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Some Results for Vacation Systems with Sojourn Time Limits

Part of: Volterra integral equations Stochastic processes Special processes

Published online by Cambridge University Press:  14 July 2016

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: katagon@silk.plala.or.jp
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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, explicit expressions for the steady-state distributions of the virtual waiting times are obtained in vacation systems with exponential and constant service times, a general vacation time, and two vacation rules.

Keywords

Sojourn time limitvacation systembalkinglevel crossingintegral equation

MSC classification

Secondary: 45D05: Volterra integral equations 60G17: Sample path properties 60K25: Queueing theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 48 , Issue 3 , September 2011 , pp. 679 - 687
Copyright
Copyright © Applied Probability Trust 2011 

References

Asmussen, S. (2003). Applied Probability and Queues (Appl. Math. 51), 2nd edn. Springer, New York.Google Scholar
Brill, P. H. (2008). Level Crossing Methods in Stochastic Models (Internat. Ser. Operat. Res. Manag. Sci. 123). Springer, New York.Google Scholar
Hokstad, P. (1979). A single-server queue with constant service time and restricted accessibility. Manag. Sci. 25, 205–208.Google Scholar
Takács, L. (1974). A single-server queue with limited virtual waiting time. J. Appl. Prob. 11, 612–617.Google Scholar
Takine, T. and Hasegawa, T. (1990). A note on M/G/1 vacation systems with waiting time limits. Adv. Appl. Prob. 22, 513–518.Google Scholar
Van der Duyn Schouten, F. A. (1978). An M/G/1 queueing model with vacation times. Z. Operat. Res. 22, 95–105.Google Scholar