Optimal scheduling and power allocation in wireless networks with heavy traffic: the infinite time horizon case

Abstract

ABSTRACTThis paper addresses the problem of joint transmit power allocation and time-slot scheduling in a wireless communication system with time-varying traffic. The system is handled by a single base station transmitting over time-varying channels. The operating time horizon is divided into time slots; a fixed amount of power is available at each time slot. The mobile users share each time slot and the power available at this time slot with the objective of minimising their expected total delay. This is reformulated, via a heavy traffic approximation, as the optimal control of a reflected diffusion in the positive orthant. We address this optimisation problem using the dynamic programming principle and establish Bellman's equation; here the main feature consists in how to deal with the reflection of the diffusion process on the boundary of its state space. A closed-form solution for the optimal control problem is provided. The proposed solution relies on, among other issues, the knowledge of the intensity of the driving process in the diffusion. Accordingly, we compute this intensity given a model for the multidimensional channel: a purely discontinuous process with known characteristics.