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Journals / Hacettepe Journal of Mathematics and Statistics / 2010 / Cilt: 39 - Sayı: 4

On the weak convergence of the ergodic distribution for an inventory model of type (s,S)

Kumru Didem ATALAY
Tahir KHANİYEV
Pages
599–611
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, the accuracy of the ap- proximation formula is tested by the Monte Carlo simulation method.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, a renewal - reward process with a discrete interference of chance is constructed.
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Key Findings & Data:This process describes in particular a semi- Markovian inventory model of type (s,S).
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Conclusion & Impact:Finally, the accuracy of the ap- proximation formula is tested by the Monte Carlo simulation method.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this study, a renewal - reward process with a discrete interference of chance is constructed. This process describes in particular a semi- Markovian inventory model of type (s,S). The ergodic distribution of this process is expressed by a renewal function, and a second-order ap- proximation for the ergodic distribution of the process is obtained as S − s → ∞ when the interference has a triangular distribution. Then, the weak convergence theorem is proved for the ergodic distribution and the limit distribution is derived. Finally, the accuracy of the ap- proximation formula is tested by the Monte Carlo simulation method.

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Cite This Article

ATALAY, K. D., KHANİYEV, T. (2022). On the weak convergence of the ergodic distribution for an inventory model of type (s,S). Hacettepe Journal of Mathematics and Statistics, Cilt: 39 - Sayı: 4, 599–611. https://ajindex.com/articles/530851

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