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On a new characterization of the exponential distribution related to a queueing system with an unreliable server

Published online by Cambridge University Press:  14 July 2016

B. Dimitrov  and
Z. Khalil
B. Dimitrov*
Affiliation:
University of Sofia
Z. Khalil*
Affiliation:
Concordia University
*
∗ Postal address: Department of Mathematics, University of Sofia, Bulgaria.
∗∗ Postal address: Department of Mathematics and Statistics, Loyola Campus, 7141 Sherbrooke Street West, Montreal, PQ, Canada H4B 1R6.
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Abstract

In this paper we derive a new property of the exponential distribution, closely related to a single-server queueing system with unreliable server. We show that this new property is another characterization of the exponential law.

Keywords

CHARACTERIZATION THEOREMBLOCKING TIMESFAILURE TIMESLAPLACE-STIELTJES TRANSFORM

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 27 , Issue 1 , March 1990 , pp. 221 - 226
Copyright
Copyright © Applied Probability Trust 1990 

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Footnotes

Research supported by the Natural Sciences and Engineering Research Council of Canada, Grant A9095.

References

[1] Azlarov, T. and Volodin, N. (1986) Characterization Problems Associated with the Exponential Distribution. Springer-Verlag, Berlin.Google Scholar
[2] Galambos, J. and Kotz, S. (1978) Characterizations of Probability Distributions: A Unified Approach with an Emphasis on Exponential and Related Models. Lecture Notes in Mathematics 675, Springer-Verlag, Berlin.Google Scholar
[3] Gnedenko, B., Danielian, E., Dimitrov, B., Klimov, G. and Matveyev, V. (1973) Priority Queues (in Russian). Moscow University Press.Google Scholar
[4] Levinson, N. and Redheffer, R. Complex Variables. Holden-Day, San Francisco.Google Scholar