Fast and accurate approximate performance analysis of multi-server facilities

Alexandre Brandwajn 1 Thomas Begin 2
2 DANTE - Dynamic Networks : Temporal and Structural Capture Approach
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme, IXXI - Institut Rhône-Alpin des systèmes complexes
Abstract : Systems with multiple servers are common in many areas and their correct dimensioning is in general a difficult problem under realistic assumptions on the pattern of user arrivals and service time distribution. We present an approximate solution for the underlying Ph/Ph/c/N queueing model. Our ap-proximation decomposes the solution of the Ph/Ph/c/N queue into solutions of simpler M/Ph/c/N and Ph/M/c/N queues. To further mitigate dimensionality is-sues, for larger numbers of servers and/or service time phases, we use a reduced state approximation to solve the M/Ph/c/N queue. The proposed approach is conceptually simple, easy to implement and produces generally accurate results for the mean number in the system, as well as the loss probability. Typical rela-tive errors for these two quantities are below 5%. A very significant speed ad-vantage compared to the numerical solution of the full Ph/Ph/c/N queue can be gained as the number of phases representing the arrival process and/or the number of servers increases.
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https://hal.inria.fr/hal-01059350
Contributeur : Thomas Begin <>
Soumis le : vendredi 29 août 2014 - 18:11:58
Dernière modification le : jeudi 12 juillet 2018 - 01:09:27

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Alexandre Brandwajn, Thomas Begin. Fast and accurate approximate performance analysis of multi-server facilities. Performance Evaluation, Elsevier, 2014, 78, pp.42-54. 〈http://www.sciencedirect.com/science/article/pii/S0166531614000558〉. 〈10.1016/j.peva.2014.06.001〉. 〈hal-01059350〉

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