Limit theorem for a semi - Markovian stochastic model of type (s,S)

Authors : Zulfiye HANALİOGLU, Tahir KHANİYEV

Pages : 605-615

View : 23 | Download : 8

Publication Date : 2019-04-01

Article Type : Research Paper

Abstract :In this study, a semi-Markovian inventory model of type $insert ignore into journalissuearticles values(s,S);$ is considered and the model is expressed by means of renewal-reward process $insert ignore into journalissuearticles values(Xinsert ignore into journalissuearticles values(t););$  with an asymmetric triangular distributed interference of chance and delay. The ergodicity of the process $Xinsert ignore into journalissuearticles values(t);$  is proved and the exact expression for the ergodic distribution is obtained. Then, two-term asymptotic expansion for the ergodic distribution is found for standardized process $Winsert ignore into journalissuearticles values(t);\equiv insert ignore into journalissuearticles values(2Xinsert ignore into journalissuearticles values(t);); / insert ignore into journalissuearticles values(S-s);$. Finally, using this asymptotic expansion, the weak convergence theorem for the ergodic distribution of the process $Winsert ignore into journalissuearticles values(t);$ is proved and the explicit form of the limit distribution is found.
Keywords : Inventory model of type s, S, , Renewal reward process, Weak convergence, Asymmetric triangular distribution, Asymptotic expansion