Extremal Traffic and Worst-Case Performance for Queues with Shaped Arrivals

. This paper presents some new results and an overview of the authors' recent work in the area of worst-case performance analysis in communication networks with stationary-ergodic traffic and regulated sample paths. Starting with a single-class network node, the problem of maximizing the buffer overflow probability is considered. Maximization is over a suitable class of stochastic processes. The problem is explicitly solved and the extremal process is identified. Moving on to a two-class queue with jointly stationary arrival processes, the analogous problem is considered. Under some rather natural assumptions the problem is again solved explicitly. The final part of the paper consists of a multiclass queue with the additional constraint that the arrival processes are independent. Bounds on performance measures, such as the tail of the stationary delay, are derived. The problem and results of this paper can be seen as being at the intersection between the effective bandwidths approach a..