Comparisons of multi-server queues with finite waiting rooms

Abstract

In this paper we consider s-server queues with capacity c, 1 ≤ s ≤ c ≤ ∞, the first-come first-served queue discipline and very general arrival and service processes. We show that the admission epochs and departure epochs decrease, so that the throughput increases, when any of the following changes occur: (1) the number of servers s increases, (2) the capacity c increases, (3) the external arrival counting process increases or (4) the service times decrease, provided that the service times are assigned in order of service initiation and that a subsequence ordering is used to compare arrival counting processes. The subsequence ordering for the arrival processes is very important for obtaining positive results with finite waiting rooms. The subsequence ordering holds between a superposition point process and its component point processes. The subsequence ordering can often be applied via its stochastic generalization, the stochastic subsequence ordering, which is implied by a failure rate ordering.