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

This paper investigates the problem of providing network coverage using wireless sensors that operate on low duty cycles (measured by the percentage time a sensor is on or active), i.e., each sensor alternates between active and sleep states to conserve energy with an average sleep period (much) longer than the active period. The dynamic change in topology as a result of such duty-cycling has potentially disruptive effect on the operation and performance of the network. This is compensated by adding redundancy in the sensor deployment. In this paper we examine the fundamental relationship between the reduction in sensor duty cycle and the required level of redundancy for a fixed performance measure, and explore the design of good sensor sleep schedules. In particular, we consider two types of mechanisms, the random sleep type where each sensor keeps an active-sleep schedule independent of another, and the coordinated sleep type where sensors coordinate with each other in reaching an active-sleep schedule. Both types are studied within the context of providing network coverage. We present specific scheduling algorithms within each type, and illustrate their coverage and duty cycle properties via both analysis and simulation. We show with either type of sleep schedule the benefit of added redundancy saturates at some point in that the reduction in duty cycles starts to diminish beyond a certain threshold in deployment redundancy. We also show that at the expense of extra control overhead, a coordinated sleep schedule is more robust and can achieve higher duty cycle reduction with the same amount of redundancy compared to a random sleep schedule.