Hostname: page-component-848d4c4894-x5gtn Total loading time: 0 Render date: 2024-06-02T02:17:28.866Z Has data issue: false hasContentIssue false
  • English
  • Français

Two results in the theory of queues

Published online by Cambridge University Press:  14 July 2016

H. Ali
H. Ali*
Affiliation:
The University of the West Indies, St. Augustine, Trinidad
Get access Rights & Permissions [Opens in a new window]

Summary

In this paper it is shown that the distribution of the instant of service of a customer is symmetric as between the distributions of service and interarrival time. Also U(t), the expected number of departures in (0, t), is a delayed renewal function for the GI/M/1 queue.

Type
Research Papers
Information
Journal of Applied Probability , Volume 7 , Issue 1 , April 1970 , pp. 219 - 226
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

Ali, H. (1968) Busy Periods and Departure Processes in Queues. M. Phil. Thesis, University of Sussex.Google Scholar
Burke, P. J. (1956) The output of a queueing system. Operat. Res. 4, 699–704.Google Scholar
Cox, D. R. (1962) Renewal Theory. Methuen, London.Google Scholar
Finch, P. D. (1959) The output process of the queueing system M/G/1. J.R. Statist. Soc. B 21, 375–380.Google Scholar
Finch, P. D. (1961) On the busy period in the queueing system GI/G/1. J. Aust. Math. Soc. 2, 217–228.Google Scholar
Kendall, D. G. (1951) Some problems in the theory of queues. J.R. Statist. Soc. B 13, 151–185.Google Scholar
Kendall, D. G. (1953). Stochastic processes occurring in the theory of queues and their analysis by the method of the embedded Markov chain. Ann. Math. Statist. 24, 338–354.Google Scholar
Kingman, J.F.C. (1962) The use of Spitzer's identity in the investigation of the busy period and other quantities in the queue GI/G/1. J. Aust. Math. Soc. 2, 345–356.Google Scholar
Lindley, D. V. (1952) The theory of queues with a single server. Proc. Camb. Phil. Soc. 277–289.Google Scholar
Reich, E. (1957) Waiting times when queues are in tandem. Ann. Math. Statist. 28, 768–773.Google Scholar
TakàCs, L. (1962) Introduction to the Theory of Queues. Oxford University Press, New York.Google Scholar