Compound geometric approximation under a failure rate constraint

Fraser Daly

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arXiv · 1504.06498

Compound geometric approximation under a failure rate constraint

Fraser Daly

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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.

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Fraser Daly. 2015-04-24. Compound geometric approximation under a failure rate constraint. https://arxiv.org/abs/1504.06498

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