%0 Journal Article
%T Compound geometric approximation under a failure rate constraint
%A Fraser Daly
%J Mathematics
%D 2015
%I arXiv
%X 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.
%U http://arxiv.org/abs/1504.06498v2