Robust Transient Multi-Server Queues and Feedforward Networks

We propose an analytically tractable approach for studying the transient behavior of multi-server queueing systems and feedforward networks with deterministic routing. We model the queueing primitives via polyhedral uncertainty sets inspired by the limit laws of probability. These uncertainty sets are characterized by parameters that control the degree of conservatism of the model. Assuming the inter arrival and service times belong to such uncertainty sets, we obtain closed form expressions for the worst case transient system time in multi-server queues and feedforward networks with deterministic routing. These analytic formulas offer rich qualitative insights on the dependence of the system times as a function of fundamental quantities in the queueing system. Moreover, we break new grounds and present an algorithm which appropriately averages worst case values obtained at different degrees of conservatism. This methodology achieves significant computational tractability and provides good approximations for the expected system time relative to simulation.