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

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

TURKISH JOURNAL OF MATHEMATICS, cilt.44, sa.4, ss.1250-1262, 2020 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 44 Sayı: 4
  • Basım Tarihi: 2020
  • Doi Numarası: 10.3906/mat-2002-72
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.1250-1262
  • Karadeniz Teknik Üniversitesi Adresli: Evet

Özet

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).