Percentage Coverage Configuration in Wireless Sensor Networks

Percentage Coverage Configuration in Wireless Sensor Networks Hongxing Bai1, Xi Chen1, Yu-Chi Ho1,2, and Xiaohong Guan1,3 1

Center for Intelligent and Networked Systems (CFINS), Tsinghua University, Beijing 100084 , China [email protected], [email protected], [email protected] 2 Division of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138 USA [email protected] 3 Systems Engineering Institute and SKLMS Lab, Xian Jiatong University, Xi’an 710049, China

Abstract. Recent researches on energy efficient coverage configuration in wireless sensor networks mainly address the goal of 100% or near 100% coverage preserving. However, we find that a small percentage of loss of coverage, which is acceptable in many applications, can result in dramatic increase in energy savings. Therefore, in this paper percentage coverage rather than complete coverage is selected as the design goal, and a location-based Percentage Coverage Configuration Protocol (PCCP) is developed to assure that the proportion of the sensing area after configuration to the original sensing area is no less than a desired percentage. Numerical testing results show that PCCP can not only guarantee the desired coverage percentage but also generate more energy efficient configuration in comparison with the existing schemes so that the system lifespan is extended significantly.

1 Introduction Energy consumption (or system lifespan, accordingly) is one of the most important issues in wireless sensor networks (WSN). Since significant energy conservation can be achieved by appropriately scheduling the sensors between ACTIVE and OFF states, where in OFF state, a sensor node consumes very little energy, coverage configuration becomes a key issue in order to assure the coverage quality. Recent study on coverage configuration concentrates on the goal of coverage preserving, which means the sensing area within the Area of Interest (AoI) even with some sensors scheduled OFF should be exactly the same as the original sensing area without any loss of coverage. The work of Tian and Georganas [6,7], Wang et al. [8] and Jiang and Dou [4], etc., belongs to this category. However, complete coverage is unnecessary in many applications, and a percentage of sensing loss below a certain threshold is acceptable. This has been noticed by many researchers as seen from the definitions of system lifetime. For example, Ye et al. [9] define coverage lifetime as the time that coverage drops below a threshold and Y. Pan et al. (Eds.): ISPA 2005, LNCS 3758, pp. 780 – 791, 2005. © Springer-Verlag Berlin Heidelberg 2005

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never comes back again. Wang et al. [8] define the overall system lifetime as the continuous operational time of the system before the coverage drops below a specified threshold. Zhang and Hou [13] define the sensor network lifetime as the entire interval in which at least α portion of the AoI is covered by at least one sensor node. Relaxing the requirement from complete coverage to a percentage of coverage can result in dramatic increase in energy savings. In [13], Zhang and Hou have derived that the upper bound of the lifetime can increase by 15% for 99%-coverage and over 20% for 95%-coverage. An intuitive explanation is: when many disks are used to cover a convex region completely, there must be much overlap of the disks; while if certain uncovered areas (sensing loss) are acceptable, the overlap can be reduced significantly. In this paper the percentage coverage preserving is proposed as a new design goal for coverage configuration such that the sensing area within the AoI with some sensors scheduled OFF should be no less than a certain percentage of the original sensing area. A location-based Percentage Coverage Configuration Protocol (PCCP) is developed to achieve this goal with assurance. Numerical testing results show that PCCP can not only guarantee the desired coverage percentage but also generate more energy efficient configuration in comparison with the existing schemes under the same circumstances so that the system lifespan is extended significantly. The rest of the paper is organized as follows. In the next section, we review the related work in the literature. In section 3, the problem is formulated and the PCCP is described in details. Simulation experiments and numerical testing results with PCCP are presented in Section 4 and are compared with the existing work. The concluding remarks are given in Section 5.

2 Related Work Energy-efficient coverage problem has attracted the interests of many researchers. Cardei and Wu [2] and Sahni and Xu [5] have given a detailed survey of the existing contributions in this area respectively. Here we only review those distributed algorithms since they are scalable and more suitable for WSN. Ye et al. [9,10] proposed a node scheduling algorithm called PEAS. In PEAS, active sensors remain working until their energy is used up, and off sensors turn active randomly. Once an off sensor become active, it checks whether there are active sensors within its probing range. If so, it turns off again; otherwise, it stays active and remains working. Though there may be sensing loss, the proportion of sensing loss is not quantified in PEAS. Tian and Georganas [6] presented a scheme to maintain complete coverage. Their scheme divides the lifetime of WSN into rounds. At the beginning of each round, every sensor will check whether its neighbors can help it to monitor its whole sensing area. If so, it will turn off. After them, Hsin and Liu [3] and Jiang and Dou [4] have developed this scheme. Wang et al. [8] proved a sufficient condition for satisfying multi-degree of complete coverage and presented a coverage configuration protocol (CCP) based on the sufficient condition. CCP can dynamically configure the network to get coverage and connectivity at the same time. Different from their work, here we only consider cov-

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erage issue, because for many off-the-shelf wireless sensors, sensing module is independent of radio module. Therefore, a coverage configuration algorithm will not affect the connectivity of the network. Zhang and Hou [11] presented a density control algorithm called OGDC, which works in rounds. In each round, with a random starting sensor, other sensors will decide whether to be active or not according to locations of themselves and the sensors which become active before them. All above work cannot afford flexible coverage percentage requirement. Tian and Georganas also proposed three location-free schemes in [7], including nearest-neighbor-based, neighbor-number-based and probability-based schemes. All of them work in rounds, and each sensor determines its own OFF-duty eligibility according to whether the nearest neighbor’s distance, the minimal neighbor number or a randomly generated number is more than a threshold D, K or p respectively. The parameter choosing of D, K or p is based on a statistical calculation (also based on the assumption that sensors are uniformly randomly deployed in the AoI) given a desired coverage percentage loss. At the first sight, their design goal is very similar to ours. However, in their work, the coverage percentage is a statistical concept and cannot be guaranteed above a desired threshold always. This is the fundamental difference between PCCP and their schemes. In fact, since location information are not used, these location-free schemes will suffer from either bad efficiency (turn on much more sensors than PCCP) or bad coverage quality (cannot assure the coverage percentage above the desired threshold), which will be shown in section 4.1.

3 Percentage Coverage Configuration 3.1 Basic Assumptions and Concepts We have the following assumptions and concepts: 1. All sensors are homogeneous. 2. All sensors are time-synchronized. Time synchronization methods in WSN can be found in [14, 15]. 3. Each sensor knows its own position. It is not impractical, since many researchers have addressed node localization problems in WSN, such as in [16, 17]. 4. Each sensor’s sensing region is a disk centered at the sensor’s location with a fixed radius Rs. 5. The communication radius is larger than two times of the sensing radius. Definition 1 (Neighbor). For any two sensors A and B, if the distance between them is less than or equal to 2*Rs, then sensor A and B are neighbors. Definition 2 (Coverage Percentage). Suppose the original sensing area is A, the sensing area within the AoI after coverage configuration is B. The ratio of B to A is called coverage percentage. In this paper, we denote the desired coverage percentage threshold as p*. Another important concept used in PCCP is Voronoi diagram. Suppose there are N sensor nodes in a two dimensional plane, if we partition the plane into N convex polygons such that each polygon contains exactly one node and every point in a given


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polygon is closer to the node in this polygon than to any other node, then we get a Voronoi diagram [1]. In a Voronoi diagram, each polygon is called a Voronoi cell. Particularly, we call a sensor node’s Voronoi cell as its Occupation Area (OA) in this paper. If two OAs share a common edge, the owner sensors of the two OAs are called Voronoi neighbors. 3.2 Description of PCCP The basic idea of our protocol is Divide and Conquer. Since all OAs constitute the AoI without overlap, we can divide the AoI into regions based on the concept of OA. More precisely, each region is a collection of several OAs in the AoI. After that, the percentage coverage configuration will be done in each region. The following is the detailed description of PCCP. In PCCP, the network lifetime is divided into a sequence of working rounds. Each round begins with a node scheduling phase, followed by a sensing phase. At the beginning of each round, all sensors turn on and enter the node scheduling phase. After deciding its state, the ACTIVE-duty sensors enter the sensing phase starting working (sensing) and the OFF-duty sensors turn off. Then each sensor stays in its state until the next round starts. The node scheduling procedure consists of two sub-phases: occupation area obtaining sub-phase and Percentage Coverage Configuration (PCC) sub-phase. In the occupation area obtaining sub-phase, each sensor broadcasts its ID and location with radio radius 2*Rs and records the ID and location information of its neighbors when hearing their messages. To avoid collision, each sensor should generate a random back-off (bounded by the length of this phase) time Tb and only broadcast when Tb expires. At the end of this phase, each sensor knows the location information of its neighbors. Then by calculating its own OA and the original sensing area within its OA (denoted by SOA), it finishes its task in this sub-phase. The OA and SOA calculation algorithm will be described in section 3.2.1 and 3.2.2. In the percentage coverage configuration sub-phase, for each sensor, there are three possible statuses: Waiting Sensor for broadcasting Start Sensing Message (SSM), Percentage Coverage Configuration Head (PCC Head) and Percentage Coverage Configuration Member (PCC Member). All sensors start with the status of a waiting sensor at the beginning of percentage coverage configuration sub-phase. Then each sensor will negotiate with its neighbors and changes its status accordingly as described in the below. For a Waiting Sensor: Each sensor of this status first generates a random delay time Td. When a waiting sensor’s Td expires, it will broadcast a Start Sensing Message (SSM), turn on its sensing module and assume itself a PCC head. If a waiting sensor receives an SSM from one of its neighbors before its own Td expires, it will stop the timer for Td, assume itself a PCC member of the SSM sender, and ignore any other SSM when it is a PCC member. For a PCC Member: A PCC member O will calculate the area of the part in sensor O’s OA which is covered by its neighbors which are PCC heads (denoted by Sc). Then this sensor sends

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SOA and Sc to its PCC head. After that, this sensor will listen to the channel until it receives an OFF-duty Eligible Neighbors Message (OENM) from its PCC head. When this sensor receives the OENM, it will check whether its ID is contained in the OENM. If so, it will turn off itself; otherwise, it will generate a random delay time Td once more and then become a waiting sensor again. What need to be pointed out is, since there are usually many PCC members sharing a common PCC head, to avoid collision, each PCC member should send its Sc and SOA with a random back-off time. The maximal back-off time should be bounded by a predetermined time Th in order to let the PCC head make sure all members have sent their messages. For a PCC Head: A PCC head will listen to the channel during the Th time interval to collect the SOA and Sc information of its PCC members. When Th expires, this sensor will execute an OFF-duty Eligible Neighbor Choosing Algorithm (as described in section 3.2.3) to judge which members can be turned off. Then it will broadcast an OENM which includes the OFF-duty eligible sensors’ IDs. After that, it will remain ACTIVE until the next round comes. Either PCC head or PCC member is a temporary role for a sensor. The relationship between head and member will disappear after the PCC head sends the OENM. Remark 1. To minimize the energy consumption overhead in percentage coverage configuration, the length of each round should be long enough compared to the configuration time, but it should be much smaller than the sensors’ average continuous working time. Remark 2. If the sensors have no IDs, they can use their locations as their IDs since they can distinguish each other according to their locations. 3.2.1 OA Calculation Algorithm In general, suppose the AoI can be described as the solution of J inequalities: a j x + b j y + c j ≤ 0 , j=1,2,…,J. Suppose there are totally N sensors in the AoI with locations (xi, yi), i=1,2,…,N respectively. Then any point (x, y) in the kth sensor’s OA should satisfy the following inequalities:

⎧⎪ ( x − x ) 2 + ( y − y ) 2 ≤ ( x − x ) 2 + ( y − y ) 2 , i = 1,2,..., N k k i i ⎨ ⎪⎩a j x + b j y + c j ≤ 0, j = 1,2,..., J

(1)

Though there are N+J inequalities above, no more than L+J of them are active constraints where L is the number of the kth sensor’s Voronoi neighbors. As any sensor’s Voronoi neighbors are usually near the sensor, in this paper we use the neighbors’ locations to calculate any sensor’s OA. We name the neighbor-based calculation result as the sensor’s Neighbor-based OA (NOA). For an arbitrary sensor node O, denote its own location as (x0, y0). Suppose sensor O has totally M neighbors with locations (zi, wi), i=1,2,…,M respectively. Then we describe sensor O’s NOA by the J+M inequalities


a j x + b j y + c j ≤ 0 , j=1,2,…, J+M where

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(2)

a J +i = 2( z i − x0 ) , bJ +i = 2( wi − y 0 ) and c J +i = ( x02 + y02 ) − ( zi2 + wi2 )

(for i=1,2,…,M) are come from the first part of (1). We assume the AoI is a convex polygon. Thus an NOA (or OA) is also a convex polygon, which can be determined by its vertices. Therefore, sensor O only needs to calculate and record the vertices of an NOA, where a vertex is an intersection of two lines a j x + b j y + c j = 0 and ak x + bk y + ck = 0 (j,k=1,2,…, J+M and j ≠ k) which is a feasible solution of (2). Thus we can calculate all the (J+M)(J+M-1)/2 intersections and select those satisfying all the inequalities in (2). According to the definition of “neighbor” we presented in section 3.1, an arbitrary sensor O’s Voronoi neighbors may not be contained in sensor O’s neighbors. As the number of constraints in (2) is less than those in (1), sensor O’s NOA may be the same as its OA, or larger than its OA. However, when a sensor uses NOA instead of OA to calculate SOA and Sc, the sensor will get the right values of SOA and Sc. This will be proved in section 3.2.2. 3.2.2 SOA and Sc Calculation Algorithm To calculate SOA, we give the following theorems in advance. Theorem 1. For an arbitrary sensor O, if some point P in sensor O’s OA is in the original sensing area, then P is covered by sensor O’s sensing disk. Proof. As point P is in sensor O’ OA, for any sensor Q in the AoI, we have dPO ≤ dPQ according to the definition of OA, where dAB denotes the distance between point A and point B. If dPO>Rs, P cannot be covered by any sensor’s sensing disk. Therefore, if P is in the original sensing area, P must be within sensor O’s sensing range. From Theorem 1 we know that a sensor O’s SOA can be calculated as the area in sensor O’s OA covered by its own sensing disk. Theorem 2. For any point P within sensor O’s sensing disk, if P is in sensor O’s NOA, P is also in sensor O’s OA, and vice versa. Proof. For any point P in sensor O’s sensing disk, for any sensor Q which is more than 2*Rs far away from sensor O, Q cannot be P’s nearest sensor, since dPO ≤ Rs and dPQ>Rs. That means, the nearest sensor to P is either sensor O or one of sensor O’s neighbors. Therefore, it is sufficient to assure sensor O is P’s nearest sensor, given dPO ≤ dPU for any U which is a neighbor of sensor O. Thus if P is in sensor O’s NOA, P is also in sensor O’s OA, and vice versa. According to Theorem 2, we propose in PCCP that any sensor obtains its SOA by calculating the area in its NOA covered by its own sensing disk. In PCCP, another important value is Sc, i.e., the part of area in a sensor’s OA that is covered by its neighbors which are PCC heads. Next we show how to calculate Sc. Theorem 3. For any sensor O, if some point P in sensor O’s NOA is covered by the sensing disk of one of sensor O’s neighbors, then P is in sensor O’s OA.

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Proof. For any point P’ within sensor O’s NOA but outside sensor O’s sensing disk, P’ cannot be covered by the sensing disk of any of sensor O’s neighbors, because sensor O is nearer to P’ than to sensor O’s neighbors, and dP’O>Rs. Since P is covered by one sensor O’s neighbor’s sensing disk, P is within sensor O’s sensing disk. According to Theorem 2, P is in sensor O’s OA. By Theorem 3, a sensor’s Sc calculated in its NOA is no more than the real Sc (calculated in its OA). Since a sensor’s NOA is always no smaller than its OA, a sensor’s real Sc is no more than the Sc calculated in its NOA. So a sensor’s real Sc is equal to its Sc calculated in its NOA. Thus we can calculate Sc based on NOA. Since a PCC member O may be OFF-duty ineligible informed by a PCC head U and then become a waiting sensor again, sensor O may become a PCC member of another PCC head V. In this case, we use an iterative way to calculate sensor O’s Sc. Limited by the length of the paper, here we only give an example as an illustration. Suppose sensor O’s OA is the pentagon p1p2p3p4p5 as in Fig. 1(a). When one of sensor O’s neighbors U becomes a PCC head, sensor O becomes a PCC member of sensor U. Then sensor O will calculate Sc as the area of the pentagon p1p6p7p4p5. Suppose sensor U has not chosen sensor O as an OFF-duty eligible neighbor, sensor O becomes a waiting sensor again. After that, sensor O hears another neighbor V broadcasting an SSM. In this case, sensor O calculates its Sc as the last-time Sc (recorded in sensor O’s memory) plus the area of the quadrangle p3p7p8p9. See Fig. 1(b).

V p5 p4 p7 U p1

(a)

p8 p9 O p6 p2

p3

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Fig. 1. An illustration of Sc calculation

3.2.3 OFF-Duty Eligible Neighbor Choosing Algorithm When a sensor becomes a PCC head, it may have many PCC members. But there may be only a part of them can be turned off to guarantee a certain coverage percentage. If there are K PCC members, the number of possible solutions is 2K. To select the optimal set of OFF-duty eligible PCC members is a NP-hard problem. Therefore, in PCCP, we only use a two-step heuristic choosing algorithm as described below: 1. For those PCC members whose Sc/SOA ≥ p*, add them into the OFF-duty Eligible Neighbors Message (OENM).


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2. For those members whose Sc/SOA