A semi-Markovian renewal reward process with $\Gamma g $ distributed demand

Authors : Aslı Bektaş Kamişlik, Büşra Alakoç, Tülay Kesemen, Tahir Khaniyev

Pages : 1250-1262

Doi:10.3906/mat-2002-72

View : 16 | Download : 0

Publication Date : 9999-12-31

Article Type : Makaleler

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