A Relay Selection with Channel Probing in Sleep-Wake Cycling Wireless Sensor Networks

In geographical forwarding of packets in a large wireless sensor network (WSN) with sleep-wake cycling nodes, we are interested in the local decision problem faced by a node that has “custody” of a packet and has to choose one among a set of next-hop relay nodes to forward the packet towards the sink. Each relay is associated with a “reward” that summarizes the benefit of forwarding the packet through that relay. We seek a solution to this local problem, the idea being that such a solution, if adopted by every node, could provide a reasonable heuristic for the end-to-end forwarding problem. Towards this end, we propose a local relay selection problem comprising a forwarding node and a collection of relay nodes, with the relays waking up sequentially at random times. At each relay wake-up instant the forwarder can choose to probe a relay to learn its reward value, based on which the forwarder can then decide whether to stop (and forward its packet to the chosen relay) or to continue to wait for further relays to wake-up. The forwarder’s objective is to select a relay so as to minimize a combination of waiting-delay, reward and probing cost. The local decision problem can be considered as a variant of the asset selling problem studied in the operations research literature. We formulate the local problem as a Markov decision process (MDP) and characterize the solution in terms of stopping sets and probing sets. We prove results illustrating the structure of the stopping sets, namely, the (lower bound) threshold and the stage-independence properties. Regarding the probing sets, we make an interesting conjecture that these sets are characterized by upper bounds. Through simulation experiments we provide valuable insights into the performance of the optimal local forwarding and its use as an end-to-end forwarding heuristic.