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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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

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

First available in Project Euclid: 8 March 2012

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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.

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