A Three-State Node Reliability Model for Sensor Networks

In this paper we formulate and analyze a model for assessing the reliability of a wireless sensor network (WSN) based on classifying the operating states of each node at any instant into one of three possible states: a state where both the sensing and wireless modules are operating, a state where only the wireless module is operating, and a state where the wireless module is failed. Thus, in the second state a node can only relay traffic among its neighbours without generating its own data. We define the reliability of a WSN as the probability that the sink node can collect data from a number of nodes whose total weight exceeds a specified threshold limit, given that each node can be in any one of the three possible states with a given probability. Existing results in the literature show that a restricted 2-state version of the problem is #P-hard even when the network is a rectangular grid. Nevertheless, for a rectangular WxL grid on n nodes where the sink node lies in one of the corners, the restricted 2-state reliability problem can be solved in O(nL2^W) time. Thus, the algorithm runs in polynomial time for any fixed W. Our work here derives an exact algorithm for the generalized 3-state reliability model on a generalized class of grids, called diagonalized grids, while maintaining the same O(nL2^W) running time. We obtain numerical results that illustrate the use of the devised algorithm as a WSN topological design tool.