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Performance of a Synchronisation Station with Abandonment

Author

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  • 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
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    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. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Yonit Barron, 2023. "The Delay Time Profile of Multistage Networks with Synchronization," Mathematics, MDPI, vol. 11(14), pages 1-30, July.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    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.
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