IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i5p628-d1342565.html
   My bibliography  Save this article

Performance of a Synchronisation Station with Abandonment

Author

Listed:
  • Dieter Fiems

    (Department of Telecommunication Systems and Information Processing, Ghent University, St-Pietersnieuwstraat 41, 9000 Gent, Belgium)

Abstract

The paper presents a Markovian queueing model for assessing the performance of synchronisation between stations in a production system. The system at hand consists of K distinct buffers, each buffer storing an item that is needed for the next production stage. Departures are immediate when all items are present. Due to the presence of multiple buffers, there is no reasonably fast way to calculate the stationary distribution of the Markov chain. Therefore, we focused on the series expansion of the stationary distribution in terms of the arrival rate. We provide a fast algorithm for calculating these terms. Comparing our results with stochastic simulation, we show that the expansion approach converges to the simulated values for a wide range of arrival rates.

Suggested Citation

  • Dieter Fiems, 2024. "Performance of a Synchronisation Station with Abandonment," Mathematics, MDPI, vol. 12(5), pages 1-12, February.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:5:p:628-:d:1342565
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/5/628/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/5/628/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Mohamed El Amine Boudella & Evren Sahin & Yves Dallery, 2018. "Kitting optimisation in Just-in-Time mixed-model assembly lines: assigning parts to pickers in a hybrid robot–operator kitting system," Post-Print hal-01736748, HAL.
    2. Blanc, J.P.C. & van der Mei, R.D., 1992. "Optimization of polling systems with Bernoulli schedules," Other publications TiSEM dd631dbc-d81c-4b05-9539-7, Tilburg University, School of Economics and Management.
    3. Mohamed El Amine Boudella & Evren Sahin & Yves Dallery, 2018. "Kitting optimisation in Just-in-Time mixed-model assembly lines: assigning parts to pickers in a hybrid robot–operator kitting system," International Journal of Production Research, Taylor & Francis Journals, vol. 56(16), pages 5475-5494, August.
    4. Ekaterina Evdokimova & Sabine Wittevrongel & Dieter Fiems, 2017. "A Taylor Series Approach for Service-Coupled Queueing Systems with Intermediate Load," Mathematical Problems in Engineering, Hindawi, vol. 2017, pages 1-10, April.
    5. Olcay Polat & Can B. Kalayci & Özcan Mutlu & Surendra M. Gupta, 2016. "A two-phase variable neighbourhood search algorithm for assembly line worker assignment and balancing problem type-II: an industrial case study," International Journal of Production Research, Taylor & Francis Journals, vol. 54(3), pages 722-741, February.
    6. Rodrigo Romero-Silva & Margarita Hurtado-Hernández, 2023. "The effects of supply variability on the performance of assembly systems," International Journal of Production Research, Taylor & Francis Journals, vol. 61(15), pages 4973-4990, August.
    7. Ananth Krishnamurthy & Rajan Suri & Mary Vernon, 2004. "Analysis of a Fork/Join Synchronization Station with Inputs from Coxian Servers in a Closed Queuing Network," Annals of Operations Research, Springer, vol. 125(1), pages 69-94, January.
    8. van den Hout, W.B., 1996. "The power-series algorithm : A numerical approach to Markov processes," Other publications TiSEM ad00ca29-7daf-4bdb-b994-c, Tilburg University, School of Economics and Management.
    9. Nico Goossens & Ananth Krishnamurthy & Nico Vandaele, 2019. "Analysis of a fork/join station with inputs from a finite population subnetwork with multi-server stations," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 41(1), pages 291-315, March.
    10. Evren Sahin & Mohamed El Amine Boudella & Yves Dallery, 2018. "Kitting optimisation in Just-in-Time mixed-model assembly lines: assigning parts to pickers in a hybrid robot–operator kitting system," Post-Print hal-01736718, HAL.
    11. Yonit Barron, 2023. "The Delay Time Profile of Multistage Networks with Synchronization," Mathematics, MDPI, vol. 11(14), pages 1-30, July.
    12. Erkut Sönmez & Alan Scheller-Wolf & Nicola Secomandi, 2017. "An Analytical Throughput Approximation for Closed Fork/Join Networks," INFORMS Journal on Computing, INFORMS, vol. 29(2), pages 251-267, May.
    13. Dieter Fiems & Tuan Phung-Duc, 2019. "Light-traffic analysis of random access systems without collisions," Annals of Operations Research, Springer, vol. 277(2), pages 311-327, June.
    14. Ram Ramakrishnan & Ananth Krishnamurthy, 2008. "Analytical Approximations For Kitting Systems With Multiple Inputs," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 25(02), pages 187-216.
    Full references (including those not matched with items on IDEAS)

    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. Yilmaz, Aysegul & Dora, Manoj & Hezarkhani, Behzad & Kumar, Maneesh, 2022. "Lean and industry 4.0: Mapping determinants and barriers from a social, environmental, and operational perspective," Technological Forecasting and Social Change, Elsevier, vol. 175(C).
    2. Emilio Moretti & Elena Tappia & Martina Mauri & Marco Melacini, 2022. "A performance model for mobile robot-based part feeding systems to supermarkets," Flexible Services and Manufacturing Journal, Springer, vol. 34(3), pages 580-613, September.
    3. Dieter Fiems & Tuan Phung-Duc, 2019. "Light-traffic analysis of random access systems without collisions," Annals of Operations Research, Springer, vol. 277(2), pages 311-327, June.
    4. Sem Borst & Onno Boxma, 2018. "Polling: past, present, and perspective," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(3), pages 335-369, October.
    5. Borba, Leonardo & Ritt, Marcus & Miralles, Cristóbal, 2018. "Exact and heuristic methods for solving the Robotic Assembly Line Balancing Problem," European Journal of Operational Research, Elsevier, vol. 270(1), pages 146-156.
    6. Gaury, E.G.A., 2000. "Designing pull production control systems : Customization and robustness," Other publications TiSEM c9b49495-f647-4583-b2ef-0, Tilburg University, School of Economics and Management.
    7. Gong, X., 2001. "Empirical studies on the labor market and on consumer demand," Other publications TiSEM eed29455-f1bf-4cc3-aff5-c, Tilburg University, School of Economics and Management.
    8. Stremersch, S., 2001. "Essays on marketing strategy in technology-intensive markets," Other publications TiSEM 51d17923-2aae-485b-a59b-5, Tilburg University, School of Economics and Management.
    9. Nico Goossens & Ananth Krishnamurthy & Nico Vandaele, 2019. "Analysis of a fork/join station with inputs from a finite population subnetwork with multi-server stations," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 41(1), pages 291-315, March.
    10. Erkut Sönmez & Alan Scheller-Wolf & Nicola Secomandi, 2017. "An Analytical Throughput Approximation for Closed Fork/Join Networks," INFORMS Journal on Computing, INFORMS, vol. 29(2), pages 251-267, May.
    11. Blanc, J.P.C., 1993. "Performance Analysis and Optimization with the Power-Series Algorithm," Discussion Paper 1993-47, Tilburg University, Center for Economic Research.
    12. Blanc, J.P.C., 1996. "Optimization of Periodic Polling Systems with Non-Preemptive, Time-Limited Service," Discussion Paper 1996-63, Tilburg University, Center for Economic Research.
    13. Girndt, T., 2000. "Cultural diversity and work-group performance : Detecting the rules," Other publications TiSEM 79060da1-f8e7-45e5-bb6b-8, Tilburg University, School of Economics and Management.
    14. Jonathan Oesterle & Lionel Amodeo & Farouk Yalaoui, 2019. "A comparative study of Multi-Objective Algorithms for the Assembly Line Balancing and Equipment Selection Problem under consideration of Product Design Alternatives," Journal of Intelligent Manufacturing, Springer, vol. 30(3), pages 1021-1046, March.
    15. Onderstal, A.M., 2002. "Papers in auction theory," Other publications TiSEM 7d84e23f-2bb6-4e3c-a689-5, Tilburg University, School of Economics and Management.
    16. van Lomwel, A.G.C., 2000. "Essays on labour economics," Other publications TiSEM 957b3422-61d0-461d-9d22-e, Tilburg University, School of Economics and Management.
    17. Delorme, Xavier & Dolgui, Alexandre & Kovalev, Sergey & Kovalyov, Mikhail Y., 2019. "Minimizing the number of workers in a paced mixed-model assembly line," European Journal of Operational Research, Elsevier, vol. 272(1), pages 188-194.
    18. Kevin Granville & Steve Drekic, 2020. "A 2-class maintenance model with dynamic server behavior," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 34-96, April.
    19. Possajennikov, A., 2000. "Learning and evolution in games and oligopoly models," Other publications TiSEM be1a3e81-e186-46b5-9101-3, Tilburg University, School of Economics and Management.
    20. van den Broek, W.A., 2001. "Uncertainty in differential games," Other publications TiSEM 195bcb68-8943-49c1-8acb-0, Tilburg University, School of Economics and Management.

    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:gam:jmathe:v:12:y:2024:i:5:p:628-:d:1342565. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.