Energy-Aware Scheduling with Quality of Surveillance Guarantee in Wireless Sensor Networks

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1 Energy-Aware Scheduing with Quaity of Surveiance Guarantee in Wireess Sensor Networks Jaehoon Jeong, Sarah Sharafkandi, and David H.C. Du Dept. of Computer Science and Engineering, University of Minnesota Minneapois, Minnesota, USA ABSTRACT We propose and evauate an energy-efficient scheduing agorithm for detection of mobie targets in wireess sensor networks. We consider a setting where the sensors are depoyed for both road surveiance and mobie target tracking. A typica exampe woud be where some sensors are depoyed aong the entrance roads of a city to detect the vehices entering the city and other sensors can wake up and track the vehices after detection. We show an important reationship between the overa energy consumed by the sensors and the average detection time of a target, both of which are very critica aspects in our probem. To this end, we define the quaity of surveiance (QoSv) as the reciproca vaue of the average detection time for vehices. We propose an optima scheduing agorithm that guarantees the detection of every target with specified QoSv and at the same time minimizes the overa energy consumed by the sensor nodes. By minimizing the energy consumed, we maximize the ifetime of the sensor network. Aso, aong with the quaity of surveiance guarantee, we ensure that no target goes undetected. We theoreticay derive the upper bound on the ifetime of the sensor network for a given QoSv guarantee and prove that our method can aways achieve this upper bound. Our simuation resuts vaidate the caims made on the agorithm optimaity and QoSv guarantee. Categories and Subject Descriptors: C.2.4 [Computer Communication Networks]: Distributed Systems Genera Terms: Agorithms Keywords: Sensor Networks, Quaity of Surveiance, Detection, Scheduing, Energy, Mobie Target, Vehice. 1. INTRODUCTION Wireess sensor networks have generay a imited amount of energy. Such wireess sensor nodes coect, store, and This work was supported by the Department of Computer Science and Engineering and Digita Technoogy Center at the University of Minnesota. Permission to make digita or hard copies of a or part of this work for persona or cassroom use is granted without fee provided that copies are not made or distributed for profit or commercia advantage and that copies bear this notice and the fu citation on the first page. To copy otherwise, to repubish, to post on servers or to redistribute to ists, requires prior specific permission and/or a fee. DIWANS 6, September 26, 26, Los Angees, Caifornia, USA. Copyright 26 ACM /6/9...$5.. Outer Boundary CITY Inner Boundary Figure 1: Surveiance for City s Boundary Roads process the information about environments as we as communicate with each other. So one important issue is how to manage the energy efficienty to perform the above tasks. One major probem in energy management is how to schedue sensors in a way that maximizes the sensor network ifetime whie the sensor networks sti satisfy the required degree of quaity of service. As an exampe in the coverage issue, if some nodes share the common sensing region and task, then we can turn off some of them to conserve energy and thus extend the ifetime of the network whie sti keeping the same coverage degree. Aso in some appications we can aow the sensor network area to be partiay covered with regard to time or space. Thus, a imited number of sensors that work intermittenty can satisfy the requirements for the appications. This can resut in a significant conservation in energy consumption which consequenty extends network ifetime. We define the quaity of surveiance (QoSv) as the reciproca vaue of the average detection time for vehices, which is used as a metric for quaity of service in surveiance appications. In this paper, we propose an energy-aware sensor scheduing to satisfy such a QoSv as we as to maximize the sensor network ifetime. Our energy-aware scheduing agorithm can detect mobie targets entering critica routes, guaranteeing the required QoSv. For exampe, in a city s boundary roads ike in Figure 1, vehices entering the roads between the specified outer boundary and inner boundary are detected to satisfy the specified average detection time by sensors depoyed on the boundary roads. This means that our scheduing agorithm can work we for both surveiance and traffic monitoring in the road system according to

2 the required QoSv. We wi show that this QoSv metric can be controed by both the number of sensors depoyed on road segments (i.e., the road segment s ength incuding sensors) and the working time for sensing on each sensor every scheduing period. Especiay, the ength of the road on which the sensors are spread is a dominant factor to determine the QoSv. Aso, the sensor network ifetime can be maximized by using as much sensor seeping time as possibe and as itte sensor working time as possibe. The seeping time is determined by the road segment s ength and the maximum vehice speed v; that is, the seeping time is equa to /v. But the seeping time shoud be used ony when it can get benefit against the turn-on overhead needed for sensors to work. The east sensor working time per scheduing period is preferabe to maximize the network ifetime as ong as the sensors on a road segment can start working appropriatey, considering sensor s warming-up time. Aso, our sensor scheduing is designed to support mobie target tracking after target detection. When a vehice is detected by our scheduing, it can be tracked since the sensors are deterministicay paced on the whoe roads between the outer boundary and inner boundary. In the surveiance phase, ony the sensors seected to satisfy the specified QoSv work and other sensors seep to save energy. In the tracking phase, the other sensors can wake up and track the vehices. The tracking is out of scope in this paper. In this paper, our contributions are: a definition of Quaity of Surveiance (QoSv), an energy-aware sensor scheduing feasibe for mobie target detection and tracking, a mathematica anaysis of QoSv-guaranteed scheduing, a proof for the reationship between the exponentia inter-arriva and uniform arriva for vehices, and a generic agorithm for sensor scheduing for compex roads. The paper is organized as foows. In Sections 2 and 3, we compare our work with the reated work and formuate our probem of energy-aware scheduing with QoSv guarantee in wireess sensor networks. Sections 4 and 5 describe the sensor scheduing for QoSv guarantee and network ifetime maximization and then prove the optimaity of our sensor scheduing. In Section 6, we anayze the average detection time for both constant vehice speed and variabe vehice speed, making a function of average detection time which is used to determine the appropriate sensor working time and the number of sensors on a road segment to satisfy the required QoSv. Section 7 describes a generic agorithm for the sensor scheduing for detecting vehices in compex roads. In Section 8 we show the performance evauation through numerica anaysis and vaidate our numerica anaysis through simuation. Finay, in Section 9, we concude this paper and suggest our future work. 2. RELATED WORK Most research on coverage for detection has so far focussed on fu coverage [2 8] rather than partia coverage [9]. In rea appications, such as the mobie target detection and measurement of temperature on the ground or air, the partia coverage which is tempora or spatia is enough to detect or measure something. In [9], a differentiated surveiance service is suggested for various target areas with different degrees in sensor networks based on an adaptabe energyefficient sensing coverage protoco. Our probem for mobie target detection can benefit from this partia coverage in terms of energy saving. Some area on a road, such as boundary roads, is under surveiance with temporay or spatiay partia coverage. A the sensors seep on the road segment during seeping period and each sensor works for a whie aternatey during working period. This seeping and scanning scheme aows for the maximization of the sensor network ifetime. Most of mobie target detection agorithms [1,11], whose main objective is to save energy, support somewhat quaity of surveiance. They assume that a mobie target starts at any point of the given area. On the other hand, we consider ony the intrusion of mobie targets coming from the outside of the city towards the city via boundary roads ike in Figure 1. In [11], the Quaity of Surveiance (QoSv) is defined as the reciproca vaue of the expected trave distance before mobie targets are first detected by any sensor. This QoSv metric is irreevant to the target s moving speed. However, our QoSv metric is determined by the target s moving speed since we define QoSv as the reciproca vaue of the expected average detection time where QoSv is a function of the target speed, road segment ength, sensor working time and the number of sensors. In [12], the theoretica foundations for aying barriers with steathy and wireess sensors are proposed in order to detect the intrusion of mobie targets approaching the barriers from the outside. The barrier coverage is the type of coverage to detect intruders as they cross a border or as they penetrate a protected area. The sensors on a barrier work a the time for the fu coverage for the barrier; that is, this work is focussed on the fu coverage in border area in terms of time and ocation coverage for the target fied, but our detection approach uses a spatiay and temporay partia coverage for the bounded road area between the outer boundary and inner boundary. Since a maximum seeping time for a the sensors is used considering the mobie target speed and road segment ength, our scheme is more appropriate for critica route surveiance in terms of energy conservation. 3. PROBLEM FORMULATION We propose a sensor scheduing for the quaity of surveiance on a city s boundary roads. Our study in this paper focuses on the sensor scheduing for the surveiance which is designed to consider the target tracking after the surveiance. Given the required quaity of surveiance, the sensors that wi participate in the surveiance are determined according to our scheduing agorithm in order to maximize the sensor network ifetime. Other sensors seep to save energy unti the target tracking has to be performed. The specific target tracking agorithm is out of scope in this paper. 3.1 Assumption We have severa assumptions as foows: Every sensor knows its ocation and its time has been synchronized with its neighbor sensors. The sensing range is a uniform-disk whose radius is r.

3 Vehice S1 Road Segment S2 S Sn Sensing Coverage Figure 2: Sensor Network Mode for Road Segment Every vehice within the sensing radius of some sensors can be detected with probabiity one [1]. A sensor s sensing radius is onger than a haf of the road s width; that is, one sensor can cover the road s width. So we do not consider the packing of sensors in order to cover the road s width fuy in the case where a sensor s sensing radius is shorter than a haf of the road s width. Every sensor has the same eve of energy that is consumed at the same rate for the sensor s turn-on and sensing operations. The cost of turn-off operation is ignorabe in terms of energy. The vehice s maximum speed is bounded as foows: speed v max. 3.2 Terminoogy We define two terms: (a) Quaity of Surveiance (QoSv) and (b) Reiabiity (or Reiabe). Definition 1. QoSv(X). Let X be the road segment, covered by a set of sensor nodes. Let ADT be the average detection time which is the average time needed for the network to detect mobie targets. We define the quaity of surveiance of network on X, denoted as QoSv(X), as the reciproca vaue of ADT, i.e., QoSv(X) 1 ADT. (1) QoSv is used as a metric to measure how quicky the sensor network detects the intrusion of mobie targets into a road segment. As we can see from the above formua, the shorter ADT is, the better QoSv(X) is. Definition 2. Reiabiity. We ca a road segment reiabe if the sensors which are spread over the road segment can detect every vehice which enters the road segment with probabiity one. 3.3 Sensor Network Mode Assume that there is a road segment between the outer boundary and inner boundary of the city in Figure 1. Every vehice entering the city s outer boundary shoud be detected before reaching the inner boundary. The sensors are spread on a road segment ike in Figure 2. Vehices arriving at each road segment entrance from the outside of the sensor network are detected by at east one sensor. Now suppose that one road segment whose ength is consists of n sensors spread to fuy cover the road segment. n sensors are contiguousy paced to detect and track vehices on the road segment, whose sensing coverage is r. The sensing coverage is assumed arge enough to cover the road s width. With the above assumption and sensor network mode, our objective is to maximize the sensor network ifetime to satisfy the foowing conditions: Provide the reiabe detection of every vehice arriving at the road in the sensor network. Guarantee the desired average detection time, which means the quaity of surveiance. Faciitate the mobie target tracking after the target detection with a imited number of sensors. We propose a sensor scheduing for a road segment in order to achieve our objective in Section 4. We extend our sensor scheduing for compex roads in Section ENERGY-AWARE SENSOR SCHEDULING We have interest in vehices entering at a road segment towards a city; that is, ony the incoming vehices are considered. So, the vehices are assumed to arrive at ony the eft end of the road segment ike in Figure 2. The vehices are assumed to move ony aong with the road; that is, they are assumed not to move out of the road and into the road again. In this section, we propose an energy-aware sensor scheduing with sensor s appropriate working time and seeping time. We assume that n sensors are depoyed according to the contiguous sensor pacement in order to support the target tracking ike in Figure 2 and the ifetime of each sensor is ife. We aso assume that there is no turn-on overhead for starting a sensor for sensing. We wi consider the turn-on overhead to reax this assumption for more reaity in Section Requirements for Scheduing Our scheduing agorithm for surveiance satisfies the foowing requirements: The specified QoSv is guaranteed. The reiabe detection of mobie targets is done. The sensor network ifetime is maximized. 4.2 Other Approaches One trivia soution is that each sensor works from the right-most sensor unti it runs out of energy and then the adjacent sensor on the eft starts sensing. In this way just one sensor works at any time. The ifetime of the network is n ife. The reverse direction of scheduing has the same network ifetime; that is, the eft-most sensor starts sensing first and the right-most sensor finishes sensing ast. Another soution is that each sensor works aternatey for some time interva either from the right to the eft or in the reverse direction. The approach has the same network ifetime as the previous one, that is, n ife. The bidirectiona scanning that performs the right-to-eft scanning and the eft-to-right aternatey aso has the same network ifetime since there is no seeping.

4 Energy Consumption [J] Working (W) Working (W) Working (W) sn... s2 s1 sn... s2 s1 Initiaization Seeping (I)..... sn... s2 s1 Time [sec] Seeping (I) Figure 3: Sensor Scheduing in Time Domain A sensors are seeping (a)vehice S1 S2 S3 S Sn-2 Sn-1 Sn Sensor Scheduing Sequnce (b) S1 S2 S3 S Sn-2 Sn-1 Sn (c) S1 S2 S3 S Sn-2 Sn-1 Sn (d) S1 S2 S3 S Sn-2 Sn-1 Sn (e) S1 S2 S3 S Sn-2 Sn-1 Sn (f) S1 S2 S3 S Sn-2 Sn-1 Sn Detected 5. OPTIMALITY OF SENSOR SCHEDULING In this section, we prove that our sensor scheduing is optima in terms of sensor network ifetime. 5.1 Sensor Network Lifetime In this section, we compute the sensor network ifetime of our outward unidirectiona scanning. Let W be the working period and et I be the seeping period. We can compute W and I, respectivey as foows: nx W = w i, (2) i=1 I = v. (3) where is the ength of the road; v is the maximum possibe speed for the vehice; w i is working time of sensor i; and n is tota number of sensors. For simpicity, we assume that a sensors have identica working time, that is, w i = w. The tota ifetime of the network (T tota ife ) is equa to: T tota ife = m [I + W]. (4) where m is the number of the scheduing periods unti sensors run out of energy. We can compute m as foows: m = T ife w where T ife is the ifetime of each sensor. Therefore, the tota ifetime of the network wi be expressed as: (5) Figure 4: Sensing Sequence for the Detection of Vehices 4.3 Our Approach Our approach is that a the sensors seep for some seeping time s and then each sensor from the right-most to the eft-most performs sensing for some working time w. Our approach is based on the observation that any vehice with maximum speed v max takes time /v max to pass through a road segment with ength. This amount of time can be used as seeping time s for a the sensors on the road segment to save energy; that is, a the sensors can seep for s = /v max without any detection missing. For exampe, et s consider a road segment ike in Figure 2 whose ony eft side the vehices approach. If the scanning for the road segment is performed from the right side to the eft side just after seeping time s, any vehice can be detected reiaby. On the other hand, if the reverse scanning from the eft-most to the right-most is used, it needs the scanning time n w to catch up with the maximum-speed vehice. So in this case, the seeping time is reduced to /v max n w. Thus, we adopt the right-to-eft scanning caed outward unidirectiona scanning rather than the eft-to-right scanning. Figure 3 shows the sensor scheduing for Figure 2. The sensor scheduing period consists of working period W and seeping period I after the initiaization of sensors. Figure 4 shows the sensing sequence for the detection of vehices entering the road segment. The sensing sequence is performed by the outward unidirectiona scanning after seeping period I = /v max. The vehice is detected by sensor S 3. T tota ife = T ife w [nw + v ] = nt ife + vw T ife. The above formua shows that T tota ife increases as each sensor s working time w decreases, ignoring the turn-on energy. Note that w cannot be infinitey sma because in reaity the sensors need some time for warming-up. We wi anayze the ower bound of w considering warming-up in Section Optimaity of Sensor Scheduing We prove the optimaity of our scheduing in terms of the sensor network ifetime. Let Schedue 1 be our outward unidirectiona scheduing with network ifetime T tota ife. Suppose that Schedue 2 is an optima scheduing in terms of network ifetime. Aso assume that the number of sensors in Schedue 2 is equa to that in Schedue 1. We know that /v is an upper bound on the seeping period for reiabe surveiance. Let X be the number of seeping periods in Schedue 2. We have the foowing inequaity: which resuts in (6) nt ife + vw T ife < nt ife + X v. (7) T ife w < X. (8) Actuay, X shoud be equa to the number of working periods because after each seeping period there shoud be a working period. So, Eq.8 is contradicted. Thus, there is no

5 scheduing with network ifetime onger than our scheduing Schedue 1. Note that the turn-on energy and warming-up time are ignored. In next section, we cacuate the network ifetime when these overheads are considered. 5.3 Turn-On and Warming-Up Overheads In reaity the sensors consume energy for turn-on operation. They aso need some time to warm up. Ignoring these parameters may resut in unreaistic concusion. In this section we cacuate the ifetime of the sensor network considering the turn-on energy E on and warming-up time T w. Our assumptions are exacty the same as the previous section. Each sensor s ifetime can be obtained according to the foowing equation: T ife = E P s + Eon w. (9) where E is the tota energy of each sensor; P s is the sensing power of each sensor for unit time; and E on is the energy needed for turning on each sensor. By repacing T ife in Eq.6 by T ife in Eq.9, we have: and T tota ife = T tota ife w E [nw + ]. (1) wp s + E on v = E(nEon Ps v ) (wp s + E on) 2. (11) Therefore, T tota ife is either an increasing function of w (ne on > P s ), or a decreasing function of w v (neon < Ps ). v In the first case, as the function is an increasing function of w, the maximum ifetime is achieved when the working time of the sensors is maximum. The maximum vaue for the working time of each sensor w is E Eon P s when the number of scheduing periods (m) is equa to one. It means that no seeping period shoud be used for scheduing; that is, the turn-on overhead is greater than the energy saved by seeping. Since the overhead for turning on each sensor is so much, it is not worth to switch the sensors from off to on more than one time. So, under this condition, each sensor works unti it runs out of energy and then the next sensor starts working. In the second case, as the function is a decreasing function of w, the maximum ifetime of the network is achieved when each sensor s working period approaches zero as ong as the sensor works we. Aso, we shoud consider that each sensor needs warmingup time after which it wi be abe to sense. If warming-up time of each sensor is onger than seeping period, working time of sensor is bounded from beow by w Tw v n 1 (12) Note that the warming-up time of each sensor cannot be onger than the time needed to turn on a the other sensors pus the seeping time of the network, which means that at the worst case after turning off each sensor, we immediatey start the warming-up process for each sensor. If the warming-up time is smaer than the seeping period, the ony constraint for w is the minimum time needed for each sensor to detect and transmit the data. We indicate this time by t. Therefore, ( T tota ife = v max + n E Eon P s ne on P s v E min(t,b)p s+e on [n min(t, b) + ] v neon < Ps v where b = Tw v n 1. (13) 6. QOSV-GUARANTEED SENSOR SCHEDULING In this section, at first, we compute the average detection time ADT for a given sensor segment ength and sensor s working time w in order to get a formua for ADT,, and w. With the obtained formua, we can determine and w for a required ADT. 6.1 Average Detection Time for Constant Vehice Speed We can cacuate the average detection time which is the average time it takes for arriving vehices to be detected by sensors. In the case where the vehices arrivas foows a uniform distribution in terms of the arriva time at the interesting road, we can compute the average detection time. See Appendix A for detaied discussion. Aso, in the case where the inter-arriva time of the vehices foows an exponentia distribution, the arrivas are sti uniformy distributed in time domain which resuts in the same average detection time as the uniform arriva distribution. Refer to our technica report for detaied derivation [15]. We first compute the average detection time E[d W] when vehices enter in working period W ike in Figure 3 and then compute the average detection time E[d I] in seeping period I. Thus, the average detection time E[d] for a vehice entering the road with ength, where n sensors have the working time w and the maximum vehice speed is v, is equa to: E[d] = nw E[dW] + /v E[dI] nw+/v nw+/v (n+2)nw2 v+2(n+1)w /v 2v(nw+/v)(nwv+) which is approximatey equa to: ADT 2v (14) (15) As we can see in Eq.14, given the maximum vehice speed v, the average detection time ADT is a function of and w. 6.2 Average Detection Time for Bounded Vehice Speed At first, we cacuate the average detection time for a variabe vehice speed v which is uniformy distributed between v min and v max. With the vehice speed distributed uniformy between v min and v max, we can then compute the average detection time for random arriva time. Refer to Appendix A.2 for more detaied computation. 6.3 QoSv-Guaranteed Scheduing under Sensing Error In reaity, there exists sensing error in sensor node. We reax one previous assumption that every vehice within the sensing radius of some sensors can be detected with probabiity one [1]. Let p be the success probabiity of sensing in each sensor node. In Figure 2, there are n sensor nodes. The

6 success probabiity P success of one scanning is p n. On the other hand, the faiure probabiity P faiure of one scanning is 1 p n. How many number of scanning is on average needed to detect vehices per working period under some sensing error? Let m be the number of scanning per working period. We assume that the arriva time of vehices is uniformy distributed during each scheduing period [15]. Since this probem is reated to the geometric distribution [13], we can see that m satisfies the foowing equaity: m = 1 = 1 (16) P success p n The sensor nodes need to perform the scanning m times in order to satisfy the required confidence interva where m is the ceiing function of m. 6.4 Determination of Scheduing Parameters Given the QoSv required, we can determine the appropriate and w with which the desired QoSv wi be satisfied where QoSv = 1/ADT. We can spread sensors on a road segment with ength and schedue them according to the working time w. Note that in Eq.15, the dominant factor in ADT is. In fact, working time w ony sighty affects the average detection time. Now, given the required ADT, we can determine the scheduing parameters, such as the sensor array ength () ike in Figure 2, the working time per sensor (w), and seeping period (s) in the foowing order: s = ( = 2v ADT from Eq.15 (17) w = Tw /v n 1 from Eq. 12 (18) mwn if v neon < Ps, v from Eq.3 & 16 (19) otherwise. If s is negative in Eq.19, then s is set to ; that is, the sensor nodes work without seeping period. When, w, and s are determined, these parameters for scheduing are deivered to each sensor node aong with its corresponding starting time on the road segment where it beongs. 7. SENSOR SCHEDULING FOR COMPLEX ROADS In this section, we describe the sensor pacement and scheduing agorithm in order to maximize the ifetime of the sensor networks surrounding the city s boundary roads ike in Figure 5(a). 7.1 Sensor Pacement The probem is how to depoy the sensors on the road network given the topoogy of the road network incuding the outer boundary and inner boundary for the city. Keep in mind that the reason why the sensors are spread on the road is that we want the sensors to perform the mobie target tracking after the target detection with our scheduing agorithm. Ony the sensors near to the outer boundary that are seected by the required QoSv are awake periodicay and scan the roads for target detection. The rest of them can seep without any sensing since they are outside the scanning area on the road network. As soon as a mobie target is detected on the road, the other seeping sensors wake up to track the target. How to track the mobie target is out of scope. 7.2 Sensor Scheduing Given the required quaity of surveiance (QoSv = 1/ADT) and a graph representing a road network, we need (i) to compute the seeping period to satisfy the QoSv, (ii) to find out the sensor nodes starting the scanning simutaneousy in the graph after every seeping period, and (iii) to determine the appropriate working time of each sensor node participating in the scheduing for the surveiance. For the seeping period s, at first we determine whether or not we can get benefit through the non-zero seeping period by using Eq.11. If there is no benefit from seeping, the sensor nodes do not use the seeping period, that is, s =. Otherwise, we can find the straight road ength to satisfy the given ADT using Eq.15 from the given road incuding the sensor nodes ike in Figure 2. This straight road of ength is the scanning segment whose sensor nodes participate in the surveiance. The sensor nodes on the scanning segment set their seeping period s to /v where v is the maximum vehice speed. Figure 5 shows the sensor scheduing to satisfy the required QoSv for the given compex roads. For the determination of the set of sensor nodes starting at first every working period in our scheduing, we search a the possibe paths from the outer boundary to the inner boundary in the given road network and then decide the scanning segments. After that, we find the sensor nodes on the scanning segments that are nearest to the inner boundary, satisfying the given QoSv. Figure 5(a) shows a road network around a city s boundary and Figure 5(b) is a graph representing the road network. Our searching agorithm performs an exhaustive searching. For exampe, it considers a the possibe paths from each entrance, such as O 1 and O 2 towards exits on the inner boundary, such as I i for i = Then it seects the appropriate starting points nearer to the outer boundary, such as S i for i = 1..6 in Figure 5(c), to satisfy the required QoSv. The starting points are determined considering a the possibe detours taken by vehices, such as path < O 2, P 2, P 1, P 3 > in Figure 5(c). Thus, the distance between any starting point and some entrance point on the outer boundary satisfies the straight road ength for the specified QoSv. Note that we use the Depth First Search (DFS) for this searching. It might be very expensive for a arge-scaed graph [15]. So we wi use a more efficient searching method ater. In the computation of matrix M containing the working time of each sensor invoved in the surveiance, we consider the sensor nodes of the edge having a joint point caed merged edge where mutipe edges are merged. If the sensor nodes on such an edge perform the scanning whenever each previous edge connected to the joint point performs the scanning, they wi consume their energy quicky to death. We make the sensor nodes on this merged edge perform ony one scanning every scheduing period by using spit-merge scanning, which (a) synchronizes mutipe scanning into one scanning at the joint point and (b) spits one scanning into mutipe scanning at the end-point of the edge connected to mutipe edges. This spit-merge scanning aows the merged edge to be scanned once. For exampe, in Figure 5(d), the scanning P 3 P 1 is spit into two scanning at the point

7 Outer Boundary Inner Boundary Outer Boundary Inner Boundary I1 I1 Vehice O1 I2 O1 P3 P6 I2 Road Network I4 I3 CITY P1 P2 P4 P5 I3 I4 O2 (a) Road Network between the Inner and Outer Boundaries I5 O2 (b) A Connected Graph for an Exempary Road Network I5 Outer Boundary Inner Boundary Outer Boundary Inner Boundary O1 P1 P2 P3 P4 S1 S2 P5 I1 P6 I2 S3 I3 S4 S5 I4 O1 P1 spit merge P2 P3 P4 S1 S2 P5 I1 P6 I2 S3 I3 S4 S5 I4 O2 (c) Construction of Scheduing Pan in Road Network S6 I5 O2 (d) Scanning in Road Network S6 I5 Figure 5: QoSv-Guaranteed Sensor Scheduing for Compex Roads P 1: (a) scanning P 1 O 1 and (b) scanning P 1 P 2. The scanning P 1 P 2 is merged with the scanning P 4 P 2. For this synchronization, the scanning time on each edge is computed considering the scanning time on its incident edges. Let t i be the starting time of scanning P 1 P 2 and et t j be the starting time of scanning P 4 P 2. In order that two scanning may be synchronized, the equaity shoud be satisfied: t i + w i n i = t j + w j n j (2) where w i: working time of sensors on edge (P 1, P 2), n i: number of sensors on edge (P 1, P 2), w j: working time of sensors on edge (P 4, P 2), and n j: number of sensors on edge (P 4, P 2). The scheduing panning agorithm, which performs the determination of the surveiance sensors and computation of scheduing parameters, is described as Pan Schedue in Agorithm 1. Since this compex computation is needed ony in the initia phase for surveiance, it can be performed in one powerfu node caed super node that is ocated outside the sensor network. The super node disseminates the scheduing parameters (e.g., the starting time, seeping period, and each sensor s working time to the sensor network). The dissemination method is out of scope in this paper. The important parameters used in Agorithm 1 and other agorithms described in [15] are specified in Tabe 1. S is Tabe 1: Notation of Parameters Parameter Description G A connected simpe digraph for a road network O A set of vertices for the outer boundary of the road network ADT Average Detection Time given by the administrator: unit is [sec] v A maximum vehice speed: unit is [m/sec] C s The onger side ength of a rectange covered by one sensor: unit is [m] E on Turn-on energy: unit is [J] P s Sensing power: unit is [watts] S A set of scanning starting sensors on scanning segments M A matrix that has each sensor s scheduing information a set of tupes (z, xy,ty PE, ) where z: scanning starting point (or vertex), xy: scanned edge incuding vertex z, TY PE {FULL, PARTIAL}, and : scanned ength on edge xy (i.e., the ength of edge xz). The type of F ULL means that the whoe edge < y, x > shoud be scanned where z = y. On the other hand, the type of PARTIAL means that ony the partia edge starting from z to x, i.e., < z, x >, shoud be scanned where z y. In Agorithm 1, the seection of set S of points starting the scanning is done by Find Starting Points. The computation of matrix M for sensor working time is done by Compute W orking Matrix. These agorithms are described in our technica report [15]. Agorithm 1 Pan Schedue(G, O, ADT, v, C s, E on, P s) 1: {Function description: (i) determine the seeping time s for the shortest path from the outer boundary towards the inner boundary that satisfies the required ADT, (ii) find the set of sensors S nearest to the outer boundary that start the scanning simutaneousy after the seeping period s, and (iii) determine the working matrix M containing the appropriate working period of each sensor that participates in the surveiance.} 2: ADT 2v {ADT = 2v } 3: if E on < C s P s /v then 4: s /v {compute seeping time s} 5: ese 6: s {seeping time s is set to zero} 7: end if 8: S Find Starting Points(G, O, ) {find the set of vertices S consisting of starting points on G to satisfy the ADT } 9: M Compute Working Matrix(G, S, O) {compute the working time matrix M whose entry vaue is working time of sensors on the corresponding edge}

8 2.5 x 16 2 E on = ne on <P s /v max ne on =P s /v max ne on >P s /v max sensing error e 1 =.1 sensing error e 2 =.5 sensing error e 3 =.1 sensor network ifetime [sec] Number of Scanning working time of each sensor during sensing period [sec] Figure 6: Sensor Network Lifetime according to Working Time and Turn-on Energy Number of Sensors Figure 8: Required Average Scanning Number for Sensing Error Probabiity 25 2 Z axis : average detection time [sec] Y axis : road segment ength [m] X axis : working time of each sensor [sec] average detection time [sec] Numerica Resut Lambda = 1/1 Lambda = 1/2 Lambda = 1/ working time of each sensor during sensing period [sec] Figure 7: Average Detection Time according to Working Time and Road Segment Length 8. PERFORMANCE EVALUATION In this section, we not ony show the numerica resuts based on our mathematica anaysis for the network ifetime and average detection time, but aso vaidate our numerica anaysis with simuation resuts. 8.1 Numerica Anaysis In this section, we compare the numerica resuts of our scheduing scheme with the formuas given in Section IV. The environment for numerica anaysis is as foows: The width of the road segment is 2 [m] and the ength of it,, is 2 [m] ike in Figure 2. Every 2 2 square of the road segment is fuy covered by one sensor in the midde of it and so the number of sensors n, eveny paced on the road segment, is 1. The radius of sensing is 1 2 [m]. The tota sensing energy in each sensor (36 [J]) can be used to sense continuousy for 36 [sec] since the sensing energy consumption rate P s is 1 [watts]. The working time of each sensor per working period is s [.1, 5]. Figure 9: Comparison between Numerica Resut and Simuation Resuts The turn-on energy consumption in each sensor is E on {,.12,.48,.96} where the unit is [J]. The vehice s maximum speed v max is 15 [km/h]. This is used as the vehice s speed, which is maintained constanty whie the vehice moves on the road segment. The vehice s arriva time with the unit [sec] conforms to the uniform distribution over (, I+W) where a seeping period I is /v max and a working period is nw. Figure 6 shows the corresponding sensor network ifetime according to working time of sensors during the sensing period. There are four curves corresponding to the different turn-on energies (E 1, E 2, E 3 and E 4). E 1 is the case where there is no turn-on overhead or it is ignorabe. In this case the shorter the working time is, the onger the network ifetime is. When there is turn-on overhead, we have three cases. In the first case of ne on < P s v max, a shorter working time gives us more benefit in terms of the tota ifetime of the network. In the second case of ne on > P s v max, since the overhead for turn-on is high, we can observe that the shorter the working time is, the shorter the ifetime is. At the extreme case the overhead for turn-on is so high that our outward unidirectiona scanning has a better ifetime without any seeping period. In genera in order to get benefit from

9 seeping period of the sensors, the saved energy due to seeping for /v max shoud be greater than the energy exhausted for sensors turn-on. Therefore, we can aow the sensor network ifetime to be extended by adopting seeping periods especiay when ne on < P s v max. One important resut is that working time w determines the network ifetime under the above condition and we can increase the tota ifetime of the network by decreasing the working time. However, as discussed before w cannot be extremey sma since it is bounded by the time needed for each sensor to detect and transmit data and aso it depends on the warming-up time of the sensors. In the third case of ne on = P s v max, there is no need for seeping since there is no benefit of seeping in our scheduing. In Figure 7, we can see the reation of the working time of each sensor during sensing period (or working period) with the average detection time that is obtained by Eq. 14. In this figure, we use ony the maximum speed for arriving vehices, but we can see that the shape of the figure using the uniformy distributed speed wi be very simiar to Figure 7. As discussed before we can aso see that from the figure the average detection time is approximatey equa to 2v max ; that is, the working time does not affect neary the average detection time, which means that it does not affect the QoSv. In fact, the working time ony affects the network ifetime. Therefore, we can maximize the ifetime of the sensor network that supports the specified QoSv by choosing the east w to satisfy the warming-up time constraint of Eq. 12. In the case where there is some sensing error in sensor nodes, we need more than one scanning per working period ike in Section 6.3. Figure 8 shows the required average scanning number for three cases of sensing error probabiity: (a) e 1 =.1, (b) e 2 =.5, and (c) e 3 =.1. The sensing error e 3 sti needs 2 scanning for the road segment having 5 sensor nodes. On the other hand, e 1 and e 2 require 195 and 13 scanning, respectivey. The sensor nodes with these sensing error probabiities are infeasibe for the surveiance. 8.2 Vaidation of Numerica Anaysis based on Simuation In order to evauate the anaysis of our numerica mode, we conducted simuations with the same parameters as the numerica anaysis. We modeed the sensor network incuding sensor and vehice on the basis of SMPL simuation mode which is one of the discrete event driven simuators [14]. We performed simuations with the same parameters as the numerica anaysis given in Section 8.1. Three kinds of the inter-arriva time were used for the simuation: (a) λ 1 = 1/1, (b) λ 2 = 1/2, and (c) λ 3 = 1/3. We can see that the average detection times of simuations according to the sensor working time are aways ess than the numerica upper bound obtained in the numerica anaysis. Thus, the vaues of the parameters, such as the sensor working time and sensor segment ength on the road segment, can be used to aow the sensors to perform the scheduing for the required QoSv in the sensor networks through Eq CONCLUSION In this work we introduce an energy-aware scheduing agorithm for detecting mobie targets that pass critica routes, such as a city s boundary roads, over which wireess sensors are depoyed. It can be used for both surveiance and traffic monitoring in the road system. This agorithm guarantees the detection of a the mobie targets and the required average detection time. Aso, our scheduing agorithm provides a maximum network ifetime. This scheduing is based on the contiguous sensor pacement that is suitabe for mobie target tracking. A the sensors seep during the seeping period. Ony one sensor is turned on through aternate sensing during the working period. This aows other sensors to turn off their sensing devices during the working period in order to save energy. We define Quaity of Surveiance (QoSv) as a metric for quaity of service in surveiance appications. We utiize the maximum moving speed of mobie target to maximize the seeping time of the sensors. When a QoSv is given, scheduing parameters, such as the number of sensors and working time, are computed using our QoSv formua and are deivered to appropriate sensors for scheduing. In future work we wi research on not ony how to enhance our scheduing scheme when the sensors are depoyed randomy cose to the roads, but aso how to extend our scheme to two-dimensiona open fied. 1. ACKNOWLEDGMENTS The authors woud ike to thank Prof. Tian He, Prof. Nicoai V. Kryov, Raghuveer Aravindan, and Changho Choi for reviewing the paper. 11. REFERENCES [1] S. Meguerdichian and M. Potkonjak, Low Power /1 Coverage and Scheduing Techniques in Sensor Networks, UCLA Technica Report, No. 31, January 23. [2] S. Meguerdichian et a., Coverage Probems in Wireess Ad-hoc Sensor Networks, IEEE INFOCOM, Apri 21. [3] J. O Rourke, Computationa Geometry Coumn 15, Internationa Journa of Computationa Geometry and Appications, Vo. 2, pp , June [4] C-F. Huang and Y-C. Tseng, The Coverage Probem in a Wireess Sensor Network, ACM WSNA, September 23. [5] X. Wang et a., Integrated Coverage and Connectivity Configuration in Wireess Sensor Networks, ACM SENSYS, November 23. [6] B. Chen et a., Span: An Energy-Efficient Coordination Agorithm for Topoogy Maintenance in Ad Hoc Wireess Networks, ACM MOBICOM, Juy 21. [7] H. Zhang and J.C. Hou, Maintaining Sensing Coverage and Connectivity in Large Sensor Networks, Ad Hoc and Sensor Wireess Networks, Vo. 1, pp Od City Pubishing, Inc., March 25. [8] S. Shakkottai, R. Srikant and N. Shroff, Unreiabe Sensor Grids: Coverage, Connectivity, and Diameter, IEEE INFOCOM, Apri 23. [9] T. Yan, T. He, and J.A. 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10 [11] C. Gui and P. Mohapatra, Power Conservation and Quaity of Surveiance in Target Tracking Sensor Networks, ACM MOBICOM, September 24. [12] S. Kumar, T. Lai and A. Arora, Barrier Coverage With Wireess Sensors, ACM MOBICOM, August 25. [13] M.H. DeGroot and M.J. Schervish, Probabiity and Statistics (3rd Edition), Addison Wesey, October 21. [14] M.H. MacDouga, Simuating Computer Systems: Techniques and Toos, MIT Press, [15] J. Jeong, S. Sharafkandi and D. Du, Energy-Aware Scheduing with Quaity of Surveiance Guarantee in Wireess Sensor Networks, Technica Report of University of Minnesota, No. 6-21, June 26: technica reports.php/?page=year&year=26 APPENDIX A. CALCULATION OF AVERAGE DETECTION TIME A.1 Average Detection Time with Constant Vehice Speed We assume that a vehice has a constant speed v (v v m where v m is a maximum vehice speed) and it enters the road on the basis of the uniform distribution for its arriva time within each period consisting of working period (W) and seeping period (I), which is W +I. That is, we focus on the average detection time for a vehice with uniform-distributed arriva time. As the system behavior for an arriving vehice is different according to whether the sensors are in the working period or in the seeping period, we anayze separatey the detection time in these two periods and then merge it. First, we compute the detection time when the vehice enters in a working period that the sensors are working (W in Figure 3). In this case, the vehice wi be detected when it moves into the sensing coverage of some working sensor: t w n v(t ta) t w (21) n where t is the detected time of a vehice, which increases from zero when a seeping period starts, and v(t t a) is the detected position of a vehice at time t which has entered the road at time t a; x and x are the ceiing function and foor function for x, respectivey. x and x satisfy the foowing inequaities: x < x + 1, x > x 1. (22) Repacing the eft sides in Eq.22 with the right sides in Eq.22, Eq.21 becomes converted as foows: ( t w + 1) n v(t ta) ( t w 1) (23) n Therefore, the detection time d W = t t a is bounded between the foowing vaues: (n 1)w t a + nwv d W (n + 1)w ta + nwv (24) We use the upper bound of the inequaities of Eq.24 in order to determine the average detection time (E[d W]), for which we cacuate the integra of d W over the interva (, nw) as foows: E[d W] = R nw R nw d W(t a)p ta (t a)dt a (n+1)w t a +nwv = n2 w 2 +2nw 2 2nw(nwv+) 1 nw dta (25) where p ta (t a) is the probabiity density function (pdf) of a vehice s arriva time which we assume is uniform in the interva (, nw). In the case where the vehice enters in a period that the sensors are seeping, the same strategy can be used for obtaining the detection time (d I). In this case, a vehice wi be detected when: t /vm /vm v(t ta) t (26) w n w n where t is the detected time of a vehice, which increases from zero when a seeping period starts, and v(t t a) is the detected position of a vehice at time t which has entered the road at time t a; t /v m since the vehice is detected after the seeping period (/v m), and so t /v m is the actua working time of sensors. In the same way as Eq.23, Eq.26 becomes converted as foows: ( t /vm +1) /vm v(t ta) (t 1) w n w n (27) In this case, the detection time d I for seeping period is bounded between: (n 1)w + 2 /v m t a + nwv d I (n + 1)w + 2 /v m t a + nwv (28) The upper bound of the inequaities of Eq.28 can be used in order to determine the average detection time (E[d I]), for which we cacuate the integra of d I over the interva (, /v m) as foows: E[d I] = R /v m d I(t a)p ta (t a)dt a R /v m = 2(n+1)wvm+2 2v m(nwv+) (n+1)w+ 2 /v m t a +nwv v m dt a (29) where p ta (t a) is the pdf of a vehice s arriva time which we assume is uniform in the interva (, /v m). Therefore, the overa average of detection time is bounded from above by: E[d] = E[d] nw nw+/v m E[d W] + /vm nw+/v m E[d I] (n+2)nw2 v m+2(n+1)w /v m 2v m(nw+/v m)(nwv+) (3) A.2 Average Detection Time for Bounded Vehice Speed The overa average of detection time for variabe vehice speed is computed in the same way as the case of constant vehice speed. When vehice speed v is bounded in [v min, v max], the average detection time in the working period (E ta,v[d W]) is: E ta,v[d W] = R v max v min E ta [d W] p v(v)dv (31) where p v(v) is the pdf of vehice speed. The average detection time in the seeping period (E ta,v[d I]) is: E ta,v[d I] = R v max v min E ta [d I] p v(v)dv (32) Refer to our technica report for detaied derivation [15].