A semi-Markovian renewal reward process with Γ(g) distributed demand
Turkish Journal of Mathematics, vol.44, no.4, pp.1250-1262, 2020 (SCI-Expanded, Scopus, TRDizin)
- Publication Type: Article / Article
- Volume: 44 Issue: 4
- Publication Date: 2020
- Doi Number: 10.3906/mat-2002-72
- Journal Name: Turkish Journal of Mathematics
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
- Page Numbers: pp.1250-1262
- Keywords: Ergodic distribution, Heavy tailed distributions, Logistic distribution, Semi-Markovian inventory model, Γ(g) class of distributions
- Open Archive Collection: Article
- Azerbaijan State University of Economics (UNEC) Affiliated: No
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 Γ(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 nth order moments of ergodic distribution of the process X(t).