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

Kamişlik A. B., Alakoç B., YAZIR T., Khaniyev T.

Turkish Journal of Mathematics, vol.44, no.4, pp.1250-1262, 2020 (SCI-Expanded) identifier

  • Nəşrin Növü: Article / Article
  • Cild: 44 Say: 4
  • Nəşr tarixi: 2020
  • Doi nömrəsi: 10.3906/mat-2002-72
  • jurnalın adı: Turkish Journal of Mathematics
  • Jurnalın baxıldığı indekslər: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Səhifə sayı: pp.1250-1262
  • Açar sözlər: Ergodic distribution, Heavy tailed distributions, Logistic distribution, Semi-Markovian inventory model, Γ(g) class of distributions
  • Açıq Arxiv Kolleksiyası: Məqalə
  • Adres: Yox

Qısa məlumat

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).