Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-28T07:36:40.464Z Has data issue: false hasContentIssue false
  • English
  • Français

An infinite-server queue subject to an extraneous phase process and related models

Published online by Cambridge University Press:  14 July 2016

P. Purdue  and
D. Linton
P. Purdue*
Affiliation:
University of Kentucky
D. Linton*
Affiliation:
University of Louisville
*
∗Postal address: Department of Statistics, University of Kentucky, Lexington, KY 40506, U.S.A.
∗∗Postal address: Department of Applied Mathematics, University of Louisville, Louisville, KY 40208, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider an infinite-server queueing system in an extraneous environment. Initially it is shown that the systems of interest can be decomposed into a two-stage system. The primary system is an infinite-server queue with many customer types subject to a clearing mechanism. The secondary system is a special type of bulk-arrival, infinite-server queue. We derive results for the primary and secondary systems separately and combine the results to find the mean steady-state behavior of the original system.

Keywords

SHOT NOISE PROCESSQUEUES IN RANDOM ENVIRONMENTBULK ARRIVALS
Type
Research Papers
Information
Journal of Applied Probability , Volume 18 , Issue 1 , March 1981 , pp. 236 - 244
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

[1] Çinlar, E. (1975) Introduction to Stochastic Processes. Prentice-Hall, New Jersey.Google Scholar
[2] Linton, D. and Purdue, P. (1979) An M/G/8 queue with m customer types subject to periodic clearing. Opsearch 16, 80–88.Google Scholar
[3] Neuts, M. F. (1971) A queue subject to an extraneous phase change. Adv. Appl. Prob. 3, 78–119.Google Scholar
[4] Neuts, M. F. (1977) The M/M/1 queue with randomly varying arrival and service rates. Dept. of Statistics & Computer Science, University of Delaware, Tech. Report No. 77/11.Google Scholar
[5] Neuts, M. F. and Chen, S. (1972) The infinite server queue with semi-Markovian arrivals and negative exponential services. J. Appl. Prob. 9, 178–184.Google Scholar
[6] Purdue, P. (1979) The single server queue in a random environment. Methods Operat. Res. 33, 365–372.Google Scholar
[7] Rice, J. (1977) On generalized shot noise. Adv. Appl. Prob. 9, 553–565.Google Scholar
[8] Stidham, S. (1974) Stochastic clearing systems. Stoch. Proc. Appl. 2, 85–115.Google Scholar
[9] Smith, W. (1973) Shot noise generated by a semi-Markov process. J. Appl. Prob. 10, 685–690.Google Scholar
[10] Takács, L. (1956) On secondary processes generated by recurrent processes. Acta. Math. Acad. Sci. Hung. 7, 17–29.Google Scholar
[11] Takács, L. (1958) On a coincidence problem in telephone traffic. Acta. Math. Acad. Sci. Hung. 9, 45–80.Google Scholar