Energy Efficient Sleep/Wake Scheduling for Multi-Hop Sensor Networks: Non-Convexity and Approximation Algorithm

We study sleep/wake scheduling for low duty cycle sensor networks. Our work is different from prior work in that we explicitly consider the effect of synchronization error in the design of the sleep/wake scheduling algorithm. In our previous work, we have studied sleep/wake scheduling for single hop communications, e.g., intra-cluster communications between a cluster head and cluster members. We showed that the there is an inherent trade-off between energy consumption and message delivery performance (defined as the message capture probability). We proposed an optimal sleep/wake scheduling algorithm, which satisfies a message capture probability threshold (assumed to be given) with minimum energy consumption. In this work, we consider multi-hop communications. We remove the previous assumption that the capture probability threshold is already given, and study how to decide the per-hop capture probability thresholds to meet the quality of services (QoS) requirements of the application. In many sensor network applications, the QoS is decided by the amount of data delivered to the base station(s), i.e., the multi-hop delivery performance. We formulate an optimization problem, which aims to set the capture probability threshold at each hop such that the network lifetime is maximized, while the multi-hop delivery performance is guaranteed. The problem turns out to be non-convex and hard to solve exactly. By investigating the unique structure of the problem and using approximation techniques, we obtain a solution that achieves at least 0.73 of the optimal performance.