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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.
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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

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 18 , Issue 1 , March 1981 , pp. 236 - 244
Copyright
Copyright © Applied Probability Trust 

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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