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August 1996 The variance constant for the actual waiting time of the $PH/PH/1$ queue
Mogens Bladt
Ann. Appl. Probab. 6(3): 766-777 (August 1996). DOI: 10.1214/aoap/1034968227

Abstract

In this paper we consider the asymptotic time average variance of the actual waiting time of the PH/PH/1 queue. To this end Poisson's equation plays a major role, since the solution to Poisson's equation is shown to be intimately connected with the desired variance. We derive explicit solutions to Poisson's equation using phase-type methodology, and present some numerical examples.

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Mogens Bladt. "The variance constant for the actual waiting time of the $PH/PH/1$ queue." Ann. Appl. Probab. 6 (3) 766 - 777, August 1996. https://doi.org/10.1214/aoap/1034968227

Information

Published: August 1996
First available in Project Euclid: 18 October 2002

zbMATH: 0881.60079
MathSciNet: MR1410115
Digital Object Identifier: 10.1214/aoap/1034968227

Subjects:
Primary: 60K25
Secondary: 60G42 , 60K05

Keywords: Actual waiting time , asymptotic time average variance , martingale , numerical methods , phase-type distribution , Poisson's equation

Rights: Copyright © 1996 Institute of Mathematical Statistics

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Vol.6 • No. 3 • August 1996
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