Breuer, Lothar (2003) Transient and stationary distributions for the GI/G/k queue with Lebesgue-dominated inter-arrival time distribution. Queueing Systems, 45 (1). pp. 47-57. ISSN 0257-0130.
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| Official URL http://dx.doi.org/10.1023/A:1025643801208 |
Abstract
In this paper, the multi-server queue with general service time distribution and Lebesgue-dominated iid inter-arival times is analyzed. This is done by introducing auxiliary variables for the remaining service times and then examining the embedded Markov chain at arrival instants. The concept of piecewise-deterministic Markov processes is applied to model the inter-arrival behaviour. It turns out that the transition probability kernel of the embedded Markov chain at arrival instants has the form of a lower Hessenberg matrix and hence admits an operator-geometric stationary distribution. Thus it is shown that matrix-analytical methods can be extended to provide a modeling tool even for the general multi-server queue.
| Item Type: | Article |
|---|---|
| Uncontrolled keywords: | GI/G/k; multi-server queue; discrete time |
| Subjects: | H Social Sciences > HA Statistics |
| Divisions: | Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science |
| Depositing User: | Judith Broom |
| Date Deposited: | 19 Dec 2007 18:32 |
| Last Modified: | 20 Apr 2012 13:45 |
| Resource URI: | http://kar.kent.ac.uk/id/eprint/839 (The current URI for this page, for reference purposes) |
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