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On the convexity of loss probabilities

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Ronald W. Wolff  and
Chia-Li Wang
Ronald W. Wolff*
Affiliation:
University of California, Berkeley
Chia-Li Wang*
Affiliation:
National Dong Hwa University
*
∗ Postal address: Department of Industrial Engineering and Operations Research, University of California, Berkeley, CA 94720, USA. Email address: wolff@ieor.berkeley.edu
∗∗ Postal address: Department of Applied Mathematics, National Dong Hwa University, Hualien, Taiwan, ROC.
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Abstract

For the M/G/c loss system, it is well known that Erlang's loss probability is convex in the number of servers. We extend this result firstly to renewal arrivals and exponential service, then to regenerative arrivals and exponential service, and finally to an arbitrary arrival process with i.i.d. service times that are independent of the arrival process.

Keywords

M/G/c loss systemErlang loss probabilitiesrenewal arrivalsregenerative processarbitrary arrival processesgeneral service distributionscoupling

MSC classification

Primary: 60K25: Queueing theory
Type
Short Communications
Information
Journal of Applied Probability , Volume 39 , Issue 2 , June 2002 , pp. 402 - 406
Copyright
Copyright © Applied Probability Trust 2002 

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References

[1] Daley, D. J. (1998). Personal communication.Google Scholar
[2] Harel, A. (1990). Convexity properties of the Erlang loss formula. Operat. Res. 38, 499–505.CrossRefGoogle Scholar
[3] Messerli, E. J. (1972). Proof of a convexity property of the Erlang B formula. Bell System Tech. J. 51, 951–953.Google Scholar
[4] Sevastyanov, B. A. (1957). An ergodic theorem for Markov processes and its application to telephone systems with refusals. Teor. Verojatnost. i Primenen 2, 106–116 (in Russian with English summary).Google Scholar
[5] Weber, R. R. (1980). On the marginal benefit of adding servers to G/GI/m queues. Manag. Sci. 26, 946–951.Google Scholar
[6] Wolff, R. W. (1989). Stochastic Modeling and the Theory of Queues. Prentice-Hall, Englewood Cliffs, NJ.Google Scholar