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Compound geometric approximation under a failure rate constraint

Part of: Distribution theory - Probability Distribution theory Markov processes

Published online by Cambridge University Press:  24 October 2016

Fraser Daly
Fraser Daly*
Affiliation:
Heriot-Watt University
*
*Postal address: Department of Actuarial Mathematics and Statistics and the Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, UK. Email address: f.daly@hw.ac.uk
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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.

Keywords

Compound geometric distributionfailure ratehazard rate orderingM/G/1 queuebirth–death processPoisson process

MSC classification

Primary: 62E17: Approximations to distributions (nonasymptotic)
Secondary: 60E15: Inequalities; stochastic orderings 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 62E10: Characterization and structure theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 53 , Issue 3 , September 2016 , pp. 700 - 714
Copyright
Copyright © Applied Probability Trust 2016 

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