Journal of Applied Probability
- J. Appl. Probab.
- Volume 49, Number 1 (2012), 60-83.
Weak convergence limits for closed cyclic networks of queues with multiple bottleneck nodes
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.
J. Appl. Probab., Volume 49, Number 1 (2012), 60-83.
First available in Project Euclid: 8 March 2012
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Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60K25: Queueing theory [See also 68M20, 90B22]
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