Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-29T06:19:24.689Z Has data issue: false hasContentIssue false
  • English
  • Français

Queues with semi-Markovian arrivals

Published online by Cambridge University Press:  14 July 2016

Erhan Çinlar
Erhan Çinlar*
Affiliation:
Northwestern University, Evanston, Illinois
Get access Rights & Permissions [Opens in a new window]

Abstract

A queueing system with a single server is considered. There are a finite number of types of customers, and the types of successive arrivals form a Markov chain. Further, the nth interarrival time has a distribution function which may depend on the types of the nth and the n–1th arrivals. The queue size, waiting time, and busy period processes are investigated. Both transient and limiting results are given.

Type
Research Papers
Information
Journal of Applied Probability , Volume 4 , Issue 2 , August 1967 , pp. 365 - 379
Copyright
Copyright © Sheffield: 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

[1] Činlar, E. (1966) Decomposition of a semi-Markov process under a state dependent rule. J. Soc. Indust. Appl. Math. 15, 252–263.CrossRefGoogle Scholar
[2] Gantmacher, F. R. (1959) The Theory of Matrices. Chelsea, New York.Google Scholar
[3] Loynes, R. M. (1962) Stationary waiting-time distributions for single server queues. Ann. Math. Statist. 23, 1323–1339.CrossRefGoogle Scholar
[4] Neuts, M. R. (1966) The single server queue with Poisson input and semi-Markov service times. J. Appl. Prob. 3, 202–230.CrossRefGoogle Scholar
[5] Pyke, R. (1961) Markov renewal processes with finitely many states. Ann. Math. Statist. 32, 1243–1259.CrossRefGoogle Scholar
[6] Romanovsky, V. I. (1936) Recherches sur les chaînes de Markoff. Acta Math. 66, 147–251.CrossRefGoogle Scholar
[7] Smith, W. L. (1955) Regenerative stochastic processes. Proc. Roy. Soc. Ser. A. 232, 6–31.Google Scholar
[8] Takács, L. (1962) Introduction to the Theory of Queues. Oxford University Press, New York.Google Scholar
[9] Wielandt, H. (1950) Unzerlegbare nicht-negative Matrizen. Math. Z. 52, 642–648.CrossRefGoogle Scholar