Scaling analysis of an extended machine-repair model
| Autor: | Michel Mandjes, Onno Boxma, J.L. Dorsman, L. R. van Kreveld |
|---|---|
| Přispěvatelé: | Stochastic Operations Research, Stochastics (KDV, FNWI) |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Queueing theory
Mathematical optimization 021103 operations research Stationary distribution Computer science 0211 other engineering and technologies 02 engineering and technology Limiting 01 natural sciences 010104 statistics & probability Dual role Machine repair 0101 mathematics Scaling Intuition |
| Zdroj: | Proceedings of the 13th EAI International Conference on Performance Evaluation Methodologies and Tools, VALUETOOLS 2020, 172-179 STARTPAGE=172;ENDPAGE=179;TITLE=Proceedings of the 13th EAI International Conference on Performance Evaluation Methodologies and Tools, VALUETOOLS 2020 VALUETOOLS Proceedings of the 13th EAI International Conference on Performance Evaluation Methodologies and Tools: VALUETOOLS 2020 : May 18-20, 2020, Tsukuba, Japan, 172-179 STARTPAGE=172;ENDPAGE=179;TITLE=Proceedings of the 13th EAI International Conference on Performance Evaluation Methodologies and Tools |
| Popis: | We consider an extension of the classic machine-repair model, where we explicitly model the fact that machines, apart from requiring service from a single repairer, also supply service themselves to products. Due to this dual role of the machines, the system exhibits an intricate relation between the processing rate of products and the performance of the repairer. To characterize this relation, we analyze this model under a Halfin-Whitt inspired scaling regime, where we amplify the arrival rate of products, the repair speed of the repairer and the number of machines appropriately. The resulting limiting stationary distribution is elegant, allows for a closed-form expression and provides intuition on the system's behavior resulting from the machines' dual role. With numerical results we illustrate the convergence, and assess under which conditions the limiting distributions lead to accurate approximations. Next to this valuable insight, the analysis in this paper can be viewed as a first step towards a unifying scaling analysis for general closed queueing networks. |
| Databáze: | OpenAIRE |
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