Convergence of Distributed WSN Algorithms: The Wake-Up Scattering Problem

In this paper, we analyze the problem of finding a periodic schedule for the wake-up times of a set of nodes in a Wireless Sensor Network that optimizes the coverage of the region the nodes are deployed on. An exact solution of the problem entails the solution of an Integer Linear Program and is hardly viable on low power nodes. Giusti et. al. [6] have recently proposed an efficient decentralized approach that produces a generally good suboptimal solution. In this paper, we study the convergence of this algorithm by casting the problem into one of asymptotic stability for a particular class of linear switching systems. For general topologies of the WSN, we offer local stability results. In some specific special cases, we are also able to prove global stability properties.

[1]  Jan Vitek,et al.  Redundancy and coverage detection in sensor networks , 2006, TOSN.

[2]  Francesco Bullo,et al.  Optimal sensor placement and motion coordination for target tracking , 2006, Autom..

[3]  Mireille E. Broucke,et al.  Formations of vehicles in cyclic pursuit , 2004, IEEE Transactions on Automatic Control.

[4]  Carl D. Meyer,et al.  Matrix Analysis and Applied Linear Algebra , 2000 .

[5]  Tarek F. Abdelzaher,et al.  Towards optimal sleep scheduling in sensor networks for rare-event detection , 2005, IPSN 2005. Fourth International Symposium on Information Processing in Sensor Networks, 2005..

[6]  Ian F. Akyildiz,et al.  Wireless sensor networks , 2007 .

[7]  Di Tian,et al.  A coverage-preserving node scheduling scheme for large wireless sensor networks , 2002, WSNA '02.

[8]  Weili Wu,et al.  Energy-efficient target coverage in wireless sensor networks , 2005, Proceedings IEEE 24th Annual Joint Conference of the IEEE Computer and Communications Societies..

[9]  Amy L. Murphy,et al.  Decentralized Scattering of Wake-Up Times in Wireless Sensor Networks , 2007, EWSN.

[10]  Xiaohua Jia,et al.  Maximizing Lifetime of Sensor Surveillance Systems , 2007, IEEE/ACM Transactions on Networking.

[11]  Jie Lin,et al.  Coordination of groups of mobile autonomous agents using nearest neighbor rules , 2003, IEEE Trans. Autom. Control..

[12]  Reza Olfati-Saber,et al.  Consensus and Cooperation in Networked Multi-Agent Systems , 2007, Proceedings of the IEEE.

[13]  Sulema Aranda,et al.  On Optimal Sensor Placement and Motion Coordination for Target Tracking , 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation.

[14]  Miodrag Potkonjak,et al.  Power efficient organization of wireless sensor networks , 2001, ICC 2001. IEEE International Conference on Communications. Conference Record (Cat. No.01CH37240).

[15]  Qunfeng Dong,et al.  Maximizing system lifetime in wireless sensor networks , 2005, IPSN 2005. Fourth International Symposium on Information Processing in Sensor Networks, 2005..

[16]  F. Bullo,et al.  On Synchronous Robotic Networks—Part I: Models, Tasks, and Complexity , 2005, IEEE Transactions on Automatic Control.

[17]  Songwu Lu,et al.  PEAS: a robust energy conserving protocol for long-lived sensor networks , 2003, 23rd International Conference on Distributed Computing Systems, 2003. Proceedings..

[18]  Luigi Palopoli,et al.  Maximizing Sensing Coverage in Wireless Sensor Networks Through Optimal Scattering of Wake-up Times , 2007 .

[19]  Ruggero Carli,et al.  Communication constraints in the average consensus problem , 2008, Autom..

[20]  Emilio Frazzoli,et al.  On synchronous robotic networks Part II: Time complexity of rendezvous and deployment algorithms , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[21]  Mingyan Liu,et al.  Network coverage using low duty-cycled sensors: random & coordinated sleep algorithms , 2004, Third International Symposium on Information Processing in Sensor Networks, 2004. IPSN 2004.