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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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    Cited by:

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    2. Zou, Bipan & Xu, Xianhao & Gong, Yeming (Yale) & De Koster, René, 2018. "Evaluating battery charging and swapping strategies in a robotic mobile fulfillment system," European Journal of Operational Research, Elsevier, vol. 267(2), pages 733-753.
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    5. Zou, B. & de Koster, M.B.M. & Xu, X., 2016. "Evaluating dedicated and shared storage policies in robot-based compact storage and retrieval systems," ERIM Report Series Research in Management ERS-2016-010-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
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    7. 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.
    8. Sergey Dudin & Alexander Dudin & Rosanna Manzo & Luigi Rarità, 2024. "Analysis of Semi-open Queueing Network with Correlated Arrival Process and Multi-server Nodes," SN Operations Research Forum, Springer, vol. 5(4), pages 1-29, December.
    9. 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.
    10. Tappia, Elena & Roy, Debjit & Melacini, Marco & De Koster, René, 2019. "Integrated storage-order picking systems: Technology, performance models, and design insights," European Journal of Operational Research, Elsevier, vol. 274(3), pages 947-965.
    11. Budhi S. Wibowo & Jan C. Fransoo, 2023. "Performance analysis of a drop-swap terminal to mitigate truck congestion at chemical sites," Flexible Services and Manufacturing Journal, Springer, vol. 35(2), pages 416-454, June.
    12. 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.
    13. 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.
    14. Bipan Zou & Xianhao Xu & Yeming Gong & René de Koster, 2016. "Modeling parallel movement of lifts and vehicles in tier-captive vehicle-based warehousing systems," Post-Print hal-01892897, HAL.
    15. 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.
    16. 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.
    17. Roy, D. & de Koster, M.B.M., 2015. "Stochastic Modeling of Unloading and Loading Operations at a Container Terminal using Automated Lifting Vehicles," ERIM Report Series Research in Management ERS-2015-005-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    18. 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.
    19. Kaveh Azadeh & René De Koster & Debjit Roy, 2019. "Robotized and Automated Warehouse Systems: Review and Recent Developments," Transportation Science, INFORMS, vol. 53(4), pages 917-945, July.
    20. 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.
    21. Carmen, Raïsa & Van Nieuwenhuyse, Inneke & Van Houdt, Benny, 2018. "Inpatient boarding in emergency departments: Impact on patient delays and system capacity," European Journal of Operational Research, Elsevier, vol. 271(3), pages 953-967.
    22. Bipan Zou & René De Koster & Xianhao Xu, 2018. "Operating Policies in Robotic Compact Storage and Retrieval Systems," Transportation Science, INFORMS, vol. 52(4), pages 788-811, August.

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