Numerical Algebra, Control and Optimization (NACO)

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

Pages: 713 - 725, Volume 1, Issue 4, December 2011      doi:10.3934/naco.2011.1.713

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Naoto Miyoshi - Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo 152-8552, Japan (email)

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.

Keywords:  Queueing theory, LCFS-PR single-server queues, Palm calculus, stochastic intensity.
Mathematics Subject Classification:  Primary: 60K25; Secondary: 60G10, 60G55.

Received: June 2011;      Revised: July 2011;      Available Online: November 2011.