Joint k-coverage, Duty-Cycling, and Geographic Forwarding in Wireless Sensor Networks

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1 Joint k-coverage, Duty-Cycling, and Geographic Forwarding in Wireless Sensor Networks Habib M. Ammari Wireless Sensor and Mobile Ad-hoc Networks (WiSeMAN) Research Lab Department of Computer Science, Hofstra University, Hempstead, NY 11549, USA Abstract Most of geographic forwarding protocols assume that all sensors are always on. Such an assumption is unrealistic for applications where sensors are switched on or off. This paper focuses on k-covered wireless sensor networks (WSNs), where each point in a field is covered by at least k sensors. First, we characterize k- coverage. Then, we propose an energy-efficient scheduling protocol for k-covered WSNs. Third, we propose the first design of a geographic forwarding protocol for duty-cycled k-covered WSNs with data aggregation. Finally, we evaluate the performance of our joint k-coverage and geographic forwarding protocol and compare it to the Coverage Configuration Protocol (CCP) with BVGF on top of it. Simulation results show that our joint protocol outperforms the resulting protocol, CCP+BVGF. 1. Introduction It is well known that the best approach to save battery-power (or energy) of the sensors is duty-cycling so the sensors can be turned on or off according to a sleep-wakeup scheduling protocol. Geographic forwarding is an energy-efficient and practical scheme for WSNs in that the sensors need only maintain local knowledge on the locations of their one-hop neighbors to select their next forwarders Motivations and Problem Statement Most of geographic forwarding protocols assume that all sensors are always on during forwarding. Such an assumption is not realistic in densely deployed WSNs, where sensors are duty-cycled to save energy. In this paper, we study the problem of joint k- coverage, duty-cycling, and forwarding in WSNs. Precisely, we focus on geographic forwarding in a duty-cycled, k-covered WSN (CWSN k ), where each point in a field is covered by at least k 3 active sensors while all the sensors are connected. Sajal K. Das Center for Research in Wireless Mobility and Networking (CReWMaN) Dept. of Comp. Science and Engineering, The Univ. of Texas at Arlington, TX, 76019, USA das@cse.uta.edu 1.2. Contributions The contributions of this paper are as follows: (1) We propose a sensor scheduling protocol to k-cover a field using a minimum number of active sensors. (2) We propose a geographic forwarding protocol running on a duty-cycled CWSN k based on virtual potential fields and using data aggregation. (3) We show that our joint k-coverage and forwarding protocol outperforms CCP with BVGF on top of it. The rest of the paper is as follows: Section 2 presents the network model. Section 3 describes our duty-cycling protocol for CWSN k. Section 4 presents our geographic forwarding protocol for duty-cycled CWSN k. Section 5 gives simulation results. Section 6 reviews related work. Section 7 concludes the paper. 2. Definitions and Assumptions In this section, we present some key definitions and assumptions useful for the description of our protocol. Definition 1: The sensing range of a sensor s i is a region where each event that takes place in this region can be sensed by s i. The sensing neighbor set SN(s i ) of s i is a set of all the sensors in its sensing range. Definition 2: The communication range of a sensor s i is a region such that s i can communicate with any sensor located in this region. The communication neighbor set CN(s i ) of s i is a set of all the sensors in its communication range. Definition 3: Let A be an area. The area A is said to be k-covered if each point p A belongs to the intersection of the sensing ranges of at least k sensors. A WSN is said to be connected if all the sensors can communicate with each other directly or indirectly. We assume that the sensing and communication ranges of the sensors are modeled by disks, called sensing and communication disks of radii r and R, respectively. Each sensor has a unique id and is aware of its location via a Global Positioning System or a localization technique [4] /09/$ IEEE 487

2 (a) Figure 1: (a) A slice and two adjacent slices 3. Duty-Cycling for CWSN k In this section, we present our scheduling protocol for CWSN k. First, we provide a sufficient condition for k-coverage of a deployment field Sufficient Condition for k-coverage First, we present Helly s Theorem [3], which characterizes the intersection of convex sets. Helly s Theorem [3]: Let E be a family of convex sets in R n such that for m n+1 any m members of E have a non-empty intersection. Then, the intersection of all members of E is non-empty. From Helly s Theorem [3], we deduce Theorem 1 in a two-dimensional space, i.e., R 2, which will help us find a tight characterization of k-coverage. Theorem 1: Let k 3. The intersection of k sensing disks is not empty if and only if the intersection of any three of those k sensing disks is not empty. Following Theorem 1, Lemma 1 states a sufficient condition for complete k-coverage of a field [1]. Lemma 1 [1]: Let r be the radius of the sensing disks of the sensors and k 3. A field is k-covered if any Reuleaux triangle region of width (i.e., the maximum distance between parallel lines that bound it) r in a field contains at least k active sensors. Note that two adjacent slices intersect in a region shaped as a lens (known as the fish bladder) so that the sides of their associated regular triangles fully coincide (Figure 1b). Note that k sensors located in the lens of two adjacent slices, say C 1 and C 2, k-cover the area associated with their union. Theorem 2 states this result. It refines the result of Lemma 1 by stating a tighter sufficient condition for complete k-coverage of a field. Theorem 2: Let k 3. A field is surely k-covered if for any slice in the field, there is at least one adjacent slice such that their lens contains at least k active sensors A Protocol for Guaranteeing k-coverage Our proposed protocol for full k-coverage of a field consists of two phases: sensor field slicing and sensor selection. Next, we describe both phases in details Sensor Field Slicing. In general, the sink is connected to an infinite source of energy, such as a wall outlet, and thus can be viewed as a line-powered node that has no energy constraint. Hence, we assume that the sensor field slicing task is done by the sink in each scheduling round (or simply round). To exploit the result of Theorem 2, we propose a slicing scheme that divides a field into overlapping slices, such that two adjacent slices intersect in a lens. Intuitively, this implies that a field is sliced into regular triangles of side r. The result of this slicing operation is called slicing grid [1] Sensor Selection for k-coverage. In addition to slicing a field, we assume that the sink is also responsible for forming clusters of slices from the randomly obtained slicing grid. Precisely, each cluster consists of at most six adjacent slices forming a disk. Because of the random generation of slicing grids and the geometry of a field, some clusters consist of an entire disk, and hence called interior clusters, while others are formed by a portion of a disk, and hence called boundary clusters. Moreover, for each cluster, the sink selects a sensor, called cluster-head, which is located as near as possible to the center of its cluster. The random generation of slicing grid ensures that all sensors are equally likely to act as cluster-heads in each round. Each cluster is defined by one point, i.e., (x,y) coordinates, representing its center and at most six other points defining its slices (or slice portions for a non-complete cluster). These seven points define the slicing information of a cluster, which the sink would broadcast to its corresponding cluster-head. Next, we define interior and boundary lenses. Definition 4: An interior lens of a cluster is not shared with any of its adjacent clusters while a boundary lens is shared by two adjacent clusters. Notice that each cluster overlaps with at most six others. By Theorem 2, sensors located in the boundary lenses of a given cluster should be selected first in order to minimize the total number of active sensors to achieve full k-coverage of a field. However, this requires certain coordination between cluster-heads. Each cluster-head is in charge of selecting some of its sensing neighbors to k-cover its cluster based on its slicing information. Precisely, each cluster-head exploits the overlap between the slices of its cluster as well as the overlap between its slices and those of its adjacent cluster-heads to select a minimum number of its sensing neighbors to k-cover its cluster. We assume that each sensor advertises its remaining energy to its sensing neighbors at the start of a round when it turns itself on. Each cluster-head s chi maintains a list E rem _List(s chi ) ={E rem (:s j SN(s chi )} of remaining energy of its sensing neighbors, where E rem ( is the remaining /09/$ IEEE 488

3 energy of s j. It uses this list to select the ones with high remaining energy to stay active by sending a SELECT message including the cluster-head s id as well as the id s of all selected sensors. This would avoid those ones with low remaining energy and help the sensors deplete their energy as slowly and uniformly as possible. We assume that at the beginning of each round, all the sensors are active. Those ones which are selected by their corresponding cluster-heads would remain active during the underlying round, while the others turn themselves off. For the sensor selection, each cluster-head assigns priorities to sensors located in boundary lenses, interior lenses, and middle of slices in descending order. That is, sensors located in boundary lenses have high priority to be selected based on Theorem 2. Given that each cluster has at most six slices, each cluster-head manages at most six interior lenses and at most six boundary lenses. Each clusterhead is responsible for selecting sensors from its interior lenses without any coordination with its adjacent cluster-heads. However, each cluster-head coordinates with at most six adjacent cluster-heads to select sensors from its boundary lenses in order to k- cover its cluster with a minimum number of sensors. Theorem 3 states a condition forconnectivity based on the structure of the clusters of slices. Theorem 3: Let k 3. A CWSN k is connected if R r, where r and R are the radii of the sensing and communication disks of the sensors, respectively. Proof: First, each cluster is connected if R r. Also, the cluster-heads are connected to each other via active sensors. Thus, A CWSN k is connected if R r. Theorem 4 characterizes the performance of CSW k in terms of the number of sensors for k-coverage. Theorem 4: CSW k selects a minimum number of active sensors in each round for k-coverage of a field. Proof: Each cluster-head coordinates with its adjacent ones and ensures that its cluster is k-covered, where each of its slices is covered by exactly k sensors. Hence, by Theorem 2, each slice of a field is k-covered with a minimum number of active sensors. Thus, CSW k guarantees that a field is k-covered with a total minimum number of active sensors. 4. Geographic Forwarding In this section, we present our first potential field [8] based solution for geographic forwarding on a dutycycled CWSN k, called Geographic Forwarding through Fish Bladders (GEFIB), where aggregated data is forwarded through fish bladders (or lenses). We assume that in each round, every active sensor has data to report to the sink. Also, only sensors selected to k- cover a field act as relays A Modeling Approach Sensors can be viewed as particles, and hence are subject to virtual forces, which attract sensors to each other. These virtual attractive forces are due to the remaining energy of the sensors and their geographic locations. Indeed, the sensors with highest remaining energy are preferred to act as relays in order to avoid energy holes (i.e., regions whose sensors depleted their energy) that may disconnect the network. Also, the sensors prefer closer relays to forward data over short distances and save energy. Using potential field terminology, each active sensor is subject to at least one attractive force, called energylocation based force and denoted by F el, which is exerted by some active sensor and defined as the gradient of a unique scalar potential field, called energy-location based potential field and denoted by U el, i.e., F el = - U el. We should mention that this notion of attractive force is symmetric. That is, if a sensor s i exerts a force on sensor s j, the latter also exerts on the former a force with the same magnitude. Also, only active sensors can exert forces on each other. Our approach to modeling the resultant force that a sensor s i exerts on its sensing neighbor s j is borrowed from electromagnetism theory. Using Coulomb s law, the magnitude of the electrostatic force F(i, between two points electric charges q i and q j depends on their magnitudes and the Euclidean distance d(i, between them, and is computed as 1 qi q j F( i, = U ( i, = 4π ε 2 d ( i, ) 0 j where ε 0 is the permittivity of free space. In our model, the charge of a sensor is its remaining energy and permittivity is the transmitter amplifier [7] in the free-space (ε fs ) model (α = 2) or the multi-path (ε mp ) model (2 < α 4), where α is the path-loss exponent. Thus, the magnitude of the force F el (i, that a sensor s i, exerts on its sensing neighbor s j is proportional to the product of their remaining energy and inversely proportional to the Euclidean distance d(i, between them. Moreover, it is important that F el (i, account for the type of model being used, i.e., free-space model vs. multi-path model. Therefore, the attractive force F el (i, is computed as 1 E ( i) E ( F ( i, U ( i, rem rem el = el = 4π ε α d ( i, where E rem (l) is the remaining energy of sensor s l and ε {ε fs, ε mp }. Similarly, there is an interaction between one sensor and a set of sensors. The resultant force exerted by sensor s i on a set of sensors S is given by s S F ( i, S) = F ( i, = U ( i, el j el s S j el /09/$ IEEE 489

4 Figure 2. Cluster-heads Communication 4.2. Forwarding with Data Aggregation In this section, we present our geographic forwarding protocol for clustered duty-cycled CWSN k. All data originated from sensors in a cluster are received by their corresponding cluster-head, which aggregates them with its own data into only one single data. Precisely, each sensor sends its data directly to its cluster-head, where data is aggregated. We distinguish two types of aggregation. In the first scenario, referred to as local data aggregation, aggregation occurs only within clusters and all data aggregated by cluster-heads are forwarded to the sink without further aggregation. Thus, the sink receives data from each cluster-head in each round. In the second scenario, referred to as global data aggregation, the sink receives only one data packet in each round that represents the aggregation of all data aggregated by cluster heads. Precisely, each cluster-head also aggregates its own aggregated data with the aggregated data it has received from a cluster-head and forwards the result to another cluster-head. Before we discuss our geographic data forwarding protocol with data aggregation on a duty-cycled CWSN k, namely GEFIB, we define best slice, best lens, and best relay of a cluster-head. Definition 5: A best slice of a cluster-head s ch with respect to a destination Dest, which could be a clusterhead or the sink, is a slice that is crossed by a line segment connecting s ch and Dest (Figure 2). A visible lens L v (i,dest) of s ch with respect to Dest, is a lens that belongs to the best slice of s ch with respect to Dest, where 1 v 3 (Figure 2). A best lens L b (i,dest) of s ch with respect to Dest, is a visible lens such that F el (i,l b (i,dest)) is the maximum over all resultant forces exerted by s ch on all its visible lenses L v (i,dest) where 1 b,v 3. A best relay s l of a cluster-head s ch with respect to a destination Dest, is a sensing neighbor of s ch selected from a best lens L b (i,dest) such that F el (i,l) is the maximum over all resultant forces exerted by s i on its neighbors located in L b (i,dest). That is, F el (i,l b (i,dest))=max{ F el (i,l v (i,dest)): 1 v 3} and F el (i,l) = max{f el (i,: s j L b (i,dest)}. First, each sensor sends its data directly to its cluster head. When a cluster head s i receives data from all sensors belonging to its cluster, it aggregates them with its own data and forwards the result, called locally aggregated data (LAD), toward the sink. In each round, the sink receives as many LAD packets as cluster-heads. Indeed, when a cluster-head receives LAD packets initiated from other cluster-heads, it just forwards them without any update. Precisely, a clusterhead finds the best slice with respect to the sink and chooses the best lens in terms of attractive force out of the three visible lenses (Figure 2). From this lens, it selects the best relay based on the potential field-based force and forwards data to it. However, when a relay receives the data, it forwards it directly to the closest cluster-head. This forwarding process between clusterheads using relays takes place through fish bladders (or lenses) and repeats until data arrives at the sink. All cluster-heads and relays apply the algorithm GEFIB. 5. Performance Evaluation In this section, we evaluate GEFIB using a highlevel simulator written in the C programming language. We consider a square sensor field of side length 1000m where sensors are randomly and uniformly deployed. We use the energy model given in [14], where energy consumption in transmission, reception, idle, and sleep modes are 60 mw, 12 mw, 12 mw, and 0.03 mw, respectively. Following [15], we define one unit of energy as the energy required for a sensor to stay idle for 1 second. We assume that the initial energy of each sensor is 60 Joules enabling a sensor to operate about 5000 seconds in reception/idle modes [14]. Here, the energy consumption is due to sensing k- coverage and to forwarding/sending data and control information. All simulations are repeated 100 times and the results are averaged Comparing CSW k and CCP In this section, we compare CSW k with CCP (Coverage Configuration Protocol) [13]. When the communication range of sensors is at least double their sensing range, Xing et al. [13] showed that full coverage implies connectivity. Otherwise, Xing et al. [13] integrated CCP with a topology maintenance protocol (Span) [5] to ensure connectivity. In all simulations, we consider r = 25m and k = 3 unless stated otherwise. Figure 3a plots the degree k of coverage versus the number n a of active sensors for CSW k as compared to CCP. It shows that CSW k requires less active sensors than CCP to achieve the same coverage degree, thus yielding significant energy /09/$ IEEE 490

5 savings. This is due not only to a higher number of active sensors required by CCP, but also to the communication overhead caused by the exchange of messages between active sensors running CCP to coordinate among themselves and provide the requested k-coverage service. Thus, CCP consumes more energy than CSW k as shown in Figure 3b. While CCP requires Span [5] to provide connectivity between active sensors when R < 2r, CSW k does not need such a topology maintenance protocol as all it requires is that R r to provide connectivity. (a) Figure 3. CSW k compared to CCP n a of active sensors required for k-coverage does not decrease any further. Indeed, when R 2r, Span [5] is not needed at all as both k-coverage and R 2r guarantee connectivity. Similarly, the performance of CCP improves as the ratio α increases, i.e., R increases (Figure 4b). That is, less number of sensors is needed to provide both k-coverage and connectivity GEFIB versus CCP+BVGF We consider CCP [13] with BVGF [12] on top of it, denoted by CCP+BVGF, and compare it to GEFIB. We have slightly updated BVGF to consider remaining energy of the sensors for a fair comparison. Figure 5 shows that GEFIB yields less average energy consumption and higher data delivery rate than CCP+BVGF. This is due in part to CCP, which uses higher number of active sensors for k-coverage than CSW k. Also, BVGF forwards data over long distances. Hence, it consumes considerable energy. Moreover, data may reach sensors whose remaining energy is not enough to progress data to the sink, which causes data to be dropped. Our potential field-based forwarding protocol selects next forwarders based on their remaining energy and location. Hence, all neighbors of a sensor are equally likely to be selected as forwarders. 6. Related Work (a) Figure 4. CSW k versus CCP (a) Figure 5. GEFIB versus CCP+BVGF Figure 4a plots n a versus R while Figure 4b plots n a versus r for different ratios α = R/r. Given the result reported in [15] with respect to the relationship between r and R for real-world sensor platforms (R r), we consider only the case α 1. Given that α 1, any increase in the communication range of sensors would not have any impact on the performance of CSW k. It would, however, affect the performance of CCP. As can be observed, n a decreases as R increases. Indeed, Span [5] would require less number of sensors to maintain connectivity between active sensors as R increases. However, at some point, (surprisingly enough, this point corresponds to R 2r), the number In this section, we review protocols for coverage, scheduling, and geographic forwarding in WSNs. Huang et al. [9] studied the relation between coverage and connectivity of WSNs and proposed distributed protocols to guarantee both of them. Gupta et al. [6] proposed algorithms for connected sensor cover so the WSN self-organizes its topology in response to a query and activate the necessary sensors to process the query. Zhang and Hou [15] proposed an optimal geographical density control protocol to keep a small number of sensors active to cover a field. Tian and Georganas [11] proved that the network formed by the active nodes is connected if the communication range of the sensors is at least twice their sensing range. The study of joint coverage and geographic forwarding has received little attention. While Biswas and Morris [2] and Zorzi and Rao [16] assumed dutycycling at the MAC layer, Nath and Gibson [10] considered both routing and duty-cycling at the network layer. In traditional routing, a sender chooses the next forwarder before transmitting its data. However, when the link quality is poor, the probability that the selected forwarder receives the data is low. In contrast, using opportunistic routing, any node that overhears the transmission and is closer to the /09/$ IEEE 491

6 destination can participate in forwarding the packet. Zorzi and Rao [16] proposed an opportunistic data transmission scheme, called geographic random forwarding (GeRaF). Biswas and Morris [2] proposed an integrated opportunistic routing and MAC protocol, called ExOR, to enhance throughput in multi-hop wireless networks. Nath and Gibbons [10] presented the first formal analysis of the performance of geographic routing on duty-cycled WSNs, where every sensor has k active neighbors. Why Our Protocol? The problem of joint coverage and geographic forwarding in WSNs has been overlooked intentionally. This is due to the fact that all sensors are assumed to be always on during forwarding. This work is an effort complementing the one by Nath and Gibbons [10]. We believe that our joint protocol could be useful for several applications and particularly those requiring data aggregation at intermediate sensors along paths to the sink. To the best of our knowledge, this is the first study of geographic forwarding on duty-cycled CWSN k. 7. Conclusion In this paper, we have characterized k-coverage of a field and proposed a minimum-energy sleep-wakeup scheduling protocol (CSW k ) for CWSN k. We have also proposed an energy-efficient geographic forwarding protocol on duty-cycled CWSN k. Our joint k-coverage and geographic forwarding (GEFIB) framework can be used for applications that demand high coverage degree, such as intruder detection and tracking. Also, it is useful for applications that require data aggregation. Our future work is three-fold. First, we plan to implement GEFIB on a sensor testbed to assess its real performance. Second, we focus on studying GEFIB using stochastic models of sensing and communication ranges of the sensors. Third, we plan to extend GEFIB to account for heterogeneous CWSN k, where the sensors do not necessarily have the same capabilities. Acknowledgments The authors thank the anonymous reviewers for their helpful comments. The work of H.M. Ammari is partially supported by a New Faculty Start-Up Research Grant from Hofstra College of Liberal Arts and Sciences Dean s Office. The work of S.K. Das is partially supported by the AFOSR grant A and US National Science Foundation (NSF) grants IIS and CNS His work is also supported by (while serving at) the NSF. Any opinion, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the NSF. References [1] H. M. Ammari and S. K. Das, Clustering-based minimum energy m-connected k-covered wireless sensor networks, Proc. EWSN, LNCS 4913, 2008, pp [2] Biswas, S. and Morris, R. ExOR: Opportunistic Multi- Hop Routing for Wireless Networks. Proc. ACM SIGCOMM, pp , [3] B. Bollobás, The Art of Mathematics: Coffee Time in Memphis, Cambridge University Press, [4] Bulusu, N., Heidemann, J., and Estrin, D. GPS-Less Low Cost Outdoor Localization for Very Small Devices. IEEE Pers. Comm. Mag., 7(5), 28-34, [5] Chen, B., Jameson, K., Balakrishnan, H., and Morris, R Span: An energy-efficient coordination algorithm for topology maintenance in ad hoc wireless networks. ACM Wireless Networks 8(5), [6] Gupta, H., Zhou, Z., Das, S., and Gu, Q. Connected Sensor Cover: self-organization of Sensor Networks for Efficient Query Execution. IEEE/ACM TON, 14(1), (2006). [7] Heinzelman, W., Chandrakasan, A., and Balakrishnan, H. An Application-Specific Protocol Architecture for Wireless Microsensor Networks. IEEE TWireless, 1(4), pp (2002). [8] Helms, L. L. V. Introduction to Potential Theory. New York, Wiley-Interscience (1969). [9] Huang, C., Tseng, Y., Wu, H. Distributed Protocols for Ensuring Both Coverage and Connectivity of a Wireless Sensor Network. ACM TOSN, 3(1), 1-24 (2007). [10] Nath, S. and Gibbons, P. B. Communicating via fireflies: geographic routing on duty-cycled sensors. Proc. IPSN, pp (2007). [11] Tian, D., Georganas, N.: Connectivity Maintenance and Coverage Preservation in Wireless Sensor Networks. Ad Hoc Networks, 3, (2005). [12] Xing, G., Lu, C., Pless, R., and Huang, Q. On Greedy Geographic Routing Algorithms in Sensing-covered Networks. Proc. ACM MobiHoc, pp (2004). [13] Xing, G., Wang, X., Zhang, Y., Lu, C., Pless, R., Gill, C. Integrated Coverage and Connectivity Configuration for Energy Conservation in Sensor Networks. ACM TOSN, 1(1), (2005). [14] Ye, F., Zhong, G., Cheng, J., Lu, S., Zhang, L. PEAS: A Robust Energy Conserving Protocol for Long-Lived Sensor Networks. Proc. ICDCS, pp (2003). [15] Zhang, H., Hou, J. Maintaining Sensing Coverage and Connectivity in Large Sensor Networks. Ad Hoc & Sensor Wireless Networks, 1(1-2), (2005). [16] Zorzi, M. and Rao, R. Geographic random forwarding (GeRaF) for ad hoc and sensor networks: Multihop performance. IEEE TMC 2(4), (2003) [17] /09/$ IEEE 492