2 APPROACHES TO OPTIMAL ROUTING AND ADMISSION CONTROL IN SYSTEMS WITHREAL-TIME TRAFFIC

This paper addresses the problem of routing and admission control of r eal-time traffic in a queueing system where customers must begin servi ce within given deadlines (or complete service within given deadlines) , otherwise they are considered lost. Performance in such systems is m easured by the probability a customer is lost. For a system of K paral lel servers with a probabilistic routing and admission control scheme, the problem of the optimal routing and admission control is considere d and two approaches are presented. Assuming the availability of a clo sed-form expression for the probability of loss at each server, the pr oblem is solved under general conditions and properties of the optimal flow allocation are given. However, such closed-form expressions are often unavailable. This motivates a second approach, which involves a gradient-based stochastic optimization algorithm with on-line gradient estimation. The gradient estimation problem for loss probabilities is solved through a recently-developed smoothed perturbation analysis (S PA) technique. The effectiveness of on-line stochastic optimization us ing this type of gradient estimator is demonstrated by combining the S PA algorithm with a sampling-controlled stochastic optimization algori thm for the aforementioned routing and admission control problem.