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September 2016 Compound geometric approximation under a failure rate constraint
Fraser Daly
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J. Appl. Probab. 53(3): 700-714 (September 2016).

Abstract

We consider compound geometric approximation for a nonnegative, integer-valued random variable W. The bound we give is straightforward but relies on having a lower bound on the failure rate of W. Applications are presented to M/G/1 queuing systems, for which we state explicit bounds in approximations for the number of customers in the system and the number of customers served during a busy period. Other applications are given to birth–death processes and Poisson processes.

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Fraser Daly. "Compound geometric approximation under a failure rate constraint." J. Appl. Probab. 53 (3) 700 - 714, September 2016.

Information

Published: September 2016
First available in Project Euclid: 13 October 2016

zbMATH: 1351.62060
MathSciNet: MR3570089

Subjects:
Primary: 62E17
Secondary: 60E15 , 60J10 , 62E10

Keywords: Birth–death process , Compound geometric distribution , failure rate , hazard rate ordering , M/G/1 queue , Poisson process

Rights: Copyright © 2016 Applied Probability Trust

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Vol.53 • No. 3 • September 2016
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