A pathwise comparison of parallel queues

Abstract

By conducting a pathwise comparison of multiple server queues, we show in what sense it is better to have more servers in ‘First Come, First Served’ or equivalently, more queues in parallel under the policy ‘Join the Shortest Workload’. This comparison result is based on the recursive representation of Kiefer and Wolfowitz, and on a non-mass conservative generalization of the Schur-Convex semi-ordering, showing in what sense it is better to send jobs to the server of least load. We also show that this pathwise result does not hold true in general for the semi-cyclic policies introduced by Scheller-Wolf, and propose a weaker ordering that suits this larger class of models.