Abstract
This paper presents some analytical results concerning an approximation procedure for closed queueing networks. The procedure is well-known and has been found useful for product-form networks where large numbers of queues, jobs or job classes prohibit an exact analysis, as well as for networks which do not possess product-form. The procedure represents the mean sojourn time at a queue as a function of the throughput of the queue, and derives a set of fixed point equations for the throughputs of the various job classes. We begin by showing that under a mild regularity condition the fixed point equations have a unique solution. Then we show that derivatives of performance measures can be readily calculated, and that their simple form provides an interesting insight into capacity allocation in closed queueing networks.
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This work was supported in part by the Nuffield Foundation
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Kelly, F.P. On a class of approximations for closed queueing networks. Queueing Syst 4, 69–76 (1989). https://doi.org/10.1007/BF01150857
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DOI: https://doi.org/10.1007/BF01150857