Compound geometric approximation under a failure rate constraint

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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.
Original languageEnglish
Pages (from-to)700-714
Number of pages15
JournalJournal of Applied Probability
Issue number3
Publication statusPublished - 24 Oct 2016


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