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

Kamislik A., Alakoc B., KESEMEN T., Khaniyev T.

TURKISH JOURNAL OF MATHEMATICS, vol.44, no.4, pp.1250-1262, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 44 Issue: 4
  • Publication Date: 2020
  • Doi Number: 10.3906/mat-2002-72
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.1250-1262
  • Recep Tayyip Erdoğan University Affiliated: Yes


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 Gamma(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).