Analysis of Controlled Multiplexing Systems via Numerical Stochastic Control Methods (Invited Paper)

The paper demonstrates the usefulness of numerical methods of stochastic control theory for the design, analysis and control of multiplexing type systems and networks, as well as ATM type systems. The sources are of the Markov-modulated type, although the final results hold for other types (e.g. low-order AR schemes). Control problems arise when we wish to control cell loss due to buffer overflows by regulating the sources. The basic control mechanism is the deletion of selected low-priority cells, according to an appropriate state dependent rule. But the same results hold for many other schemes (e.g. purchasing incremental bandwidth). By exploiting the large size of the system (large number of users), the systems can be efficiently approximated by diffusion type processes, whether there is a control term or not, and for many types of control mechanisms. The basic controls are of the "low-priority cell deletion" type, and various extensions. They might be state dependent, and we can obtain optimal controls for cost functions that weigh buffer overflow, controller cell deletion loss as well as queue length. The limit equations are an effective aggregation of the original system. It is shown that there are substantial savings in losses with the use of optimal control techniques. The numerical methods can be used to balance the losses at the control with those due to buffer overflow, to minimize losses at the controller subject to constraints on buffer overflow, and to explore various approximations, systems aggregations, the interaction of multiple source classes of different priorities. >