Approximations to Study the Impact of the Service Discipline in Systems with Redundancy

In this paper we develop the first methods to approximate the queue length distribution in a queueing system with redundancy under various service disciplines. We focus on a system with exponential job sizes, i.i.d. copies, and a large number of servers. In the case of Processor Sharing, we provide a pair and a triplet approximation. We also develop a pair approximation for First-Come-First-Served, Limited Processor Sharing and Last-Come-First-Served servers. We present numerical evidence that shows that all the approximations presented in the paper are highly accurate, but that none of them are asymptotically exact (as the number of servers goes to infinity).