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Some characterizations of the exponential and geometric distributions arising in a queueing system with an unreliable server

Part of: Stochastic processes Distribution theory

Published online by Cambridge University Press:  14 July 2016

Wen-Jang Huang  and
Jyh-Ming Shoung
Wen-Jang Huang
Affiliation:
National Sun Yat-sen University
Jyh-Ming Shoung*
Affiliation:
National Sun Yat-sen University
*
∗ Postal address for both authors: Institute of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, Taiwan 80424, ROC.
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Abstract

In this article, we generalize results by Dimitrov and Khalil (1990), Khalil et al. (1991), and van Harn and Steutel (1991) and obtain some characterizations of the exponential and geometric laws.

Keywords

RENEWAL PROCESSSERVICE TIME DISTRIBUTION

MSC classification

Primary: 62E10: Characterization and structure theory
Secondary: 60G55: Point processes
Type
Short Communications
Information
Journal of Applied Probability , Volume 30 , Issue 4 , December 1993 , pp. 985 - 990
Copyright
Copyright © Applied Probability Trust 1993 

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Footnotes

Support for this research was provided in part by the National Science Council of the Republic of China, Grant No. NSC 80–0208-M1 10–06.

References

Dimitrov, B. and Khalil, Z. (1990) On a new characterization of the exponential distribution related to a queueing system with an unreliable server. J. Appl. Prob. 27, 221–226.Google Scholar
Van Harn, K. and Steutel, F. W. (1991) On a characterization of the exponential distribution. J. Appl. Prob. 28, 947–949.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
Lau, K. S. and Rao, B. L. S. P. (1990) Characterization of the exponential distribution by the relevation transform. J. Appl. Prob. 27, 726–729.Google Scholar