CONTROLLED AND OPTIMALLY CONTROLLED MULTIPLEXING SYSTEMS - A NUMERICAL EXPLORATION

Large controlled multiplexing systems are approximated by diffusion ty pe processes yielding a very efficient way of approximation and good n umerical methods. The ''limit'' equations are an efficient aggregation of the original system, and provide the basis of the actual numerical approximation to the control problem. The numerical approximations ha ve the structure of the original problem, but are generally much simpl er. The control can occur in a variety of places; e.g., ''leaky bucket '' controllers, control of ''marked cells'' at the transmitter buffer, or control of the transmitter speed. From the point of view of the li mit equations, those are equivalent. Various forms of the optimal cont rol problem are explored, where the main aim is to control or balance the losses at the control with those due to buffer overflow. It is sho wn that much can be saved via the use of optimal controls or reasonabl e approximations to them. We discuss systems with one to three classes of sources, various aggregation methods and control approximation sch emes. There are qualitative comparisons of various systems with and wi thout control and a discussion of the variations of control and perfor mance as the systems data and control bounds vary. The approach is a v ery useful tool for providing both qualitative and quantitative inform ation which would be hard to get otherwise. The results have applicati ons to various forms of the ATM and broadband integrated data networks .