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Scale functions of Lévy processes and busy periods of finite-capacity M/GI/1 queues

Part of: Special processes Markov processes

Published online by Cambridge University Press:  14 July 2016

Parijat Dube ,
Fabrice Guillemin  and
Ravi R. Mazumdar
Parijat Dube*
Affiliation:
IBM Research
Fabrice Guillemin*
Affiliation:
France Télécom
Ravi R. Mazumdar*
Affiliation:
Purdue University
*
∗ Postal address: IBM T. J. Watson Research Center, Yorktown Heights, NY 10598, USA. Email address: pdube@us.ibm.com
∗∗ Postal address: France Télécom, Division R&D, 2 Avenue Pierre Marzin, 22300 Lannion, France. Email address: fabrice.guillemin@francetelecom.com
∗∗∗ Postal address: School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907-1285, USA. Email address: mazum@ecn.purdue.edu
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Abstract

In this paper we use the exit time theory for Lévy processes to derive new closed-form results for the busy period distribution of finite-capacity fluid M/G/1 queues. Based on this result, we then obtain the busy period distribution for finite-capacity queues with on–off inputs when the off times are exponentially distributed.

Keywords

Queuebusy periodLévy processscale functionLaplace transformon–off input

MSC classification

Primary: 60K25: Queueing theory
Secondary: 60J50: Boundary theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 41 , Issue 4 , December 2004 , pp. 1145 - 1156
Copyright
Copyright © Applied Probability Trust 2004 

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