Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-05T05:45:25.958Z Has data issue: false hasContentIssue false
  • English
  • Français

The equality of the workload and total attained waiting time in average

Published online by Cambridge University Press:  14 July 2016

Genji Yamazaki  and
Masakiyo Miyazawa
Genji Yamazaki*
Affiliation:
Tokyo Metropolitan Institute of Technology
Masakiyo Miyazawa*
Affiliation:
Science University of Tokyo
*
∗Postal address: Department of Engineering Management, Tokyo Metropolitan Institute of Technology, 6–6, Asahigaoka, Hino-City, Tokyo 191, Japan.
∗∗Postal address: Department of Information Sciences, Science University of Tokyo, Noda City, Chiba 278, Japan.
Get access Rights & Permissions [Opens in a new window]

Abstract

It has recently been shown that, for the FCFS G/G/1 queue, the workload and attained waiting time of a customer in service have the same stationary distribution. We show that, for a general queueing system setting, the workload and total attained waiting time of customers in service are identical in average but the equality of the distributions is not true in general except for the FCFS G/G/1 queue.

Keywords

QUEUESAMPLE AVERAGE
Type
Short Communications
Information
Journal of Applied Probability , Volume 28 , Issue 1 , March 1991 , pp. 238 - 244
Copyright
Copyright © Applied Probability Trust 1991 

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

Franken, P., König, O., Arndt, U. and Schmidt, V. (1982) Queues and Point Processes. Wiley, Chichester.Google Scholar
Heyman, D. P. and Stidham, S. Jr. (1980) The relation between customer and time averages in queues. Operat. Res. 28, 983–994.CrossRefGoogle Scholar
Miyazawa, M. (1979) A formal approach to queueing processes in the steady state and their applications. J. Appl. Prob. 16, 332–346.Google Scholar
Miyazawa, M. and Yamazaki, G. (1991) Convex ordering of the attained waiting times in single server queues and related problems. J. Appl. Prob. 28. To appear.CrossRefGoogle Scholar
Sakasegawa, H. and Wolff, R. W. (1990) The equality of the virtual delay and attained waiting time distributions. Adv. Appl. Prob. 22, 257–259.Google Scholar
Sengupta, B. (1989) An invariance relationship for the G/G/1 queue. Adv. Appl. Prob. 21, 956–957.Google Scholar
Stidham, S. Jr. (1974) A last word on L = ?W. Operat. Res. 22, 417–421.Google Scholar
Stidham, S. Jr. (1979) On the relation between time averages and customer averages in stationary random marked point processes. NCSU-IE Technical Report No. 79-1.Google Scholar