Computer Science – Networking and Internet Architecture
Scientific paper
2011-07-28
Computer Science
Networking and Internet Architecture
24 pages, 5 figures
Scientific paper
Motivated by the problem of distributed geographical packet forwarding in a wireless sensor network with sleep-wake cycling nodes, we propose a local forwarding model comprising a node that wishes to forward a packet towards a destination, and a set of next-hop relay nodes, each of which is associated with a reward that summarises the cost/benefit of forwarding the packet through that relay. The relays wake up at random times, at which instants they reveal only the probability distributions of their rewards (e.g., by revealing their locations). To determine a relay's exact reward, the forwarding node has to further probe the relay, incurring a probing cost. Thus, at each relay wake-up instant, the source, given a set of relay reward distributions, has to decide whether to stop (and forward the packet to an already probed relay), continue waiting for further relays to wake-up, or probe an unprobed relay. We formulate the problem as a Markov decision process, with the objective being to minimize the packet forwarding delay subject to a constraint on the effective reward (the difference between the total probing cost and the actual reward of the chosen relay). Our problem can be considered as a variant of the asset selling problem with partial revelation of offers. The most general class of decision policies can keep awake any or all the relays that have woken up. In this paper, we study the optimum over a restricted class of policies which, at any time, can keep only one unprobed relay awake, in addition to the best among the probed relays. We prove that the optimum stopping policy over this class is of threshold type, where the same threshold is used at each relay wake-up instant. Numerically, we find that the performance of the optimum over the restricted class is very close to that over the unrestricted class.
Kumar Anurag
Naveen K. P.
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