Delay optimal multiaccess communication for general packet length distributions

An M-user Gaussian multiaccess channel with noise density No/2 and bandwidth W is studied. The M data sources generate packets according to independent Poisson processes with a common rate A. The goal is to design a controller, which allocates rates from C to the transmitters as a function of the joint queue state, so as to minimize average system delay. We consider the multiaccess channel with general packet length distributions. A policy giving longer queues higher rates (LQHR) for all increasing, Schur-convex functions is showed. A new technique combining dynamic programming and renewal theory to prove that a modified version of the LQHR policy minimizes for the two-user case is deviced.