Hostname: page-component-76dd75c94c-7vt9j Total loading time: 0 Render date: 2024-04-30T07:31:07.976Z Has data issue: false hasContentIssue false
  • English
  • Français

A new approach to the G/G/1 queue with generalized setup time and exhaustive service

Part of: Special processes Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Huan Li  and
Yixin Zhu
Huan Li
Affiliation:
State University of New York, Buffalo
Yixin Zhu
Affiliation:
State University of New York, Buffalo
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider a class of G/G/1 queueing models with independent generalized setup time and exhaustive service. It is shown that a variety of single-server queueing systems with service interruption are special cases of our model. We give a simple computational scheme for the moments of the stationary waiting time and sojourn time. Our numerical investigations indicate that the algorithm is quite accurate and fast in general. For the M/G/1 case, we are able to derive a recursive formula for the moments of the stationary waiting time, which includes the Takács formula as a special case. It immediately results in the stochastic decompòsition property which can be found in the literature.

Keywords

MOMENTSMACLAURIN SERIESRECURSIVE FORMULA

MSC classification

Primary: 90B22: Queues and service
Secondary: 60K25: Queueing theory
Type
Research Article
Information
Journal of Applied Probability , Volume 31 , Issue 4 , December 1994 , pp. 1083 - 1097
Copyright
Copyright © Applied Probability Trust 1994 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Doshi, B. (1985) A note on stochastic decomposition in a GI/G/1 queue with vacation or set-up times. J . Appl. Prob. 23, 419–428 Google Scholar
Doshi, B. (1986) Queueing system with vacations – a survey. Queueing Systems 1, 29–66.Google Scholar
Doshi, B. (1990) Single server queues with vacations. In Stochastic Analysis of Computer and Communication Systems , ed. Takagi, H., pp. 217–266. North-Holland, Amsterdam.Google Scholar
Gong, W. B. and Hu, J. Q. (1992) The MacLaurin expansion for the GI/G/1 queue. J. Appl. Prob. 29, 176–184.CrossRefGoogle Scholar
Lemoine, A. (1975) Limit theorems for generalized single server queues: the exception system. SIAM J. Appl. Math. 28, 596–606.Google Scholar
Neuts, M. F. (1986) Generalizations of the Pollaczek-Khinchin integral equation in the theory of queueing systems. Adv. Appl. Prob. 18, 952–990.Google Scholar
Shanthikumar, J. G. (1988) On stochastic decomposition in M/G/1 type queues with generalized server vacations. Operat. Res. 36, 566–569.Google Scholar
Shanthikumar, J. G. and Sumita, U. (1989) Modified Lindley process with replacement: dynamic behavior, asymptotic decomposition and application. J. Appl. Prob. 26, 552–565.CrossRefGoogle Scholar
Teghem, J. Jr. (1986) Control of the service process in a queueing system. Eur. J. Operat. Res. 23, 141–158.Google Scholar