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The Service Time Properties of an Unreliable Server Characterize the Exponential Distribution

Part of: Distribution theory - Probability Special processes Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Z. Khalil  and
B. Dimitrov
Z. Khalil*
Affiliation:
Concordia University
B. Dimitrov*
Affiliation:
University of Sofia
*
* Postal address: Mathematics and Statistics, Concordia University, 7141 Sherbrooke Street West, Montreal, Quebec, Canada H4B 1R6.
** Postal address: University of Sofia, Bul. James Boucher 5, 1126 Sofia, Bulgaria.
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Abstract

Consider the total service time of a job on an unreliable server under preemptive-repeat-different and preemptive-resume service disciplines. With identical initial conditions, for both cases, we notice that the distributions of the total service time under these two disciplines coincide, when the original service time (without interruptions due to server failures) is exponential and independent of the server reliability. We show that this fact under varying server reliability is a characterization of the exponential distribution. Further we show, under the same initial conditions, that the coincidence of the mean values also leads to the same characterization.

Keywords

CHARACTERIZATION THEOREMFAILURE TIMESBLOCKING TIMESLAPLACE–STIELTJES TRANSFORMS

MSC classification

Primary: 60E10: Characteristic functions; other transforms
Secondary: 60G50: Sums of independent random variables; random walks 60K10: Applications (reliability, demand theory, etc.)
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 26 , Issue 1 , March 1994 , pp. 172 - 182
Copyright
Copyright © Applied Probability Trust 1994 

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Footnotes

Research partially supported by Natural Sciences and Engineering Research Council of Canada Grant No. A9095, and Bulgarian Council of Science Grant No. 43–87.

References

Azlarov, T. A. and Volodin, N. A. (1986) In Characterization Problems Associated with the Exponential Distribution, ed. Olkin, I., Springer-Verlag, New York.Google Scholar
Dimitrov, B. and Khalil, Z. (1990) On a new characterizing property of the exponential distribution related to a queuing system with an unreliable server. J. Appl. Prob. 27, 221–226.Google Scholar
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, New York.Google Scholar
Jaiswal, N. K. (1968) Priority Queues. Academic Press, New York.Google Scholar
Khalil, Z., Dimitrov, B. and Petrov, P. (1990) On the total execution time on an unreliable server with explicit breakdowns. Technical Rep. 8190, Concordia University, Montreal.Google Scholar
Khalil, Z., Dimitrov, B. and Dion, J.-P. (1991) A characterization of the geometric distribution related to random sums. Commun. Statist. Stoch. Models 7, 321–326.Google Scholar