Analysis of controlled multiplexing systems via stochastic control theory

Large controlled multiplexing systems can often be approximated by diffusion type processes, via weak convergence methods. The system is large in that there are many independent users, each generating cells according to a Markov modulated model. The “limit” equations can be viewed as a type of aggregation of the original system, and they are the basis of the actual numerical approximation for the control problem. The method and results well illustrate the power of current numerical methods in stochastic control to handle complex and realistic problems in applications. The numerical approximations have the structure of the original problem, but are generally much simpler. The control can occur in a variety of places. Various forms of the optimal control problem are explored, where the main aim is to control or balance the losses at the control with those due to buffer overflow. The numerical data shows that much can be saved by the use of optimal controls or reasonable approximations to them. We discuss various aggregation methods and control approximation schemes. There are qualitative comparisons of various systems with and without control and a discussion of the variations of control and performance as the systems data and control bounds vary