Hostname: page-component-77c89778f8-vsgnj Total loading time: 0 Render date: 2024-07-17T23:24:55.719Z Has data issue: false hasContentIssue false
  • English
  • Français

An M/G/1 queue with multiple types of feedback and gated vacations

Part of: Special processes Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Onno J. Boxma  and
Uri Yechiali
Onno J. Boxma*
Affiliation:
CWI
Uri Yechiali*
Affiliation:
Tel Aviv University
*
∗Postal address: P.O. Box 94079, 1090 GB Amsterdam, The Netherlands.
∗∗Postal address: Department of Statistics, School of Mathematical Sciences, Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel.
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper considers a single-server queue with Poisson arrivals and multiple customer feedbacks. If the first service attempt of a newly arriving customer is not successful, he returns to the end of the queue for another service attempt, with a different service time distribution. He keeps trying in this manner (as an ‘old' customer) until his service is successful. The server operates according to the ‘gated vacation' strategy; when it returns from a vacation to find K (new and old) customers, it renders a single service attempt to each of them and takes another vacation, etc. We study the joint queue length process of new and old customers, as well as the waiting time distribution of customers. Some extensions are also discussed.

Keywords

M/G/1 QUEUEFEEDBACKGATED VACATIONSQUEUE LENGTH

MSC classification

Primary: 60K25: Queueing theory
Secondary: 90B22: Queues and service
Type
Research Papers
Information
Journal of Applied Probability , Volume 34 , Issue 3 , September 1997 , pp. 773 - 784
Copyright
Copyright © Applied Probability Trust 1997 

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.)

Footnotes

This paper is based on an invited presentation at the Applied Probability conference in honour of J. Gani and T. E. Hannan, held in Athens in March 1995.

References

[1] Altman, E. and Yechiali, U. (1994) Polling in a closed network. Prob. Eng. Inf. Sci. 8, 327–343.Google Scholar
[2] Borst, S. C. and Boxma, O. J. (1997) Polling models with and without switchover times. Operat. Res. To appear.Google Scholar
[3] Boxma, O. J. (1994) Polling systems. In From Universal Morphisms to Megabytes: A Baayen Space Odyssey. (Liber Amicorum for P. C. Baayen) . ed. Apt, K. R., Schrijver, A. and Temme, N. M. CWI, Amsterdam. pp. 215–230.Google Scholar
[4] Cohen, J. W. (1982) The Single Server Queue. North-Holland, Amsterdam.Google Scholar
[5] Eisenberg, M. (1972) Queues with periodic service and changover time. Operat. Res. 20, 440–451.Google Scholar
[6] Sidi, M., Levy, H. and Fuhrmann, S. W. (1992) A queueing network with a single cyclically roving server. Queueing Systems 11, 121–144.Google Scholar
[7] Takács, L. (1963) A queueing model with feedback. Operat. Res. 11, 345–354.Google Scholar
[8] Takagi, H. (1991) Queueing Analysis. Vol. 1: Vacation and Priority Systems. North-Holland, Amsterdam.Google Scholar
[9] Takine, T., Takagi, H. and Hasegawa, T. (1991) Sojourn times in vacation and polling systems with Bernoulli feedback. J. Appl. Prob. 28, 422–432.Google Scholar