Relay selection with channel probing for geographical forwarding in WSNs

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. Each of the relays is associated with a “reward” that summarizes the cost/benefit of forwarding the packet through that relay. We seek a locally optimal solution to this problem, the idea being that such a solution, if adopted by every node, could provide a reasonable local heuristic for the end-to-end forwarding problem. Towards this end, we propose a local forwarding problem where the relays wake-up at random times, at which instants they reveal the probability distributions of their rewards. To determine a relay's exact reward, the source has to further probe the relay, incurring a probing cost. Thus, at each relay wake-up instant, the forwarding node, given the reward value of an already probed relay and the reward distribution of an unprobed relay, has to decide whether to stop (and forward the packet to the probed relay), continue waiting for further relays to wake-up, or probe the unprobed relay. We formulate this local forwarding problem as a Markov decision process (MDP) and obtain some interesting structural results on the optimal policy. Our problem can be considered as a new variant of the asset selling problem studied in the operations research literature.