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- Title
- A large closed queueing network with autonomous service and bottleneck
- Author(s)
- Abramov, Vyacheslav M.
- Abstract
- This paper studies the queue-length process in a closed Jackson-type queueing network with the large number N of homogeneous customers by methods of the theory of martingales and by the up- and down-crossing method. The network considered here consists of a central node (hub), being an infinite-server queueing system with exponentially distributed service times, and k single-server satellite stations (nodes) with generally distributed service times with rates depending on the value N. The service mechanism of these k satellite stations is autonomous, i.e., every satellite server j serves the customers only at random instants that form a strictly stationary and ergodic sequence of random variables. Assuming that the first k - 1 satellite stations operate in light usage regime the paper considers the cases where the kth satellite station is a bottleneck node. The approach of the paper is based both on development of the method from the paper by Kogan and Liptser [16], where a Markovian version of this model has been studied, and on development of the up- and down-crossing method.
- Publication Type
- Journal article
- Source
- Queueing Systems, Vol. 35, no. 1-4 (Jul 2000), pp. 23-54
- Publication Year
- 2000
- FOR Code(s)
- 0102 Applied Mathematics; 0103 Numerical and Computational Mathematics; 0104 Statistics
- Keyword(s)
- Autonomous service; Bottleneck; Closed queueing network; Diffusion and fluid approximation; Martingales; Semimartingales; Up- and down-crossings
- Publisher
- Springer
- Publisher URL
- http://dx.doi.org/10.1023/A:1019129708268
- Copyright
- Copyright © J.C. Baltzer AG, Science Publishers (2000).
- ISSN
- 0257-0130
- Peer Reviewed
