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On the planning of Wireless Sensor Networks: Energy-Efficient Joint Clustering and Routing under Coverage Constraint Ali Chamam, Student Member, IEEE, Hichem Ayed Harhira, Student Member, IEEE and Samuel Pierre, Senior Member, IEEE Department of Electrical Engineering Polytechnique, Montréal, Canada Present by C.T. Lee 2007 / 10 / 2 1/38 Outline I. II. III. IV. V. VI. VII. VIII. Introduction Related Work Problem Statement and Assumption Problem Modeling Proposed Heuristic Simulation Results Conclusion Comments 2/38 I. Introduction (1/5) Minimizing energy dissipation and maximizing network lifetime are among the central concerns when designing sensor networks’ applications and protocols. Authors address the global problem of maximizing network lifetime under the joint clustering, routing and coverage constraints. First, authors formulate this global problem as an Integer Linear Programming model. Then, authors implement a greedy heuristic algorithm to tackle the exponentially-increasing problem. Experimental results show that the proposed centralized algorithm provides near-optimal network lifetime values while performing low computation times, 3/38 practically suitable for large-size sensor networks. Introduction (2/5) Generally, energy conservation is dealt with on five different levels 1. Efficient scheduling of sensor states to alternate between sleep and active modes; 2. Efficient control of transmission power to ensure an optimal tradeoff between energy consumption and connectivity; 3. Energy-efficient routing, clustering and data aggregation; 4. Data compression (source coding) to reduce the amount of transmitted data; 5. Efficient channel access and packet retransmission protocols on the Data Link Layer. The scope of this paper includes both the first and the third levels. 4/38 Introduction (3/5) Authors consider a sensor network that is deployed in a certain area A to monitor some given events. The network is dense, sensing ranges of neighbor sensors usually overlap. That means that when an event occurs at a point P of A, it will be detected and reported by all the sensors that are switched-on and whose sensing range encompasses P. 5/38 Introduction (4/5) To save network energy and increase its lifetime, authors propose to switch on only a subset of sensors that covers A (above a given pre-defined coverage rate) while all other sensors will be turned off. Figure 2 depicts an example of full-covering sensor set. 6/38 Introduction (5/5) However, in the best of authors' knowledge, the optimal global planning of sensors’ states maximizing network lifetime while considering the joint clustering, coverage and routing constraints within the same optimization process has not been addressed. In authors' architecture, only CHs can route data Because they have enough energy to do so. 7/38 Outline I. II. III. IV. V. VI. VII. VIII. Introduction Related Work Problem Statement and Assumption Problem Modeling Proposed Heuristic Simulation Results Conclusion Comments 8/38 II. Related Work Cluster formation is typically based on the energy reserve of sensors and sensors proximity to the cluster head. For instance, LEACH (Low-Energy Adaptive Clustering Hierarchy). It uses single-hop routing where each node can transmit directly to the cluster-head and the sink. Therefore, it is not applicable to networks deployed in large regions. PEGASIS (Power-Efficient GAthering in Sensor Information Systems) is improvements of LEACH. Rather than forming multiple clusters. PEGASIS forms chains of sensor nodes so that each node transmits and receives from a neighbor and only one node is selected from that chain to transmit to the PN. Excessive delay In [8], Yao and Giannakis propose an algorithm that finds minimizes the dissipated energy of the whole network over the period T. But no coverage constraint is considered. 9/38 Outline I. Introduction II. Related Work III. Problem Statement and Assumption IV. Problem Modeling V. Proposed Heuristic VI. Simulation Results VII. Conclusion VIII. Comments 10/38 III. Problem Statement and Assumption (1/4) As shown in [5] for the case of WINS Rockwell seismic sensors, a sensor can be in one of the following four activity modes, characterized by their respective power consumptions: Transmit (0.38 - 0.7 W), Receive (0.36 W), Idle (0.34 W) and Sleep (0.03 W). As depicted in Figure 3, authors will consider, without loss of generality, that each sensor can be in one of three states: Sleep, Active and Cluster Head (CH) having respectively power consumptions ESleep, EActive and ECH per time unit, where ESleep << EActive < ECH. 11/38 Problem Statement and Assumption (2/4) Data received by CHs from sensors has to be routed toward the PN. As shown on Figure 4, this makes the overlay network formed by the CHs sufficient to route data from any sensor toward the PN. 12/38 Problem Statement and Assumption (3/4) Definition 1: A set of sensors Sc is a covering set of area A if and only if: point PA; i Sc such as i covers P. In this problem, the optimal network configuration must: contain a full-covering set of active sensors; contain a set of CHs so that connectivity of every sensor to a CH is ensured; ensure that all CHs belong to a spanning tree over which data will be routed toward the PN. Authors' objective is to find the optimal allocation of sensors’ states (Active, Sleep, CH) that meets these three conditions, while minimizing the consumed energy of each node. 13/38 Problem Statement and Assumption (4/4) Before modeling authors' problem, authors make the following assumptions: 1. The ID and the position of each sensor are fixed and known to both the PN and the sensor itself. 2. Active sensors capture events occurring in their range and transmit data associated with these events straightaway, without any buffering, because sensors are usually not equipped with large (and costly) buffers. 3. All sensors have the same sensing range Rc. 4. Only CHs can perform data routing. Routing over the overlay network composed of CHs can be performed using one of the energy-efficient routing protocols for sensor networks proposed in the literature [14]. However, authors do not address any specific routing mechanism. 5. Each sensor has an initial energy E0. The Sink is assumed to have no energy limitation. Authors assume that, when a sensor is Active, it dissipates the same energy during a unit of time, no matter how the events’ distribution is. 6. The network is dense enough so that when all the sensors are Active, the monitored area is fully covered. Besides, authors assume that the sensor network is connected with respect to the sensors’ transmission range. 7. Network lifetime is defined as the time separating the instant the network starts operating and the instant of the first node failure due to energy exhaustion. 8. Authors assume ideal MAC layer conditions. That is, perfect transmission of data on a node-to-node wireless link. 9. Authors assume that sensors have idealized sensing capabilities. That is, inside the sensor’s range, quality of sensing does not depend on the distance 14/38 from the sensor. Outline I. II. III. IV. V. VI. VII. VIII. Introduction Related Work Problem Statement and Assumption Problem Modeling Proposed Heuristic Simulation Results Conclusion Comments 15/38 IV. Problem Modeling (1/10) Objective of the problem is to find the optimal allocation of states to sensors that maximizes the network lifetime. To maximize network lifetime minimizing total energy consumption and energy consumption balancing among sensors Original ILP (exponentially-increasing number of subsets of S) Reformulation (non-linear term) ILP (linearize, NPC) Greedy heuristic algorithm 16/38 Problem Modeling (2/10) To model this optimization problem, authors first define the following sets and constants: Then, authors define following binary decision variables i = 1..|S|; j = 1..|S|: 17/38 Problem Modeling (3/10) To balance energy consumption among nodes, authors choose to minimize an objective function that is a linear combination of sensors scores. The score of a sensor i is defined by: System favors the activation of sensors having relatively higher residual energy. Eri is the remaining energy of sensor i. Edi≒5 18/38 Problem Modeling (4/10) 19/38 Problem Modeling (5/10) 20/38 Problem Modeling (6/10) Objective function (1a) aims to balance the energy consumption over the network. Constraint (1b) guarantees a full coverage of the monitored area, such that every elementary cell is covered by at least one Active sensor. Constraint (1d) ensures that there exist at least a CH located one hop from the PN. Constraints (1e) to (1h) ensure that every Active and non-CH sensor is connected to at least one CH within its range. Constraint (1i) gives an upper bound on the clusters size, such that a CH serves at most Nmax Active sensors. Equations (1j) to (1n) describe the routing constraint ensuring that the overlay network composed of CHs is connected and hence, there exist a tree-like partial subgraph. 1o are the integrality constraints. To ensure that a spanning tree connecting all the CHs exists in any solution, constraints (1m) and (1n) require the enumeration of all the subsets of S. 21/38 Problem Modeling (7/10) Even though these constraints represent the theoretical conditions to have a spanning tree in any graph (no cycles and a connected graph), they quickly result in a combinatorial explosion of the number of constraints due the exponentiallyincreasing number of subsets of S. To circumvent this problem, authors will proceed differently to force any solution to have all its CHs connected to the same spanning tree: authors represent the routing constraint of authors' problem as a multi-flow routing problem. 22/38 Problem Modeling (8/10) To model this virtual flow routing problem, authors define a binary variable representing the use of the wireless link lk to convey a flow (i, j), where i, j, k and l are CHs and i, j are respectively the source and destination of the flow. Let: 23/38 Problem Modeling (9/10) The following constraints ensure that the network contains a spanning tree connecting all CHs: Intermediate node Source node Destination node 24/38 Problem Modeling (10/10) Equation (2a) is the flow constraint ensuring that a feasible path exists between any pair of CHs to convey an elementary unit of flow. Remaining constraints (2b) to (2e) limit the relevance of this virtual flow problem to the overlay network. Constraint (2f) is finally the integrality constraints. In (2a) is a non-linear term that needs to be linearized. For that, authors define: To have a logical equivalence between Uij and Xi,Yj , authors add the following constraints: 25/38 Outline I. Introduction II. Related Work III. Problem Statement and Assumption IV. Problem Modeling V. Proposed Heuristic VI. Simulation Results VII. Conclusion VIII. Comments 26/38 V. Proposed Heuristic (1/3) Authors propose a greedy heuristic algorithm that finds acceptable solutions in reasonable computation times. As shown on Algorithm 1. At each iteration, the node having the highest score f as a CH. The score of a sensor i is given by: Where i is the number of its neighboring sensors that are not already connected to any CH. The shape of this score function is shown on Figure 6. 27/38 Proposed Heuristic (3/3) 28/38 Proposed Heuristic (2/3) maximizing maximizing >=1 29/38 Outline I. II. III. IV. V. VI. VII. VIII. Introduction Related Work Problem Statement and Assumption Problem Modeling Proposed Heuristic Simulation Results Conclusion Comments 30/38 VI. Simulation Results (1/3) A. Comparative performance evaluation: GR-RCC vs. CPLEX For instance, for a topology of 49 sensors, the gap between GR-RCC and CPLEX is about 35/43 = 81.4% which is quite acceptable. 31/38 Simulation Results (2/3) B. Performance evaluation of GR-RCC: Impact of the sensing range 32/38 Simulation Results (3/3) C. Performance evaluation: of GR-RCC: Impact of the maximum cluster size 33/38 Outline I. II. III. IV. V. VI. VII. VIII. Introduction Related Work Problem Statement and Assumption Problem Modeling Proposed Heuristic Simulation Results Conclusion Comments 34/38 VII. Conclusion In this paper, authors proposed a novel centralized mechanism for near-optimal state assignment to sensors in large-scale cluster-based monitoring sensor networks. GR-RCC’s mechanism maximizes network lifetime while ensuring the full coverage of the monitored area and the network connectivity. Despite its centralized aspect, GR-RCC’s mechanism exhibits low complexity and low computation times making its practical implementation adaptable for large-scale networks. As future research directions, authors intend to develop a more sophisticated heuristic algorithm to improve the network lifetime Furthermore, authors intend to consider distancedependent probabilistic event detection LR approach solves this problem 35/38 Outline I. II. III. IV. V. VI. VII. VIII. Introduction Related Work Problem Statement and Assumption Problem Modeling Proposed Heuristic Simulation Results Conclusion Comments 36/38 VIII. Comments Strengths Authors propose an optimal allocation of states to sensors that maximizes the network lifetime, while ensuring simultaneously full area coverage, connectivity of every sensor to a CH and connectivity of the overlay network composed of CHs References are sufficient and appropriate Weaknesses In page 11 Fig. 5, authors do not make it clear Recommended Changes Page 5: For example, in [17], Yaoand Giannakis propose [8] Page 12: (1n) |S| S Page 12: Equations (1b) to (??) Equations (1b) to (1o) Page 16: (5b) RHS >=1 Page 16: minimizing maximizing Recommendation 37/38 Authors should prepare a minor revision Q&A Thank You for Your Attention. 38/38