Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-10T13:40:36.548Z Has data issue: false hasContentIssue false
  • English
  • Français

A queueing system with Markov-dependent arrivals

Published online by Cambridge University Press:  14 July 2016

Pyke Tin
Pyke Tin*
Affiliation:
University of Rangoon
*
∗Postal address: Department of Mathematics, University of Rangoon, Rangoon, Burma.
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper considers a single-server queueing system with Markov-dependent interarrival times, with special reference to the serial correlation coefficient of the arrival process. The queue size and waiting-time processes are investigated. Both transient and limiting results are given.

Keywords

INTERARRIVAL TIMESQUEUE SIZEWAITING TIME
Type
Research Papers
Information
Journal of Applied Probability , Volume 22 , Issue 3 , September 1985 , pp. 668 - 677
Copyright
Copyright © Applied Probability Trust 1985 

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

Finch, P. D. and Pearce, C. (1965) A second look at queueing system with moving average input process. J. Austral. Math. Soc. 5, 100–106.Google Scholar
Jackson, R. R. P. and Nickols, D. G. (1956) Some equilibrium results for the queueing process Ek/M/1. J. R. Statist. Soc. B 18, 275–279.Google Scholar
Kingman, J. F. C. (1962) On queues in heavy traffic. J. R. Statist. Soc. B 24, 383–392.Google Scholar
Kuczma, M. (1968) Functional Equations in a Single Variable. Polska Akademia Nauk Monografia Matematyczma, Warszawa.Google Scholar
Lampard, D. G. (1968) A stochastic process whose successive intervals between events form a first order Markov chain — I. J. Appl. Prob. 5, 648–668.Google Scholar
Loynes, R. M. (1962) Stationary waiting time distributions for single server queues. Ann. Math. Statist. 23, 1323–1339.Google Scholar
Pearce, C. (1966) A queueing system with general moving average input and negative exponential service time. J. Austral. Math. Soc. 6, 223–236.Google Scholar
Phatarfod, R. M. (1971) Some approximate results in renewal and dam theories. J. Austral. Math. Soc. 12, 425–432.Google Scholar
Phatarfod, R. M. (1974) Note on the reversible counters system of Lampard. J. Appl. Prob. 11, 624–628.Google Scholar
Read, A. H. (1952) The solution of a functional equation. Proc. R. Soc. Edinburgh A 63, 336–365.Google Scholar
Runnenburg, J. Th. (1960) On the Use of Markov Processes in Server Waiting Time Problems and Renewal Theory. .Google Scholar
Runnenburg, J. Th. (1961) An example illustrating the probabilities of renewal theory and waiting time theory for Markov dependent arrival intervals. Proc. Ser. A. Kon. Nederl. Akad. Weten. 64, 560–576.Google Scholar