Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-23T05:07:53.284Z Has data issue: false hasContentIssue false
  • English
  • Français

On a stochastic process occurring in queueing systems

Published online by Cambridge University Press:  14 July 2016

U. N. Bhat
U. N. Bhat*
Affiliation:
The University of Western Australia and Michigan State University
Get access Rights & Permissions [Opens in a new window]

Summary

Transition distribution functions (d.f.) of the stochastic process u + t − X(t), where X(t) has a compound Poisson distribution, are used to derive explicit results for the transition d.f.s of the waiting time processes in the queueing systems M/G/1 and GI/M/1.

Type
Short Communications
Information
Journal of Applied Probability , Volume 2 , Issue 2 , December 1965 , pp. 467 - 469
Copyright
Copyright © Applied Probability Trust 

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

Gani, J. and Pyke, R. (1960) The content of a dam as the supremum of an infinitely divisible process. J. Math. and Mech. 2, 639–652.Google Scholar
Prabhu, N. U. (1960a) Applications of storage theory to queues with Poisson arrivals. Ann. Math. Statist. 31, 475–482.Google Scholar
Prabhu, N. U., (1960b) Some results for the queue with Poisson arrivals. J. R. Statist. Soc. B 22, 104–107.Google Scholar
Prabhu, N. U., (1964) A waiting time process in the queue GI/M/1. Acta Math. Acad. Sci. Hung. (to appear).CrossRefGoogle Scholar
TakáCs, L. (1964) Applications of ballot theorems in the theory of queues. Symposium on Congestion Theory, University of North Carolina.Google Scholar