Incorporating load dependent servers in approximate mean value analysis

Abstract

Queueing network performance modelling technology has made tremendous strides in recent years. Two of the most important developments in facilitating the modelling of large and complex systems are hierarchical modelling , in which a single load dependent server is used as a surrogate for a subsystem, and approximate mean value analysis , in which reliable approximate solutions of separable models are efficiently obtained. Unfortunately, there has been no successful marriage of these two developments; that is, existing algorithms for approximate mean value analysis do not accommodate load dependent servers reliably. This paper presents a successful technique for incorporating load dependent servers in approximate mean value analysis. We consider multiple class models in which the service rate of each load dependent server is a function of the queue length at that server. In other words, load dependent center k delivers “service units” at a total rate of f @@@@ (n @@@@ ) when n @@@@ customers are present. We present extensive experimental validation which indicates that our algorithm contributes an average error in response times of less than 1% compared to the (much more expensive) exact solution. In addition to the practical value of our algorithm, several of the techniques that it employs are of independent interest.

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