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Weak Convergence Limits for Closed Cyclic Networks of Queues with Multiple Bottleneck Nodes

Part of: Special processes

Published online by Cambridge University Press:  04 February 2016

Ole Stenzel  and
Hans Daduna
Ole Stenzel*
Affiliation:
University of Hamburg
Hans Daduna*
Affiliation:
University of Hamburg
*
∗ Current address: Institute of Stochastics, Ulm University, Helmholtzstrasse 18, 89069 Ulm, Germany.
∗∗ Postal address: Center of Mathematical Statistics and Stochastic Processes, University of Hamburg, Bundesstrasse 55, 20146 Hamburg, Germany. Email address: [email protected]
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Abstract

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We consider a sequence of cycles of exponential single-server nodes, where the number of nodes is fixed and the number of customers grows unboundedly. We prove a central limit theorem for the cycle time distribution. We investigate the idle time structure of the bottleneck nodes and the joint sojourn time distribution that a test customer observes at the nonbottleneck nodes during a cycle. Furthermore, we study the filling behaviour of the bottleneck nodes, and show that the single bottleneck and multiple bottleneck cases lead to different asymptotic behaviours.

Keywords

Cyclic exponential networkcycle timeidle timefilling behaviourbottleneck structurecentral limit theorem

MSC classification

Primary: 60K25: Queueing theory
Type
Research Article
Information
Journal of Applied Probability , Volume 49 , Issue 1 , March 2012 , pp. 60 - 83
Copyright
© Applied Probability Trust 

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