A semi-Markovian renewal reward process with (g) distributed demand

Abstract

We consider a classical semi-Markovian stochastic model of type (s, S) with Logistic distributed demand random variables. Logistic distribution is a member of special distribution class known as (g) that encounters in many real-life applications involving extreme value theory. The objective of this study is to observe some major characteristics of a stochastic process X(t) which represents semi-Markovian renewal reward process of type (s, S). We used new approximation results for renewal function that allow us to obtain three-term asymptotic expansion for ergodic distribution function and for $n^{th}$ order moments of ergodic distribution of the process X(t).