Game-Theoretic Based Distributed Scheduling Algorithms for Minimum Coverage Breach in Directional Sensor Networks

A directional sensor network, where a lot of sensors are intensively and randomly deployed, is able to enhance coverage performances, since working directions can be partitioned into different K covers which are activated in a round-robin fashion. In this paper, we consider the problem of direction set K-Cover for minimum coverage breach in directional sensor networks. First, we formulate the problem as a game called direction scheduling game (DSG), which we prove as a potential game. Thus, the existence of pure Nash equilibria can be guaranteed, and the optimal coverage is a pure Nash equilibrium, since the potential function of DSGs is consistent with the coverage objective function of the underlying network. Second, we propose the synchronous and asynchronous game-theoretic based distributed scheduling algorithms, which we prove to converge to pure Nash equilibria. Third, we present the explicit bounds on the coverage performance of the proposed algorithms by theoretical analysis of the algorithms' coverage performance. Finally, we show experimental results and conclude that the Nash equilibria can provide a near-optimal and well-balanced solution.