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Vacation queues with Markov schedules

Published online by Cambridge University Press:  01 July 2016

M. A. Wortman  and
Ralph L. Disney
M. A. Wortman*
Affiliation:
Texas A & M University
Ralph L. Disney*
Affiliation:
Texas A & M University
*
∗Postal address for both authors: Industrial Engineering, College of Engineering, Texas A & M University, College Station, TX 77843-3131, USA.
∗Postal address for both authors: Industrial Engineering, College of Engineering, Texas A & M University, College Station, TX 77843-3131, USA.
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Abstract

This paper identifies a probability structure for queues that belong to the class of vacation systems operating according to Markov schedules, admitting a wide variety of server scheduling disciplines including most disciplines associated with those M/GI/1/L vacation systems reported in the literature. The conditions that define these schedules are identified, and it is shown that when these conditions are satisfied, queueing behavior is governed by an underlying Markov renewal/semi-regenerative structure. A simple example is examined (the M/GI/1 vacation system with limited batch service) to demonstrate the usefulness and generality of the underlying probability structure.

Keywords

MARKOV RENEWAL PROCESSESSEMI-REGENERATIVE PROCESSES
Type
Research Article
Information
Advances in Applied Probability , Volume 22 , Issue 3 , September 1990 , pp. 730 - 748
Copyright
Copyright © Applied Probability Trust 1990 

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Footnotes

This material is based upon work supported in part by the National Science Foundation under Grant No. ECS 8501217.

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