Upper and lower bounds for dynamic cluster assignment for multi-target tracking in heterogeneous WSNs

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Highlights

  • Modeling a cluster-based target tracking problem in WSNs as an Integer Linear Programming model.

  • Lagrangian relaxation upper bound shows a better bound than pure LP relaxation.

  • LP relaxation with Randomized Rounding provides a good lower bound.

  • Results of heuristic clustering methods remain between the upper and lower bounds.

  • Dynamic clustering methods are better than hybrid ones in small numbers of targets.

Abstract

In this paper, we consider the problem of cluster task assignment to maximize total utilities of nodes for target coverage in heterogeneous Wireless Sensor Networks. We define this problem as assigning the tasks of Cluster Head (CH) and Cluster Members (CM) to nodes for each target and requiring communication connectivity between every CH with its members. The utility of each node for each target is defined as a function of its distance to the target and its remaining energy. We propose an upper bound based on Lagrangian Relaxation (LR) and a lower bound by Linear Programming (LP) relaxation with a combination of Randomized Rounding (RR) and a greedy-based heuristic. Furthermore, we propose a distributed heuristic algorithm based on matching and a general assignment problem. Dynamic movements of targets are taken into account by intra/inter-cluster task reassignments. Simulation results, compared with optimal values, reveal that the LR upper bound performs better than the bound reached by pure LP relaxation. The lower bound obtained by LP relaxation combined with the RR technique provides close results in comparison with the distributed heuristic algorithm. Furthermore, the results of the distributed heuristic algorithm remain between the upper and lower bounds and close to optimal values.

Introduction

Wireless Sensor Networks (WSNs) consist of small-sized low cost sensor nodes with limited resources of computation, energy and wireless communications. Traditional applications of these networks include long time monitoring of environments, event detection and mobile target tracking  [30].

From the application layer point of view, a WSN’s mission (or application) can be represented as a set of tasks (or roles)  [17]   [19]. Task assignment has received a lot of attention, especially in parallel processing, distributed systems and servers  [21]   [25]. It also stays in close relation with some resource allocation and scheduling problems  [8], [16], [27], [29].

For WSNs, optimal task assignment remains an important issue due to their scarce availability of resources and their application-dependent nature. For instance, in cluster-based target tracking methods, dynamic movements of targets require task reassignments which may induce high energy consumption and considerable amount of message exchanges among nodes  [24], [18].

In this paper, we consider a target tracking mission from the task assignment point of view in a pre-deployed configuration of sensors. The mission consists of Cluster Head (CH) and Cluster Member (CM) tasks which are reassigned to nodes when the targets have dynamic movements. We assume a slow dynamic (time varying) environment such that each target is assigned to one sensor node holding the CH task and a number of other nodes which hold the CM tasks. The cluster members send their readings to the CH which performs a localization algorithm for determining the location of the target. We assume passive sensors, such as acoustic sensor nodes, and the localization of targets by sensors’ location is performed via the lateration method which is based on distances  [4]. For the special method of Trilateration, three CM nodes are required while multilateration requires more nodes to improve the accuracy which degrades due to errors in measurements. Therefore, we define the number of CM nodes to remain within a minimum and maximum value. In our problem, connectivity constraint is additionally required between each CH and its CMs, while we assume heterogeneous sensor nodes with different communication and sensing ranges for different nodes.

The main contributions of this paper are that we provide an Integer Linear Programming (ILP) model for this problem and propose an upper bound according to the Lagrangian relaxation. A lower bound is also obtained with LP relaxation together with the Randomized Rounding technique and a greedy-based heuristic algorithm. Furthermore, a distributed heuristic is provided based on matching and assignment which considers task reassignments for the case of targets movements with intra/inter-cluster reassignments.

Despite that the upper and lower bound algorithms are executed in a centralized manner, they have great importance in providing an insight into the level of correctness of optimal and heuristic results. To the best of our knowledge, these approaches have not been taken into account in any of the task assignment related studies especially for target tracking in WSNs. In addition, the method we present here for obtaining the upper and lower bounds can be applied to any other complicated and developed clustering technique as long as the constraints are defined within an LP model (or more generally a convex model). Results of these methods are compared with optimal values in terms of performance measures, such as the number of CH and CM nodes, total utilities of nodes and overhead of control packets.

The rest of this paper is as follows: Section  2, reviews some of the most related studies according to our problem. Section  3, defines the assumptions and the formulation of our problem. In Section  4, we provide the upper and lower bounds with the distributed heuristic algorithm. In Section  5, simulation results are presented and finally in Section  6 we conclude the paper.

Section snippets

Related work

The clustering concept has been taken into account in the past by many researches in the field of WSN. In LEACH  [11], as the most well-known method for clustering in WSNs, each node is selected as a cluster head in each round with a probability. In  [5], CPEQ is a cluster-based periodic, event-driven and query-based protocol which improves the routing strategy PEQ through data aggregation when comparing their energy maps. Due to the fact that the clustering measure is mostly dependent on the

Assumptions and problem formulation

We assume that the tracking WSN consists of a set of static sensor nodes denoted as S={s1,s2,,sN} and the set of targets or objects with O={o1,o2,,oM}, such that M<N, i.e., there are more sensor nodes in the area than the targets. These nodes and targets are distributed randomly across the area. We divide the total duration of the target tracking network into a finite number of time intervals, in which the targets are assumed to be static in these intervals, but their locations are not

Lower and upper bounds and algorithms

In this section, we provide three solutions to the problem 1-CTA in centralized and distributed fashions. We have used two approaches in this section in addition to the heuristic method.

  • By LP relaxation of the integer variables and rounding the fractional solutions by the Randomized Rounding technique  [23] and a greedy-based heuristic.

  • By Lagrangian Relaxation (LR) of the original ILP problem.

Despite that the LR method does not necessarily reach feasible solutions for xij and yij variables,

Simulation results

To evaluate and compare the performance of our algorithms, we implemented DAMA and LPR3, as application layer algorithms, with the C++ programming language, the LRUB method and the fractional solutions of LPR3 by AIMMS 3.11  [3], and the results of HCTT algorithm from our previous work  [10]. The latter is chosen as a hybrid clustering target tracking method implemented by the Castalia 3.2 framework  [26]. We evaluated the measures of the number of CH nodes, number of CM nodes, total utility of

Conclusion and future work

In this paper, we investigated the possibility of obtaining upper and lower bounds for a dynamic cluster assignment scenario. We assumed the tasks of CH and CM for nodes and a utility function for each node based on its distance to the targets and its remaining energy. An upper bound is reached with applying the Lagrangian relaxation which shows near optimal values and is much better than LP relaxation upper bound. The lower bound is obtained by LP relaxation and rounding the results by

Acknowledgment

This work was supported in part by Iran Telecommunications Research Center (ITRC) under grant #1042/500. The authors would like to thank Dr. Khonsari and Mr. Seyed Majid Zahedi at the Institute for Research in Fundamental Sciences (IPM), and Ms. Farnaz Hooshmand at the Mathematics Department of Amirkabir University of Technology, Tehran, Iran, for their precious assistance.

Marjan Naderan received her B.Sc. degree in Computer Engineering in 2004 and the M.Sc. degree in Information Technology in 2006 both from Sharif University of Technology, Tehran, Iran. She received the Ph.D. degree in Computer Engineering, major in computer networks in Feb. 2012, from Amirkabir University of Technology (AUT), Tehran, Iran. Dr. Naderan has joined the Computer Engineering Department of Shahid Chamran University in Ahwaz, Iran since 2012. She has reviewed papers in several

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  • Cited by (0)

    Marjan Naderan received her B.Sc. degree in Computer Engineering in 2004 and the M.Sc. degree in Information Technology in 2006 both from Sharif University of Technology, Tehran, Iran. She received the Ph.D. degree in Computer Engineering, major in computer networks in Feb. 2012, from Amirkabir University of Technology (AUT), Tehran, Iran. Dr. Naderan has joined the Computer Engineering Department of Shahid Chamran University in Ahwaz, Iran since 2012. She has reviewed papers in several journals and conferences such as VTC, ICC, JNCA, JPDC, Journal of Supercomputing and Transactions on Communications. Her research interests include computer networks, wireless and mobile networks, object tracking, network optimization and simulation of network protocols.

    Mehdi Dehghan received his B.Sc. degree in Computer Engineering from Iran University of Science and Technology (IUST), Tehran, Iran, in 1992, and his M.Sc. and Ph.D. degrees from Amirkabir University of Technology (AUT), Tehran, Iran, in 1995, and 2001, respectively. He joined the Computer Engineering and Information Technology Department of Amirkabir University of Technology in 2004. Currently, as an Associate Professor, Dr. Dehghan is the Director of the Mobile Ad hoc and Wireless Sensor Lab at AUT. His research interests include high speed networks, network management, mobile ad hoc networks and fault-tolerant computing.

    Hossein Pedram received his B.Sc. degree in Electrical Engineering in 1977 from Sharif University of Technology, Tehran, Iran. He continued with the M.Sc. degree in Electrical Engineering in 1980 from Ohio State University, Columbus, Ohio, USA, and the Ph.D. degree in Computer Engineering in 1992 from Washington State University, Pullman, Washington, USA. Dr. Pedram is currently an associate professor at the Computer Engineering and Information Technology Department in Amirkabir University of Technology (AUT), Tehran, Iran, and he is also the director of the Asynchronous lab at AUT. His research interests include computer architecture, asynchronous design, network on chip, innovations in computer architecture, distributed systems and networking.

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    Postal address: Mobile Ad hoc and Wireless Sensor Networks lab, Department of Computer Engineering and Information Technology, Amirkabir University of Technology, PO Box 15875-4413, 424 Hafez Avenue, Tehran, Iran.

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