for mobile3) Bj ¼ Bk , cj ¼ 1, and ck 1. (These conditions are the sensors to finish their dispatch schedules in a fewsame as those in the centralized algorithm.) Then, si sends rounds. This average time can help adjust the length ofout CFMs and RJTs, updates its DSi , and deducts its the dispatch phase in the following rounds.remaining capability accordingly. Remark 2. There are three different designs between the To deal with issue 4, we propose a two-level TSP scheme. distributed algorithm and the centralized one. First, sinceGiven the dispatch schedule DSi , si first applies any TSP both event grids and mobile sensors have no globalsolution on DSi by regarding each event grid in DSi as one knowledge, messages such as ADVs and REQs needed tonode (for example, this node can be the center of all event be exchanged in the dissemination phase between eventlocations in the corresponding event grid). This TSP grids and mobile sensors. We adopt grid-quorum tosolution forms the first-level solution. For the second level, facilitate such message exchanges. Second, unlike thefor each event grid in DSi , si can apply any TSP solution centralized algorithm, an event grid does not know theagain to visit all event locations inside that grid. Many TSP existence of other event grids, so it has to send INVs toheuristics already exist, so we omit the details. compete for mobile sensors. With INVs, we can realize We then analyze the message complexity of our dis- the competition in a distributed manner. Third, since it istributed algorithm. For the competition phase, we consider difficult to cluster event grids in a distributed manner,
- 20. WANG ET AL.: ENERGY-BALANCED DISPATCH OF MOBILE SENSORS IN A HYBRID WIRELESS SENSOR NETWORK 1845 we adopt the iteration counter i to handle the case TABLE 2 when event grids are more than mobile sensors. In this Comparison on the System Lifetime under way, multiple event grids can choose the same mobile Different Dispatching Algorithms sensor to visit them.6 EXPERIMENTAL RESULTSTo evaluate the performances of our proposed algorithms,we have developed a simulator in Java. In our simulator,the sensing field is set as a 450 m Â 300 m rectangle onwhich there are 400 static sensors randomly3 deployed. Thecommunication distance of each sensor is set to 80 m, andstatic sensors can form a connected network. In each result in a longer system lifetime because they adjust thesimulation, we randomly select a number of static sensors clustering result of K-means to reduce the total cluster cost.as event locations (i.e., L) and randomly deploy a number of When jLj ¼ 140, the balanced clustering scheme has amobile sensors (i.e., S). The energy consumption of mobile longer system lifetime than the MaxMin clustering schemesensors is the one caused by their movement. Since we because the balanced clustering scheme not only reducesfocus on evaluating the energy efficiency of dispatch the total cluster cost but also tries to balance the costsalgorithms, we ignore the effect of communication impair- among clusters. When jLj 80, the distributed algorithmments. In other words, we assume that communications are has a longer system lifetime than the centralized algorithm.reliable and each mobile sensor can obtain the exact value of The reason is that the distributed algorithm clusters eventn (i.e., the total number of mobile sensors) from INVs. We locations into grids, and thus, reduces the energy consump-set
- 21. ¼ 4 in our proposed algorithms. (We will discuss tion of mobile sensors to visit them. However, whenthe effect of
- 22. on the system performance in Section 6.6.) jLj ¼ 140, since the number of event girds is large, mobileThe grid size is 15 m Â 15 m in the distributed algorithm, so sensors may be asked to visit multiple event grids, and thus,the sensing field is partitioned into 30 Â 20 grids. For each move longer distances. We will further discuss the energysimulation, at least 100 experiments (with different random consumption of mobile sensors under different dispatchingseeds) are repeated, and we take their average. algorithms in Section 6.3.6.1 System Lifetime 6.2 Survived Mobile SensorsWe first investigate the system lifetime under different We then examine the number of survived mobile sensors indispatch algorithms. The number of mobile sensors is 40. each round under different dispatching algorithms. WeAccording to [42], the moving energy consumption of a consider two scenarios. In the scenario of jSj jLj, wemobile sensor is 0.21 J (joule) per inch (i.e., 8.27 J per meter). randomly select [10, 15] static sensors as event locations inWe assume that each mobile sensor is equipped with two each round. On the other hand, in the scenario of jSj jLj, webatteries, each of energy capacity 1,350 mAh (milliampere- randomly select [120, 160] static sensors as event locations inhour), for its moving energy, so we have einit ¼ 29;160 J for i each round. The number of mobile sensors is 50.i ¼ 1::n. During each round, we randomly select 20, 80, and Fig. 7a shows the result in the scenario of jSj jLj. For the140 static sensors as event locations. Mobile sensors then greedy algorithm, the first mobile sensor exhausts its energymove to event locations based on the dispatch algorithms very early in the 53rd round. After 248 rounds, all mobileand stay at their last visiting locations to wait for their next sensors drain out their energy. For the centralized algorithm,dispatch schedules. We compare the centralized and since we have jSj jLj in most rounds, the effect of differentdistributed algorithms against the greedy algorithm dis- clustering schemes is not significant. The first mobile sensorcussed in Section 1. When mobile sensors are fewer than exhausts its energy in the 440th round, and the systemevent locations, the three clustering schemes in Section 4.2 lifetime is 475 rounds. For the distributed algorithm, the firstare adopted to group event locations in the centralized mobile sensor exhausts its energy in the 367th round, andalgorithm. For the greedy algorithm, we dispatch mobile the system lifetime is 546 rounds. With a grid structure, thesensors to visit a subset L0 L of event locations, where distributed algorithm has a longer system lifetime than thejL0 j jSj, and then make L ¼ L À L0 . We iteratively repeat centralized algorithm when jSj jLj.the above procedure, until L is empty. Fig. 7b shows the result in the scenario of jSj jLj. For Table 2 shows the system lifetime under different the greedy algorithm, the first mobile sensor exhausts itsdispatch algorithms. The greedy algorithm has the shortest energy very early in the 9th round and the system lifetime issystem lifetime due to two reasons. First, the greedy 25 rounds. For the centralized algorithm, different cluster-algorithm does not balance the energy consumption among ing schemes affect the number of survived mobile sensors.mobile sensors, which may lead some mobile sensors early Specifically, the first mobile sensor exhausts its energy into exhaust their energy. Second, the greedy algorithm does the 21st, 16th, and 23rd rounds under the K-means,not cluster event locations when jLj jSj, leading mobile MaxMin, and balanced clustering schemes, respectively.sensors to move a longer distance. For the centralized Note that since MaxMin may generate unbalanced clusters,algorithm, different clustering schemes affect the system it spends the fewest rounds to let the first mobile sensorlifetime when jLj jSj. In particular, both the MaxMin and exhaust the energy. The system lifetimes are 32, 31, and 33balanced clustering schemes help the centralized algorithm rounds under the K-means, MaxMin, and balanced cluster- ing schemes, respectively. These results show the benefit of 3. In our simulations, the term “random” means uniformly random. both balancing energy consumption of mobile sensors and
- 23. 1846 IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, VOL. 21, NO. 12, DECEMBER 2010Fig. 7. Comparison on the number of survived mobile sensors under Fig. 8. Comparison on the energy consumption of mobile sensors underdifferent dispatch algorithms. (a) Scenario of jSj jLj. (b) Scenario of different dispatch algorithms. (a) Average of energy consumption.jSj jLj. (b) Standard deviation of energy consumption.clustering event locations to extend the system lifetime. For energy consumption when jLj ! 30. Both the MaxMin andthe distributed algorithm, the first mobile sensor exhausts balanced clustering schemes help the centralized algorithmits energy in the 21st round and the system lifetime is to reduce the average of energy consumption because they29 rounds. Without global information, the distributed try to adjust the clustering result of K-means by reducing thealgorithm has a shorter system lifetime than the centralized total cluster cost. For the distributed algorithm, it has aalgorithm when jSj jLj. smaller average than the centralized algorithm when jLj 50. Interestingly, the distributed algorithm even incurs6.3 Energy Consumption a smaller average than the greedy algorithm when jLj 20.We then evaluate the energy consumption of mobile sensors This is due to two reasons. First, in the distributed algorithm,under different dispatch algorithms. The number of mobile some mobile sensors might be asked to visit their currentsensors is 20, and the number of events is ranged from 10 to grids, thereby reducing their energy consumption. Second,80. In the simulation, mobile sensors have infinite energy. each event grid automatically clusters those event locationsWe observe the average and standard deviation of energy inside itself. That is, it naturally clusters event locations whenconsumption per mobile sensor per round. jSj ! jLj. However, when jLj increases, the number of event Fig. 8a shows the average energy consumption of mobile grids may become larger, and thus, a mobile sensor maysensors. The averages of energy consumption under all need to visit multiple event grids. In this case, since theschemes increase when the number of event locations distributed algorithm does not have global information,increases because each mobile sensor has to visit more event mobile sensors may need to move longer distances aslocations. For the greedy algorithm, when jLj 70, it has a compared to the centralized algorithm.smaller average than the centralized algorithm because the Fig. 8b shows the standard deviation of energy consump-greedy algorithm always tries to minimize the total energy tion of mobile sensors. The greedy algorithm has a largerconsumption of mobile sensors. However, when jLj ¼ 80, the standard deviation than the centralized algorithm (under thegreedy algorithm has a larger average than the centralized K-means and balanced clustering schemes). The reason is thatalgorithm. This shows the necessity of clustering event the greedy algorithm does not balance the energy consump-locations, especially when the number of event locations is tion among mobile sensors, which causes some mobilemuch larger than that of the mobile sensors (around jLj ! sensors to exhaust their energy earlier. For the centralized4 Á jSj as shown in Fig. 8a). For the centralized algorithm, algorithm, different clustering schemes result in differentdifferent clustering schemes have impacts on the average of standard deviations. The balanced clustering scheme has the
- 24. WANG ET AL.: ENERGY-BALANCED DISPATCH OF MOBILE SENSORS IN A HYBRID WIRELESS SENSOR NETWORK 1847 Fig. 10. Comparison on the ratio of one-node clusters under different schemes. average cluster cost because it always splits the cluster with the longest intracluster edge and then merges two clusters with the shortest intercluster edge. In this way, the total cluster cost is greatly reduced. On the other hand, the balanced clustering scheme also adjusts the clustering result of K-means by splitting the cluster with the maximum cost, thus incurring a smaller average cluster cost. Fig. 9b shows the standard deviation of cluster costs under different schemes. Since the MaxMin clustering scheme has a goal of reducing the total cluster cost, it may generate unbalanced clusters, thus increasing the standard deviation. This effect is more prominent when the number of event locations increases. In Fig. 9b, when jLj ¼ 30, the MaxMin clustering scheme has a smaller standard deviation than K-means. The reason is that theFig. 9. Comparison on the cluster costs under different schemes. average number of event locations in each cluster is only(a) Average of cluster costs. (b) Standard deviation of cluster costs. 1.5. By adjusting the clustering result of K-means, the MaxMin clustering scheme could have more balancedsmallest standard deviation because it tries to balance the clusters. On the other hand, the balanced clustering schemecosts among clusters. On the other hand, the standard has the minimum standard deviation because it tries todeviation of the MaxMin clustering scheme significantly balance the costs between two split clusters.increases when jLj increases. The reason is that the MaxMin In Fig. 9b, the MaxMin clustering scheme has the largestclustering scheme tries to reduce the overall cluster cost, standard deviation. This is because MaxMin always groupsresulting in unbalanced clusters. (We will further discuss this sparse event locations into zero-cost one-node clusters. Fig. 10issue in Section 6.4.) For the distributed algorithm, since event shows the ratio of one-node clusters under different schemes.grids are not clustered and they do not have global knowl- When jLj ¼ 30, the ratios of all schemes are more thanedge, some mobile sensors may be asked to visit more event 60 percent because the average number of event locations ingrids, thereby increasing the standard deviation. each cluster is smaller than 2. When jLj increases, the ratio From Fig. 8, we conclude that the distributed algorithm tends to decrease. Such an effect is more significant under thecan reduce the average energy consumption of mobile K-means and balanced clustering schemes. The ratio ofsensors when there are fewer event locations, but increase MaxMin is always larger than 37.8 percent, which makes itsthe standard deviation of energy consumption of mobile standard deviation increase (as shown in Fig. 9b). On thesensors. With the K-means and MaxMin clustering schemes, other hand, since the balanced clustering scheme has thethe centralized algorithm can reduce both the average and smallest ratio, it can result in more balanced clusters.standard deviation of energy consumption of mobile sensors. 6.5 Communication Cost6.4 Impact of Clustering We then measure the number of messages incurred by theWe then evaluate the clustering results derived by different centralized and distributed algorithms. We set 10 jLjschemes. We set the number of mobile sensors as 20 and 80 and let jSj ¼ jLj. The centralized algorithm may incur therandomly select 30, 40, 50, 60, 70, and 80 static sensors as following message costs:event locations. We compare the K-means, MaxMin, andbalanced clustering schemes. 1. The sink (or the server) broadcasts commands to all Fig. 9a shows the average cluster costs under different static and mobile sensors to ask them to report theirschemes. The MaxMin clustering scheme has the minimum current states.
- 25. 1848 IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, VOL. 21, NO. 12, DECEMBER 2010Fig. 11. Comparison on the number of messages incurred by thecentralized and distributed algorithms. 2. Static sensors report any detected event. 3. Mobile sensors report their locations and remaining energy to the sink. 4. The sink transmits its dispatch schedules to all mobile sensors. Fig. 11 shows the numbers of messages sent by bothalgorithms. The centralized algorithm incurs more messageexchanges because the sink needs to notify all sensors toreport their information through network flooding.4 On theother hand, the grid structure makes the distributedalgorithm more message efficient for two reasons. First,no costly flooding is incurred. Second, only grid heads needto conduct intergrid message exchanges. Fig. 12. Effect of
- 26. value on the average and standard deviation of6.6 Effect of
- 27. Value energy consumption of mobile sensors. (a) Twenty event locations.We finally investigate the effect of the system parameter
- 28. (b) Eighty event locations.on the performance of the centralized algorithm. Toeliminate the effect of clustering, we set the numbers of between the numbers of mobile sensors and event locations.both event locations and mobile sensors as 20 and 80. The Our dispatch algorithms can extend the system lifetime byvalue of
- 29. is increased from 1 to 10. We observe the average reducing and balancing the energy consumption of mobileand standard deviation of energy consumption of mobile sensors. In the centralized algorithm, when there are moresensors, as shown in Fig. 12. The average energy consump- mobile sensors, we translate the sensor dispatch problem intotion decreases while the standard deviation of energy a maximum matching problem in a weighted completeconsumption increases when
- 30. grows. The reason is that bipartite graph. On the other hand, when there are more eventeach event location can have more candidate mobile sensors locations, they are grouped into clusters and then each mobileand its bound value will increase faster. In this case, some sensor is assigned to one cluster of event locations. In theevent locations could match mobile sensors closer to them, distributed algorithm, a grid-quorum approach is adopted tothereby reducing the total energy consumption of mobile reduce the message complexity for event grids to obtain thesensors. On the other hand, some other event locations may information of mobile sensors. Then, by applying the boundbe asked to match mobile sensors relatively farther from concept in the centralized algorithm, event grids can bid forthem, and thus, make the energy consumption of mobile mobile sensors. Mobile sensors then apply the proposed two-sensors unbalanced. In Fig. 12, we find the best value of
- 31. to level TSP scheme to visit event locations. Simulation resultsbe around 4 or 5 since both the average and standard have shown that our proposed dispatch algorithms candeviation of energy consumption can be kept quite small. extend the system lifetime compared to the greedy algorithm. Next, we give several future research topics. In this work, we consider dispatching mobile sensors in a sensing7 CONCLUSIONS AND FUTURE WORK field without obstacles. Several studies [43], [44], [45] haveIn this paper, we have proposed energy-balanced centralized discussed how to find the shortest path for a mobile sensorand distributed algorithms to efficiently dispatch mobile to reach its destination without colliding with any obstacle.sensors in a hybrid WSN. We formulate a general sensor These results can help extend our dispatch solutions. Indispatch problem that allows an arbitrary relationship addition, we make several assumptions on the movement model of mobile sensors such as uniform moving speed and 4. Here, we adopt the naive flooding scheme. Although a more efficient uniform energy consumption. How to relax these assump-broadcast scheme can be used, it is out of the scope of this work. tions deserves further investigation. Finally, for some

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