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Solving Semi-Open Queuing Networks

Author

Listed:
  • Jing Jia

    (Barclays Bank of Delaware, Wilmington, Delaware 19801)

  • Sunderesh S. Heragu

    (Department of Industrial Engineering, University of Louisville, Louisville, Kentucky 40292)

Abstract

A semi-open queuing network (SOQN) is a special type of a queuing network consisting of two parts: an inner network with a population constraint and an external queue to accommodate jobs whose entrance is delayed. We first study an SOQN with a single class of jobs in tandem configuration and then extend our study to multiclass configurations. Multiclass SOQNs fall into two categories: general pallet and dedicated pallet SOQNs. For the general pallet case, we aggregate all classes and solve the resulting single-class SOQN. For the dedicated pallet case, we construct a method based on an existing product-form approximation method for general, multiclass closed networks. Our approximation method combines the matrix-geometric method with the decomposition-aggregation approach. Numerical results show that our approximations have desirable accuracy and efficiency.

Suggested Citation

  • Jing Jia & Sunderesh S. Heragu, 2009. "Solving Semi-Open Queuing Networks," Operations Research, INFORMS, vol. 57(2), pages 391-401, April.
    • Handle: RePEc:inm:oropre:v:57:y:2009:i:2:p:391-401
    DOI: 10.1287/opre.1080.0627
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    References listed on IDEAS

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    1. Ronald Buitenhek & Geert‐Jan van Houtum & Henk Zijm, 2000. "AMVA‐based solution procedures for open queueing networks with population constraints," Annals of Operations Research, Springer, vol. 93(1), pages 15-40, January.
    2. Yao, David D. & Buzacott, J. A., 1986. "The exponentialization approach to flexible manufacturing system models with general processing times," European Journal of Operational Research, Elsevier, vol. 24(3), pages 410-416, March.
    3. B. Avi-Itzhak & D. P. Heyman, 1973. "Approximate Queuing Models for Multiprogramming Computer Systems," Operations Research, INFORMS, vol. 21(6), pages 1212-1230, December.
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    10. Valeriy A. Naumov & Yuliya V. Gaidamaka & Konstantin E. Samouylov, 2019. "On Truncation of the Matrix-Geometric Stationary Distributions," Mathematics, MDPI, vol. 7(9), pages 1-10, September.
    11. Roy, Debjit & de Koster, René, 2018. "Stochastic modeling of unloading and loading operations at a container terminal using automated lifting vehicles," European Journal of Operational Research, Elsevier, vol. 266(3), pages 895-910.
    12. Balsamo, Simonetta & Marin, Andrea, 2013. "Separable solutions for Markov processes in random environments," European Journal of Operational Research, Elsevier, vol. 229(2), pages 391-403.
    13. Bipan Zou & Yeming (Yale) Gong & Xianhao Xu & Zhe Yuan, 2017. "Assignment rules in robotic mobile fulfilment systems for online retailers," International Journal of Production Research, Taylor & Francis Journals, vol. 55(20), pages 6175-6192, October.
    14. Dhingra, Vibhuti & Kumawat, Govind Lal & Roy, Debjit & Koster, René de, 2018. "Solving semi-open queuing networks with time-varying arrivals: An application in container terminal landside operations," European Journal of Operational Research, Elsevier, vol. 267(3), pages 855-876.
    15. Nishant Mishra & Debjit Roy & Jan-Kees van Ommeren, 2017. "A Stochastic Model for Interterminal Container Transportation," Transportation Science, INFORMS, vol. 51(1), pages 67-87, February.
    16. Debjit Roy & René De Koster & René Bekker, 2020. "Modeling and Design of Container Terminal Operations," Operations Research, INFORMS, vol. 68(3), pages 686-715, May.
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    19. 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.
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    21. Chesoong Kim & Sergey Dudin & Alexander Dudin & Konstantin Samouylov, 2019. "Analysis of a Semi-Open Queuing Network with a State Dependent Marked Markovian Arrival Process, Customers Retrials and Impatience," Mathematics, MDPI, vol. 7(8), pages 1-19, August.

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