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

Published online by Cambridge University Press:  14 July 2016

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: [email protected]
∗∗ Postal address: France Télécom, Division R&D, 2 Avenue Pierre Marzin, 22300 Lannion, France. Email address: [email protected]
∗∗∗ Postal address: School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907-1285, USA. Email address: [email protected]

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.

MSC classification

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 2004 

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