Extensions of proportional-fair sharing algorithms for multi-access control of mobile communications: constraints and bursty data processes

We are concerned with the scheduling of transmitter time, bandwidth and power for multi-access mobile communications for data communications when the channels are randomly time varying. Time is divided into small scheduling intervals, called slots, and information on the current channel rates for the various users is available at the start of the slot, when the user selections are made. The proportional fair sharing method (PFS) balances the conflict between selecting the users with the best immediate rates and helping those with poor average throughputs. We have analyzed the convergence and basic qualitative properties (Kushner, H.J. and Whiting, P.A., Proc. Allerton Conf., 2002; IEEE Trans. Wireless Commun., vol.3, p.1250-9, 2004). The paths of the throughputs converge to the solution of an ODE, akin to a mean flow. The behavior of the ODE describes the behavior of PFS. It has a unique equilibrium point that is asymptotically stable and optimal for PFS in that it is the maximizer of a concave utility function. Most past work assumed an infinite backlog of data. The data arrival process is often bursty with the data queued until transmitted, minimal throughput constraints, or a balance between queue length (or delay) and throughput, might be sought. There might be preemption by priority users. Natural modifications of PFS for these cases are shown to have some of the same properties. Simulations illustrate many of the features and the possible tradeoffs.