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Modelling and analysis of Markovian continuous flow systems with a finite buffer

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  • Barış Tan
  • Stanley Gershwin

Abstract

In this study, a Markovian fluid flow system with two stages separated by a finite buffer is considered. Fluid flow models have been analyzed extensively to evaluate the performance of production, computer, and telecommunication systems. Recently, we developed a methodology to analyze general Markovian continuous flow systems with a finite buffer. The flexibility of this methodology allows us to analyze a wide range of systems by specifying the transition rates and the flow rates associated with each state of each stage. In this study, in order to demonstrate the applicability of our methodology, we model and analyze a range of models studied in the literature. The examples we analyze as special cases of our general model include systems with phase-type failure and repair-time distributions, systems with machines that have multiple up and down states, and systems with multiple unreliable machines in series or parallel in each stage. For each case, the Markovian model is developed, the transition and flow rates are determined, and representative numerical results are obtained by using our methodology. Copyright Springer Science+Business Media, LLC 2011

Suggested Citation

  • Barış Tan & Stanley Gershwin, 2011. "Modelling and analysis of Markovian continuous flow systems with a finite buffer," Annals of Operations Research, Springer, vol. 182(1), pages 5-30, January.
    • Handle: RePEc:spr:annopr:v:182:y:2011:i:1:p:5-30:10.1007/s10479-009-0612-6
    DOI: 10.1007/s10479-009-0612-6
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    References listed on IDEAS

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    1. Yeralan, Sencer & Franck, Wallace E. & Quasem, Mohammad A., 1986. "A continuous materials flow production line model with station breakdown," European Journal of Operational Research, Elsevier, vol. 27(3), pages 289-300, December.
    2. Tan, BarIs & Gershwin, Stanley B., 2009. "Analysis of a general Markovian two-stage continuous-flow production system with a finite buffer," International Journal of Production Economics, Elsevier, vol. 120(2), pages 327-339, August.
    3. Stefan Helber & Hanifa Jusić, 2004. "A New Decomposition Approach for Non-Cyclic Continuous Material Flow Lines with a Merging Flow of Material," Annals of Operations Research, Springer, vol. 125(1), pages 117-139, January.
    4. Hervé Le Bihan & Yves Dallery, 2000. "A robust decomposition method for the analysis of production lines with unreliable machines and finite buffers," Annals of Operations Research, Springer, vol. 93(1), pages 265-297, January.
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    Cited by:

    1. Elisa Gebennini & Andrea Grassi & Cesare Fantuzzi, 2015. "The two-machine one-buffer continuous time model with restart policy," Annals of Operations Research, Springer, vol. 231(1), pages 33-64, August.
    2. Fitouhi, Mohamed-Chahir & Nourelfath, Mustapha & Gershwin, Stanley B., 2017. "Performance evaluation of a two-machine line with a finite buffer and condition-based maintenance," Reliability Engineering and System Safety, Elsevier, vol. 166(C), pages 61-72.
    3. Ünsal Özdoğru & Tayfur Altiok, 2015. "Continuous material flow systems: analysis of marine ports handling bulk materials," Annals of Operations Research, Springer, vol. 231(1), pages 79-104, August.
    4. Zhang, Ning & Qi, Faqun & Zhang, Chengjie & Zhou, Hongming, 2022. "Joint optimization of condition-based maintenance policy and buffer capacity for a two-unit series system," Reliability Engineering and System Safety, Elsevier, vol. 219(C).
    5. Yifan Zhou & Chao Yuan & Tian Ran Lin & Lin Ma, 2021. "Maintenance policy structure investigation and optimisation of a complex production system with intermediate buffers," Journal of Risk and Reliability, , vol. 235(3), pages 458-473, June.

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