IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v182y2011i1p5-3010.1007-s10479-009-0612-6.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-009-0612-6
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-009-0612-6?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ding Zhang & Yi Luo & Qiang Liu, 2024. "Reliability evaluation of production systems with finite buffers subject to time-dependent and operation-dependent failures," Annals of Operations Research, Springer, vol. 340(1), pages 671-691, September.
    2. 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.
    3. 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.
    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. 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.
    6. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Marcello Colledani & Stanley Gershwin, 2013. "A decomposition method for approximate evaluation of continuous flow multi-stage lines with general Markovian machines," Annals of Operations Research, Springer, vol. 209(1), pages 5-40, October.
    3. 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.
    4. Sachs, F.E. & Helber, S. & Kiesmüller, G.P., 2022. "Evaluation of Unreliable Flow Lines with Limited Buffer Capacities and Spare Part Provisioning," European Journal of Operational Research, Elsevier, vol. 302(2), pages 544-559.
    5. Cigdem Gurgur, 2013. "Optimal configuration of a decentralized, market-driven production/inventory system," Annals of Operations Research, Springer, vol. 209(1), pages 139-157, October.
    6. Sorensen, Kenneth & Janssens, Gerrit K., 2001. "Buffer allocation and required availability in a transfer line with unreliable machines," International Journal of Production Economics, Elsevier, vol. 74(1-3), pages 163-173, December.
    7. Papadopoulos, H. T. & Heavey, C., 1996. "Queueing theory in manufacturing systems analysis and design: A classification of models for production and transfer lines," European Journal of Operational Research, Elsevier, vol. 92(1), pages 1-27, July.
    8. Cruz, F.R.B. & Van Woensel, T. & Smith, J. MacGregor, 2010. "Buffer and throughput trade-offs in M/G/1/K queueing networks: A bi-criteria approach," International Journal of Production Economics, Elsevier, vol. 125(2), pages 224-234, June.
    9. 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).
    10. Beixin Xia & Binghai Zhou & Ci Chen & Lifeng Xi, 2016. "A generalized-exponential decomposition method for the analysis of inhomogeneous assembly/disassembly systems with unreliable machines and finite buffers," Journal of Intelligent Manufacturing, Springer, vol. 27(4), pages 765-779, August.
    11. Barış Tan, 2019. "Production Control with Price, Cost, and Demand Uncertainty," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 41(4), pages 1057-1085, December.
    12. Yaghoubi, Saeed & Noori, Siamak & Azaron, Amir & Fynes, Brian, 2015. "Resource allocation in multi-class dynamic PERT networks with finite capacity," European Journal of Operational Research, Elsevier, vol. 247(3), pages 879-894.
    13. Andrea Matta & Francesca Simone, 2016. "Analysis of two-machine lines with finite buffer, operation-dependent and time-dependent failure modes," International Journal of Production Research, Taylor & Francis Journals, vol. 54(6), pages 1850-1862, March.
    14. Wei, Shuaichong & Nourelfath, Mustapha & Nahas, Nabil, 2023. "Analysis of a production line subject to degradation and preventive maintenance," Reliability Engineering and System Safety, Elsevier, vol. 230(C).
    15. Liu, Jialu & Yang, Sheng & Wu, Aiguo & Hu, S. Jack, 2012. "Multi-state throughput analysis of a two-stage manufacturing system with parallel unreliable machines and a finite buffer," European Journal of Operational Research, Elsevier, vol. 219(2), pages 296-304.
    16. Kucuksayacigil, Fikri & Roni, Mohammad & Eksioglu, Sandra D. & Bhuiyan, Tanveer H. & Chen, Qiushi, 2022. "Optimal control to handle variations in moisture content and reactor in-feed rate," Energy, Elsevier, vol. 248(C).
    17. Kolb, Oliver & Göttlich, Simone, 2015. "A continuous buffer allocation model using stochastic processes," European Journal of Operational Research, Elsevier, vol. 242(3), pages 865-874.
    18. Hatice Ucar Guner & Alper Murat & Ratna Babu Chinnam, 2024. "Performance analysis of a production system with two deteriorating machines and a finite buffer," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 32(3), pages 621-651, September.
    19. Sorensen, Kenneth & Janssens, Gerrit K., 2004. "A Petri net model of a continuous flow transfer line with unreliable machines," European Journal of Operational Research, Elsevier, vol. 152(1), pages 248-262, January.
    20. Jung Baek & Ho Lee & Se Lee & Soohan Ahn, 2013. "A MAP-modulated fluid flow model with multiple vacations," Annals of Operations Research, Springer, vol. 202(1), pages 19-34, January.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:annopr:v:182:y:2011:i:1:p:5-30:10.1007/s10479-009-0612-6. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.