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Analysis of a Fork/Join Synchronization Station with Inputs from Coxian Servers in a Closed Queuing Network

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  • Ananth Krishnamurthy
  • Rajan Suri
  • Mary Vernon

Abstract

Fork/join stations are commonly used to model the synchronization constraints in queuing models of computer networks, fabrication/assembly systems and material control strategies for manufacturing systems. This paper presents an exact analysis of a fork/join station in a closed queuing network with inputs from servers with two-phase Coxian service distributions, which models a wide range of variability in the input processes. The underlying queue length and departure processes are analyzed to determine performance measures such as throughput, distributions of the queue length and inter-departure times from the fork/join station. The results show that, for certain parameter settings, variability in the arrival processes has a significant impact on system performance. The model is also used to study the sensitivity of performance measures such as throughput, mean queue lengths, and variability of inter-departure times for a wide range of input parameters and network populations. Copyright Kluwer Academic Publishers 2004

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:125:y:2004:i:1:p:69-94:10.1023/b:anor.0000011186.14865.19
    DOI: 10.1023/B:ANOR.0000011186.14865.19
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    Citations

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    Cited by:

    1. 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.
    2. Dieter Fiems, 2024. "Performance of a Synchronisation Station with Abandonment," Mathematics, MDPI, vol. 12(5), pages 1-12, February.
    3. 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.
    4. Roy, Debjit & van Ommeren, Jan-Kees & de Koster, René & Gharehgozli, Amir, 2022. "Modeling landside container terminal queues: Exact analysis and approximations," Transportation Research Part B: Methodological, Elsevier, vol. 162(C), pages 73-102.

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