A Methodology for Optimal MAC Protocol Generation: Case Study of a Synchronous MAC Channel

We describe a methodology that incorporates the impact of control information transfer into MAC protocol optimization. We apply this methodology to the problem of a synchronous broadcast MAC channel, to generate the optimal protocol when the objective function is the average network throughput per slot. We describe a recursive procedure for the symbolic generation of the optimization program for any choice of the objective function. We demonstrate that this methodology produces the Random Access Channel and protocols with control information as special cases in the regimes where they are optimal. We examine the scaling of optimal throughput and of computational complexity as a function of the number of nodes and the control lifetime.