Scaling Limits for Stochastic Network Models Application to Wireless Communications

The capacity of a wireless communication system is constrained by a set of scarce resources. These transmission resources must be allocated so as to maximize the capacity at the physical layer. Here stochastic control and optimization offer a powerful mathematical framework to address the issue of resource sharing; they allow to account for random behavior and dynamics at higher network layers. This work is a continuation of the research on the problem of joint power allocation and time slot scheduling in a wireless communication system. The system has time varying traffic and is handled by a single base station transmitting over time varying channels. The mobile users share each time slot and the power available at this time slot, and the performance of the allocation algorithm can be characterized by the average delay experienced by the data transmitted in the network. The proposal of an antecedent article was a heavy traffic analysis for the physical system on hand, i.e., appropriate re-scaling which lead to a diffusion approximation of the system in the sense of weak convergence. In the present article a closed form solution to the resource sharing problem is provided; the solution relies on the ergodicity of the approximate diffusion.