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Analysis of non-product form parallel queues using a Markovian process algebra

Nigel Thomas, Jeremy T. Bradley

Book Chapter
Network Performance Engineering
Next Generation Internet: Performance Evaluation and Applications
Lecture Notes in Computer Science
Volume 5233
April, 2011
Springer Verlag
DOI 10.1007/978-3-642-02742-0_15

In this paper we use the Markovian process algebra PEPA to specify and analyse a class of queueing models which, in general, do not give rise to a product form solution but can nevertheless be decomposed into their components to obtain a scalable solution. Such a decomposition gives rise to expressions for marginal probabilities which may be used to derive potentially interesting system performance measures, such as the average number of jobs in the system. It is very important that some degree of confidence in such measures can also be given; however, we show here that it is not generally possible to calculate the variance exactly from the marginal probabilities. Hence, two approximations for the variance of the total population are presented and compared numerically.

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