Fluid And Diffusion Approximation For A Multi-User Wireless Communication System

A MIMO downlink system in which data is transmitted to multi-users over com-mon wireless channel is considered in this paper. We suppose that the channel is time-varying according to an ergodic Markov process. The time interval between adjacent arriving packets and the length of the packets for each user are general distributed. In addition, the ratio of anticipated average arrival rates for the users, also known as the relative traffic rate is fixed. A packet-based traffic model is considered where data for each user is queued at the transmit end. Such system is difficult to study even under the simplest strategy with Markovian assumption. So, in this paper, we will employ the fluid and diffusion approximation to analyze the system. Our main work is to prove that the workload process under fluid scaling converges to zero under heavy traffic assump-tion, and then we discuss the limitations of the workload processes under diffusion scaling.