Hostname: page-component-669899f699-7xsfk Total loading time: 0 Render date: 2025-04-24T10:47:07.675Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on M/G/1 vacation systems with waiting time limits

Published online by Cambridge University Press:  01 July 2016

T. Takine  and
T. Hasegawa
T. Takine*
Affiliation:
Kyoto University
T. Hasegawa*
Affiliation:
Kyoto University
*
∗Postal address: Department of Applied Mathematics and Physics, Faculty of Engineering, Kyoto University, Kyoto 606, Japan.
∗Postal address: Department of Applied Mathematics and Physics, Faculty of Engineering, Kyoto University, Kyoto 606, Japan.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We consider two variants of M/G/1 queues with exhaustive service and multiple vacations; (1) customers cannot wait for their services longer than an interval of length T, and (2) customers cannot stay in the system longer than an interval of length T. We show that the probability distribution functions of the waiting times for the two systems are given in terms of those for the corresponding M/G/1 vacation systems without any residence-time limits.

Keywords

STEADY STATE DISTRIBUTIONACTUAL WAITING TIMEVIRTUAL WAITING TIMEUP- AND DOWNCROSSINGS
Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 22 , Issue 2 , June 1990 , pp. 513 - 518
Copyright
Copyright © Applied Probability Trust 1990 

References

Brill, P. H. and Posner, M. J. M. (1977) Level crossings in point processes applied to queues: single-server case. Operat. Res. 25, 662–674.CrossRefGoogle Scholar
Cohen, J. W. (1977) On up- and downcrossings. J. Appl. Prob. 14, 405–410.Google Scholar
Cohen, J. W. (1982) The Single Server Queue, 2nd edn, Chaps. III.4 and III.5. North-Holland, Amsterdam.Google Scholar
Daley, D. J. (1964) Single-server queueing systems with uniformly limited queueing time. J. Austral. Math. Soc. 4, 489–505.CrossRefGoogle Scholar
Doshi, B. T. (1986) Queueing systems with vacation–a survey. Queueing Sys. 1, 29–66.CrossRefGoogle Scholar
Keilson, J. and Servi, L. D. (1987) Dynamics of the M/G/1 vacation model. Operat. Res. 35, 575–582.Google Scholar
Keilson, Y. and Yechiali, U. (1989) Blocking probability for M/G/1 vacation systems with occupancy level dependent schedules. Operat. Res. 37, 134–140.CrossRefGoogle Scholar
Levy, Y. and Yechiali, U. (1975) Utilization of idle time in an M/G/1 queueing system. Management Sci. 22, 202–211.Google Scholar
Rubin, I. and Ouaily, M. (1988) Performance of communication and queueing processors under message delay limits. Proc. IEEE GLOBECOM '88, Hollywood FL, 501–505.Google Scholar
Shanthikumar, J. G. (1980) Some analysis on the control of queues using level crossings of regenerative processes. J. Appl. Prob. 17, 814–821.CrossRefGoogle Scholar
Takács, L. (1967) The distribution of the content of finite dams. J. Appl. Prob. 4, 151–161.Google Scholar
Takács, L. (1974) A single server queue with limited virtual waiting time. J. Appl. Prob. 11, 612–617.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