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The departure process of the M/G/1 queueing model with server vacation and exhaustive service discipline

Part of: Operations research and management science Special processes

Published online by Cambridge University Press:  14 July 2016

Yinghui Tang
Yinghui Tang*
Affiliation:
University of Electronic Science and Technology of China, Chengdu
*
∗Postal address: Department of Applied Mathematics, University of Electronic Science and Technology of China, Chengdu, Sichuan, China.
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Abstract

In this paper we study the departure process of M/G/1 queueing models with a single server vacation and multiple server vacations. The arguments employed are direct probability decomposition, renewal theory and the Laplace–Stieltjes transform. We discuss the distribution of the interdeparture time and the expected number of departures occurring in the time interval (0, t] from the beginning of the state i (i = 0, 1, 2, ···), and provide a new method for analysis of the departure process of the single-server queue.

Keywords

DECOMPOSITIONRENEWAL THEORYLAPLACE–STIELTJES TRANSFORM

MSC classification

Primary: 60K25: Queueing theory
Secondary: 90B22: Queues and service
Type
Research Article
Information
Journal of Applied Probability , Volume 31 , Issue 4 , December 1994 , pp. 1070 - 1082
Copyright
Copyright © Applied Probability Trust 1994 

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References

Cohen, J. W. (1982) The Single Server Queue. North-Holland, Amsterdam.Google Scholar
Cooper, R. B. (1970) Queues served in cyclic order: waiting times. Bell System Tech. J. 49, 399–413.CrossRefGoogle Scholar
Doshi, B. T. (1985) Stochastic decomposition in a GI/G/1 queue with vacations. J. Appl. Prob. 22, 419–428.CrossRefGoogle Scholar
Fuhrmann, S. W. (1983) A note on the M/G/1 queue with server vacations. Operat. Res. 32, 1368–1373.CrossRefGoogle Scholar
Fuhrmann, S. W. and Cooper, R. B. (1985) Stochastic decomposition in the M/G/1 queue with generalized vacations. Operat. Res. 33, 1117–1129.CrossRefGoogle Scholar
Heyman, D. P. (1977) The T-policy for the M/G/1 queue. Management Sci. 23, 775–778.CrossRefGoogle Scholar
Levy, Y. and Yechiali, U. (1975) Utilization of idle time in an M/G/1 queueing system. Management Sci. 22, 202–211.CrossRefGoogle Scholar
Ross, S. M. (1983) Stochastic Processes. Wiley, New York.Google Scholar
Scholl, M. and Kleinrock, L. (1983) On the M/G/1 queue with rest period and certain service-in dependent queueing disciplines. Operat. Res. 31, 705–719.CrossRefGoogle Scholar
Widder, D. V. (1941) The Laplace Transform. Princeton University Press.Google Scholar