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Lower bounds for the probability of overload in certain queueing networks

Published online by Cambridge University Press:  14 July 2016

Marek Kanter
Marek Kanter*
Affiliation:
Mentor Graphics, Santa Clara
*
∗Postal address: 2134 Grant St, Berkeley, CA 94703, USA.
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Abstract

Conservative estimates for the probability that open queueing networks are not overloaded during any finite set of time points are derived. The queueing networks have infinitely many servers at each queue and general service times. A key preliminary result is that for multidimensional Markov population processes, the correspondence between initial distributions and their temporal development preserves stochastic order.

Keywords

MARKOV POPULATION PROCESSESSTOCHASTIC ORDERINGMETHOD OF STAGES
Type
Research Papers
Information
Journal of Applied Probability , Volume 22 , Issue 2 , June 1985 , pp. 429 - 436
Copyright
Copyright © Applied Probability Trust 1985 

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References

Doob, J. L. (1952) Stochastic Processes. Wiley, New York.Google Scholar
Horduk, A. and Van Dijk, A. (1982) Stationary probabilities for networks of queues. In Applied Probability and Computer Science, the Interface, ed. Disney, R. L. and Ott, T. J., Birkaüser, Boston.Google Scholar
Kelly, F. (1979) Reversibility and Stochastic Networks. Wiley, New York.Google Scholar
Kingman, J. F. C. (1969) Markov population processes. J. Appl. Prob. 6, 1–18.CrossRefGoogle Scholar
Lehman, E. (1955) Ordered families of distributions. Ann. Math. Statist. 26, 399–419.Google Scholar
Lehman, E. (1966) Some concepts of dependence. Ann. Math. Statist. 37, 1137–1153.Google Scholar
Ross, S. M. (1983) Stochastic Processes. Wiley, New York.Google Scholar