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.
Citation
Ole Stenzel. Hans Daduna. "Weak convergence limits for closed cyclic networks of queues with multiple bottleneck nodes." J. Appl. Probab. 49 (1) 60 - 83, March 2012. https://doi.org/10.1239/jap/1331216834
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