Approximating Many Server Queues by Means of Single Server Queues

Abstract
Obtaining time dependent results for many server queues is, under general structural assumptions, a hard problem. This paper makes an attempt to approximate stochastically the behaviour of a general many server queue by using single server queues as stochastic bounds. We propose three alternative ways of constructing approximating single server queues. The first technique utilizes special classes of service time distributions (new better than used, new worse than used), the second is via dividing the service times by the number of servers, and the third is based on a grouping idea of the customers. The first and third techniques yield in fact two bounding queues each, one of which is faster and one slower than the original s-server queue.

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