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On the time-dependent occupancy and backlog distributions for the GI/G/∞ queue

Part of: Stochastic processes Special processes

Published online by Cambridge University Press:  14 July 2016

H. Ayhan ,
J. Limon-Robles  and
M. A. Wortman
H. Ayhan*
Affiliation:
Georgia Institute of Technology
J. Limon-Robles*
Affiliation:
ITESM, Monterrey
M. A. Wortman*
Affiliation:
Texas A&M University
*
∗Postal address: School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA. Email address: hayhan@isye.gatech.edu
∗∗Postal address: Department of Control Engineering, ITESM, Monterrey, Mexico.
∗∗∗Postal address: Department of Industrial Engineering, Texas A&M University, College Station, TX 77843, USA.
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Abstract

We consider an infinite server queueing system. An examination of sample path dynamics allows a straightforward development of integral equations having solutions that give time-dependent occupancy (number of customers) and backlog (unfinished work) distributions (conditioned on the time of the first arrival) for the GI/G/∞ queue. These integral equations are amenable to numerical evaluation and can be generalized to characterize GIX/G/∞ queue. Two examples are given to illustrate the results.

Keywords

Infinite serverintegral equationsoccupancybacklog

MSC classification

Primary: 60K25: Queueing theory
Secondary: 60G35: Signal detection and filtering
Type
Research Papers
Information
Journal of Applied Probability , Volume 36 , Issue 2 , June 1999 , pp. 558 - 569
Copyright
Copyright © Applied Probability Trust 1999 

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Footnotes

This research has been supported by National Science Foundation Grants DMI-9622138 and DMI-9215662.

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