Turkish Journal of Mathematics
DOI
10.3906/mat-2002-72
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 $n^{th}$ order moments of ergodic distribution of the process $X(t)$.
Keywords
Logistic distribution, $\Gamma(g)$ class of distributions, heavy tailed distributions, semi-Markovian inventory model, ergodic distribution
First Page
1250
Last Page
1262
Recommended Citation
KAMIŞLIK, ASLI BEKTAŞ; ALAKOÇ, BÜŞRA; KESEMEN, TÜLAY; and KHANİYEV, TAHİR
(2020)
"A semi-Markovian renewal reward process with $\Gamma(g)$ distributed demand,"
Turkish Journal of Mathematics: Vol. 44:
No.
4, Article 13.
https://doi.org/10.3906/mat-2002-72
Available at:
https://journals.tubitak.gov.tr/math/vol44/iss4/13
