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A flow-based reliability measure for wireless sensor networks

In Wireless Sensor Networks (WSNs), reliable monitoring of a phenomenon depends on the collective data provided by clusters of sensor nodes and not on any individual node. Thus, the design of a WSN may impose constraints on the minimum average data rate that is required to be gathered from the sensor nodes and delivered to a sink node. In this paper, we define a WSN reliability measure that quantifies the likelihood that a network can deliver such minimum required data flow where the individual sensor components are subject to random failures. Given a specification of the average data rate generated by each sensor node, the operation probability of each sensor and the connectivity graph of a WSN, we formulate the reliability measure and show that the problem of computing the exact reliability of any arbitrary WSN is #P-hard. Thus, it is unlikely that an efficient algorithm for computing exact solutions exists. We present two exponential algorithms for handling networks with arbitrary topologies. We then consider some special cases where we can either compute or approximate the reliability efficiently. Finally, we present numerical results that demonstrate potential applications of the devised algorithms in WSN design.