On the rate of convergence of the asymptotic expansion for the ergodic distribution of a semi-markov (s,S) inventory model

A stochastic process is considered that describes the so-called (s, S) inventory model. The asymptotic behavior of the ergodic distribution of the process is investigated. It is established that the ergodic distribution of the process on the interval [s, S] tends to the uniform distribution for sufficiently large values of the parameter ?=S-s and the convergence rate is estimated. © 2012 Springer Science+Business Media, Inc.