On the MAP/G/1 queue with Lebesgue-dominated service time distribution and LCFS preemptive repeat service discipline

Breuer, Lothar (2002) On the MAP/G/1 queue with Lebesgue-dominated service time distribution and LCFS preemptive repeat service discipline. Stochastic Models, 18 (4). pp. 589-595. ISSN 1532-6349. (The full text of this publication is not available from this repository)

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Official URL
http://dx.doi.org/10.1081/STM-120016446

Abstract

The present paper contains an analysis of the MAP/G/1 queue with last come first served (LCFS) preemptive repeat service discipline and Lebesgue-dominated service time distribution. The transient distribution is given in terms of a recursive formula. The stationary distribution as well as the stability condition are obtained by means of Markov renewal theory via a QBD representation of the embedded Markov chain at departures and arrivals.

Item Type: Article
Additional information: The use of special features of a service discipline in order to simplify the analysis of a queue has always been one of the objectives in queueing theory. In this paper it is shown how the LCFS (last come first served) discipline with preemptive repeat rule can be exploited to yield a Markovian analysis of an initially non-Markovian system. This is possible under the assumption of absolutely continuous service time distributions, using a hazard rate representation and combining this with the explonential form of the Markovian arrival process.
Uncontrolled keywords: MAP; last come first served; preemptive repeat; QBD
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 18:17
Last Modified: 20 Apr 2012 13:44
Resource URI: http://kar.kent.ac.uk/id/eprint/488 (The current URI for this page, for reference purposes)
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