Finally, using this asymptotic expansion, the weak convergence theorem for the ergodic distribution of the process $W(t)$ is proved and the explicit form of the limit distribution is found.
📌 3 Maddede Bu Makale
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Amaç & Hipotez:In this study, a semi-Markovian inventory model of type $(s,S)$ is considered and the model is expressed by means of renewal-reward process $(X(t))$ with an asymmetric triangular distributed interference of chance and delay.
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Temel Bulgular & Veri:Then, two-term asymptotic expansion for the ergodic distribution is found for standardized process $W(t)\equiv (2X(t)) / (S-s)$.
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Sonuç & Katkı:Finally, using this asymptotic expansion, the weak convergence theorem for the ergodic distribution of the process $W(t)$ is proved and the explicit form of the limit distribution is found.
🔬Tür:Modelleme & Sayısal Simülasyon
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Inventory model of type $(s · S)$ · Renewal-reward process
Abstract
In this study, a semi-Markovian inventory model of type $(s,S)$ is considered and the model is expressed by means of renewal-reward process $(X(t))$ with an asymmetric triangular distributed interference of chance and delay. The ergodicity of the process $X(t)$ 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 $W(t)\equiv (2X(t)) / (S-s)$. Finally, using this asymptotic expansion, the weak convergence theorem for the ergodic distribution of the process $W(t)$ is proved and the explicit form of the limit distribution is found.
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