Randomly Duty-cycled Wireless Sensor Networks: Dynamics of Coverage

This paper studies wireless sensor networks that operate in low duty cycles, measured by the percentage of time a sensor is on or active. The dynamic change in topology as a result of such duty-cycling has potentially disruptive effect on the performance of the network. We limit our attention to a class of surveillance and monitoring applications and random duty-cycling schemes, and analyze certain coverage property. Specifically, we consider coverage intensity defined as the probability distribution of durations within which a target or an event is uncovered/unmonitored. We derive this distribution using a semi-Markov model, constructed using the superposition of alternating renewal processes. We also present the asymptotic (as the number of sensors approaches infinity) distribution of the target uncovered duration when at least one sensor is required to cover the target, and provide an asymptotic lower bound when multiple sensors are required to cover the target. The analysis using the semi-Markov model serves as a tool with which we can find suitable random duty-cycling schemes satisfying a given performance requirement. Our numerical observations show that the stochastic variation of duty-cycling durations affects performance only when the number of sensors is small, whereas the stochastic mean of duty-cycling durations impacts performance in all cases studied. We also show that there is a close relationship between coverage intensity and the measure of path availability, defined as the probability distribution of durations within which a path (of a fixed number of nodes) remains available. Thus the results presented here are readily applicable to the study of path availability in a low duty-cycled sensor network