On the weak convergence of the ergodic distribution for an inventory model of type (s,S)

Abstract

In this study, a renewal - reward process with a discrete interference of chance is constructed. This process describes in particular a semi- Markovian inventory model of type (s,S). The ergodic distribution of this process is expressed by a renewal function, and a second-order ap- proximation for the ergodic distribution of the process is obtained as S − s → ∞ when the interference has a triangular distribution. Then, the weak convergence theorem is proved for the ergodic distribution and the limit distribution is derived. Finally, the accuracy of the ap- proximation formula is tested by the Monte Carlo simulation method.