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A stationary Poisson departure process from a minimally delayed infinite server queue with non-stationary Poisson arrivals

Part of: Stochastic processes Operations research and management science Special processes

Published online by Cambridge University Press:  14 July 2016

John A. Barnes  and
Richard Meili
John A. Barnes*
Affiliation:
Virginia Commonwealth University
Richard Meili*
Affiliation:
Virginia Commonwealth University
*
∗Postal address: Department of Mathematical Sciences, Virginia Commonwealth University, 1015 West Main Street, Box 2014, Richmond, VA 23284-2014, USA.
∗Postal address: Department of Mathematical Sciences, Virginia Commonwealth University, 1015 West Main Street, Box 2014, Richmond, VA 23284-2014, USA.
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Abstract

The points of a non-stationary Poisson process with periodic intensity are independently shifted forward in time in such a way that the transformed process is stationary Poisson. The mean shift is shown to be minimal. The approach used is to consider an Mt/Gt/∞ queueing system where the arrival process is a non-stationary Poisson with periodic intensity function. A minimal service time distribution is constructed that yields a stationary Poisson departure process.

Keywords

POISSON PROCESSNON-STATIONARY POISSON PROCESSINFINITE SERVER QUEUE

MSC classification

Primary: 60G55: Point processes 60K25: Queueing theory
Secondary: 90B22: Queues and service
Type
Research Papers
Information
Journal of Applied Probability , Volume 34 , Issue 3 , September 1997 , pp. 767 - 772
Copyright
Copyright © Applied Probability Trust 1997 

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References

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