Formal Analysis of a Scheduling Algorithm for Wireless Sensor Networks

In wireless sensor networks (WSNs), scheduling of the sensors is considered to be themost effective energy conservation mechanism. The random and unpredictable deployment of sensors in many WSNs in the open fieldsmakes the sensor scheduling problemvery challenging and thus randomized scheduling algorithms are used. The performance of these algorithms is usually analyzed using simulation techniques, which do not offer 100% accurate results. Moreover, probabilistic model checking, when used, does not include a strong support to reason accurately about statistical quantities like expectation and variance. In this paper, we overcome these limitations by using higher-order-logic theorem proving to formally analyze the coverage-based random scheduling algorithm for WSNs. Using the probabilistic framework developed in the HOL theorem prover, we formally reason about the expected values of coverage intensity, the upper bound on the total number of disjoint subsets, for a given expected coverage intensity, the lower bound on the total number of nodes and the average detection delay inside the network.

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