A pathwise comparison result for parallel queues

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We introduce the appropriate framework for pathwise comparison of multiple server queues under general stationary ergodic assumptions. We show in what sense it is better to have more servers for a system under FCFS ('First Come, First Served') or equivalently, more queues in a system of parallel queues under the JSW ('Join the Shortest Workload') allocation policy. 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. We also show that the latter result does not hold true in general, for the larger class of systems applying the semi-cyclic allocation policy introduced by Scheller-Wolf in SW03.