Optimal Dynamic Routing for the Wireless Relay Channel
  Consider a communication network with a source, a relay and a destination. Each time interval, the source may dynamically choose between a few possible coding schemes, based on the channel state, traffic pattern and its own queue status. For example, the source may choose between a direct route to the destination and a relay-assisted scheme. Clearly, due to the difference in the performance achieved, as well as the resources each scheme uses, a sender might wish to choose the most appropriate one based on its status.   In this work, we formulate the problem as a Semi-Markov Decision Process. This formulation allows us to find an optimal policy, expressed as a function of the number of packets in the source queue and other parameters. In particular, we show a general solution which covers various configurations, including different packet size distributions and varying channels. Furthermore, for the case of exponential transmission times, we analytically prove the optimal policy has a threshold structure, that is, there is a unique value of a single parameter which determines which scheme (or route) is optimal. Results are also validated with simulations for several interesting models. 
Asaf Cohen, Dennis Goeckel, Omer Gurewitz, Daniel S. Menasche, Mark   Shifrin
cs.IT cs.SY math.IT