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


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

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

  • Publication Type: Article / Article
  • Volume: 44 Issue: 4
  • Publication Date: 2020
  • Doi Number: 10.3906/mat-2002-72
  • Title of Journal : TURKISH JOURNAL OF MATHEMATICS
  • Page Numbers: pp.1250-1262

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 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).