Compound geometric approximation under a failure rate constraint

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.