Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-06T05:22:29.942Z Has data issue: false hasContentIssue false
  • English
  • Français

On the moments of the cumulative idle time in an M/D/∞ queue

Published online by Cambridge University Press:  14 July 2016

R. D. Foley  and
M. Yadin
R. D. Foley*
Affiliation:
Virginia Polytechnic Institute and State University
M. Yadin*
Affiliation:
Technion–Israel Institute of Technology
*
∗ Postal address: Department of Industrial Engineering and Operations Research, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, U.S.A.
∗∗ Postal address: Faculty of Industrial Engineering and Management, Technion—Israel Institute of Technology, Technion City, Haifa, Israel.
Get access Rights & Permissions [Opens in a new window]

Abstract

Let I denote the fraction of time that an M/D/∞ queue is idle during [0, t]. We give a simple proof that the nth moment of I conditioned on k arrivals equals the kth moment of I conditioned on n arrivals.

Keywords

IDLE TIMEM/D/∞QUEUECUMULATIVE IDLE TIMEMOMENTS
Type
Short Communications
Information
Journal of Applied Probability , Volume 20 , Issue 2 , June 1983 , pp. 445 - 447
Copyright
Copyright © Applied Probability Trust 1983 

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

Ailam, G. (1966) Moments of coverage and coverage spaces. J. Appl. Prob. 3, 550–555.Google Scholar
Foley, R. D. (1980) Stationary Poisson departure processes from nonstationary queues. Technical Report #8104, Department of Industrial Engineering and Operations Research, Virginia Polytechnic Institute and State University, Blacksburg, Virginia.Google Scholar
Foley, R. D. (1982) The non-homogeneous M/G/8 queue. Opsearch 19, 40–48.Google Scholar
Greenberg, I. (1980) The moments of coverage of a linear set. J. Appl. Prob. 17, 865–868.CrossRefGoogle Scholar