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A Note on M/G/1 Vacation Systems with Sojourn Time Limits

Part of: Special processes Stochastic processes Volterra integral equations

Published online by Cambridge University Press:  30 January 2018

Tsuyoshi Katayama
Tsuyoshi Katayama*
Affiliation:
Chubu Teletraffic Engineering Laboratory
*
∗ Postal address: Chubu Teletraffic Engineering Laboratory, Naka-taikouyama 4-66, Imizu-shi, Toyama, 939-0363, Japan. Email address: [email protected]
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Abstract

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In this paper we deal with an M/G/1 vacation system with the sojourn time (wait plus service) limit and two typical vacation rules, i.e. multiple and single vacation rules. Using the level crossing approach, we derive recursive equations for the steady-state distributions of the virtual waiting times in M/G/1 vacation systems with a general vacation time and two vacation rules.

Keywords

Sojourn time limitvacation systembalkinglevel crossingintegral equation

MSC classification

Primary: 45D05: Volterra integral equations 60G17: Sample path properties 60K25: Queueing theory
Type
Research Article
Information
Journal of Applied Probability , Volume 49 , Issue 4 , December 2012 , pp. 1194 - 1199
Copyright
© Applied Probability Trust 

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