Decentralized control for optimal energy-delay tradeoff in cooperative relay communications

In a multi-hop cooperative communication scenario, where a transmitter can transmit a packet directly to the receiver or indirectly through a relay, there is an inherent trade-off between energy and delay. While it may consume more energy to transmit a packet directly to the receiver than transmitting through a relay, the transmission through relay incurs more delay. We consider the MAC layer of a transmission scheme involving a transmitter, a receiver and a relay, where average delay is related to the queue size of the transmitter and relay. We pose this problem as an infinite horizon stochastic control problem in a decentralized setup where the information about the queue size of a node is not available to the other node. We prove a structural result that the optimal policy is the solution of a dynamic programming equation and the optimization is done over a time invariant state space.