Transient and stationary distributions for the GI/G/k queue with Lebesgue-dominated inter-arrival time distribution

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. (The full text of this publication is not available from this repository)

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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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