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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. (doi:10.1023/A:1025643801208) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:839)

The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided.
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
DOI/Identification number: 10.1023/A:1025643801208
Uncontrolled keywords: GI/G/k; multi-server queue; discrete time
Subjects: H Social Sciences > HA Statistics
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Judith Broom
Date Deposited: 19 Dec 2007 18:32 UTC
Last Modified: 16 Nov 2021 09:39 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/839 (The current URI for this page, for reference purposes)

University of Kent Author Information

Breuer, Lothar.

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