Reducing the complexity of the performance analysis of a multi- server facilities

Tulin Atmaca 1 Thomas Begin 2 Alexandre Brandwajn 3 Hind Castel-Taleb 1
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 approximation decomposes the solution of the Ph/Ph/c/N queue into solutions of simpler M/Ph/c/N and Ph/M/c/N queues. It is conceptually simple, easy to implement and produces generally accurate results for the mean number in the system, as well as the loss probability. A significant speed advantage 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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Tulin Atmaca, Thomas Begin, Alexandre Brandwajn, Hind Castel-Taleb. Reducing the complexity of the performance analysis of a multi- server facilities. [Research Report] RR-8617, Institut Telecom, Telecom SudParis, Evry, France; Université Lyon 1 / LIP (UMR INRIA, ENS Lyon CNRS, UCBL), Lyon France; University of California Santa Cruz, Baskin School of Engineering, USA; INRIA. 2014. ⟨hal-01076366⟩

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