Hostname: page-component-6bb9c88b65-fsdjw Total loading time: 0 Render date: 2025-07-24T12:03:22.830Z Has data issue: false hasContentIssue false
  • English
  • Français

ON THE LAW OF THE iTH WAITING TIME IN A BUSY PERIOD OF G/M/c QUEUES

Published online by Cambridge University Press:  18 December 2007

Opher Baron
Opher Baron
Affiliation:
Rotman School of Management University of Toronto Toronto, ON, Canada M5S 3E6 E-mail: opher.baron@rotman.utoronto.ca
Get access Rights & Permissions [Opens in a new window]

Abstract

We use induction to derive the distribution of the waiting time of the ith waiting customer in a busy period for a G/M/1 queue with a first come–first serve service. A trivial implication gives the law for the ith waiting time in a busy period for a G/M/c queue. Finally, we use the Lindley recursion to relate our results to the distribution of random walks.

Information

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 22 , Issue 1 , January 2008 , pp. 75 - 80
Copyright
Copyright © Cambridge University Press 2008

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.)

Article purchase

Temporarily unavailable

References

1.Adan, I., Boxma, O.J., & Perry, D. (2005). The G/M/1 queue revisited. Mathematical Methods in Operations Research 62: 437–452.CrossRefGoogle Scholar
2.Asmussen, S. (2003). Applied probability and queues, 2nd ed.New York: Springer-Verlag.Google Scholar
3.Cohen, J.W. (1982). The single server queue, 2nd ed.Amsterdam: North-Holland.Google Scholar
4.Prabhu, N.U. (1965). Queues and inventories. New York: Wiley.Google Scholar
5.Ross, S.M. (1983). Stochastic processes. Wiley Series in Probability and Mathematical Statistics. New York: Wiley.Google Scholar
6.Wolff, R.W. (1988). Stochastic modeling and the theory of queues. Prentice-Hall International Series in Industrial and Systems Engineering. Englewood Cliffs, NJ: Prentice-Hall.Google Scholar