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Analysis of a fork/join station with inputs from a finite population subnetwork with multi-server stations

Author

Listed:
  • Nico Goossens

    (UZ Brussel)

  • Ananth Krishnamurthy

    (University of Wisconsin-Madison)

  • Nico Vandaele

    (Katholieke Universiteit Leuven)

Abstract

Forks/join stations are commonly used to model synchronization constraints in queuing networks. This paper presents an exact analysis of a fork/join station with inputs from stations composed of multiple exponential servers. The queue length process at the input buffers is analyzed exactly using the underlying Markov process. The semi-Markov kernel characterizing the departure process is analyzed to derive expressions for the marginal and joint distributions of inter-departure times from the fork/join station. These analyses are used to study the effect of inputs from multiple servers on key performance measures at a fork/join station. Comparison studies show that inputs from multiple servers have a significant effect on performance measures such as throughput, synchronization delays and queue lengths at the individual buffers. These insights are important to obtain better representation of synchronization constraints in closed queuing network models of computer networks, fabrication/assembly systems and material control strategies for manufacturing systems.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:orspec:v:41:y:2019:i:1:d:10.1007_s00291-018-0528-0
    DOI: 10.1007/s00291-018-0528-0
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    References listed on IDEAS

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    1. Liu, Y. C. & Perros, H. G., 1991. "Approximate analysis of a closed fork/join model," European Journal of Operational Research, Elsevier, vol. 53(3), pages 382-392, August.
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    3. 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.
    4. Maria Di Mascolo & Yannick Frein & Yves Dallery, 1996. "An Analytical Method for Performance Evaluation of Kanban Controlled Production Systems," Operations Research, INFORMS, vol. 44(1), pages 50-64, February.
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    Cited by:

    1. Dieter Fiems, 2024. "Performance of a Synchronisation Station with Abandonment," Mathematics, MDPI, vol. 12(5), pages 1-12, February.

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