On the stationary LCFS-PR single-server queue:       A characterization via stochastic intensity

Naoto Miyoshi

doi:10.3934/naco.2011.1.713

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2011, Volume 1, Issue 4: 713-725. Doi: 10.3934/naco.2011.1.713

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On the stationary LCFS-PR single-server queue: A characterization via stochastic intensity

Naoto Miyoshi^1,

1.
Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo 152-8552

Received: June 2011

Revised: July 2011

Published: October 2011

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Abstract

We consider a stationary single-server queue with preemptive-resume last-come, first-served (LCFS-PR) queueing discipline. The LCFS-PR single-server queue has some interesting properties and has been studied in the literature. In this paper, we generalize the previous results such that the input process to the queue is given as a general stationary marked point process and derive some formulas concerning the joint distribution of queue length and remaining service times of respective customers in the system at arbitrary time instances as well as at arrival instances. The tool for derivation is the Palm-martingale calculus; that is, the connection between the notion of Palm probability and that of stochastic intensity.

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Mathematics Subject Classification: Primary: 60K25; Secondary: 60G10, 60G55.

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