  We consider a wireless sensor network whose main function is to detect
certain infrequent alarm events, and to forward alarm packets to a base
station, using geographical forwarding. The nodes know their locations, and
they sleep-wake cycle, waking up periodically but not synchronously. In this
situation, when a node has a packet to forward to the sink, there is a
trade-off between how long this node waits for a suitable neighbor to wake up
and the progress the packet makes towards the sink once it is forwarded to this
neighbr. Hence, in choosing a relay node, we consider the problem of minimizing
average delay subject to a constraint on the average progress. By constraint
relaxation, involving a Lagrange multiplier, we formulate this next hop relay
selection problem as a Markov decision process (MDP). The exact optimal
solution (BF (Best Forward)) can be found, but is computationally intensive.
Next, we consider a mathematically simplified model for which the optimal
policy (SF (Simplified Forward)) turns out to be a simple one-step-look-ahead
rule. Simulations show that SF is very close in performance to BF, even for
reasonably small node density. We then study the end-to-end performance of SF
in comparison with two extremal policies: Max Forward (MF), which makes the
maximum possible progress per hop and thus reduces network energy consumption,
and First Forward (FF), which forwards the packet to the first node to wake up,
and thus tends to make end-to-end forwarding delays small. We find that, with
appropriate choice of one hop average progress constraint, SF can be tuned to
provide a favorable trade-off between end-to-end packet delay and the number of
hops in the forwarding path.
