Journal of Applied Probability

Weak convergence limits for closed cyclic networks of queues with multiple bottleneck nodes

Ole Stenzel and Hans Daduna

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Abstract

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.

Article information

Source
J. Appl. Probab., Volume 49, Number 1 (2012), 60-83.

Dates
First available in Project Euclid: 8 March 2012

Permanent link to this document
https://projecteuclid.org/euclid.jap/1331216834

Digital Object Identifier
doi:10.1239/jap/1331216834

Mathematical Reviews number (MathSciNet)
MR2952882

Zentralblatt MATH identifier
1242.60099

Subjects
Primary: 60K25: Queueing theory [See also 68M20, 90B22]

Keywords
Cyclic exponential network cycle time idle time filling behaviour bottleneck structure central limit theorem

Citation

Stenzel, Ole; Daduna, Hans. Weak convergence limits for closed cyclic networks of queues with multiple bottleneck nodes. J. Appl. Probab. 49 (2012), no. 1, 60--83. doi:10.1239/jap/1331216834. https://projecteuclid.org/euclid.jap/1331216834


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