Novel solutions for closed queueing networks with load-dependent stations

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Title: Novel solutions for closed queueing networks with load-dependent stations
Authors: Casale, G
Harrison, P
Wai Hong, O
Item Type: Conference Paper
Abstract: Load-dependent closed queueing networks are difficult toapproximate since their analysis requires to consider state-dependent service demands. Commonly employed evaluationtechniques, such as mean-value analysis, are not equallyefficient in the load-dependent setting, where mean queue-lengths are insufficient alone to recursively determine themodel equilibrium performance.In this paper, we contribute to addressing this problem byobtaining novel solutions for the normalizing constant of stateprobabilities in the load-dependent setting. For single-classload-dependent models, we provide the first explicit exactformula for the normalizing constant that applies to modelswith arbitrary load-dependent rates, while retainingO(1)complexity with respect to the total population size. Fromthis result, we derive two novel integral forms for the normal-izing constant in multiclass load-dependent models, whichinvolve integration in the real and complex domains. Thepaper also illustrates through experiments the computationalgains and accuracy of the obtained expressions.
Issue Date: 28-Jun-2019
Date of Acceptance: 1-Jun-2019
URI: http://hdl.handle.net/10044/1/72090
Publisher: ACM
Copyright Statement: This paper is embargoed until publication.
Sponsor/Funder: Commission of the European Communities
Funder's Grant Number: 825040
Conference Name: Workshop on MAthematical performance Modeling and Analysis (MAMA)
Publication Status: Accepted
Start Date: 2019-06-28
Conference Place: Phoenix, Arizona, USA
Embargo Date: publication subject to indefinite embargo
Appears in Collections:Computing



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