An SMDP Approach to Optimal PHY Configuration in Wireless Networks

In this work, we study the optimal configuration of the physical layer in wireless networks by means of Semi-Markov Decision Process (SMDP) modeling. In particular, assume the physical layer is characterized by a set of potential operating points, with each point corresponding to a rate and reliability pair; for example, these pairs might be obtained through a now-standard diversity-vs-multiplexing tradeoff characterization. Given the current network state (e.g., buffer occupancies), a Decision Maker (DM) needs to dynamically decide which operating point to use. The SMDP problem formulation allows us to choose from these pairs an optimal selection, which is expressed by a decision rule as a function of the number of awaiting packets in the source's finite queue, channel state, size of the packet to be transmitted. We derive a general solution which covers various model configurations, including packet size distributions and varying channels. For the specific case of exponential transmission time, we analytically prove the optimal policy has a threshold structure. Numerical results validate this finding, as well as depict muti-threshold policies for time varying channels such as the Gilber-Elliott channel.