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AMVA‐based solution procedures for open queueing networks with population constraints

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  • Ronald Buitenhek
  • Geert‐Jan van Houtum
  • Henk Zijm

Abstract

We propose a new method for the performance evaluation of Open Queueing Networks with a Population Constraint (represented by a set of tokens). The method is based on the application of Approximate Mean Value Analysis (AMVA) algorithms. We present procedures for single class networks and for multiple class networks, subject to either a common constraint (shared tokens) or to class‐based constraints (dedicated tokens). In fact, the new method is a unified framework into which all procedures for the different types of networks fit. We show how the new method relates to well‐known methods and present some numerical results to indicate its accuracy. Copyright Kluwer Academic Publishers 2000

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:93:y:2000:i:1:p:15-40:10.1023/a:1018967622069
    DOI: 10.1023/A:1018967622069
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    1. Roy, Debjit & Nigam, Shobhit & de Koster, René & Adan, Ivo & Resing, Jacques, 2019. "Robot-storage zone assignment strategies in mobile fulfillment systems," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 122(C), pages 119-142.
    2. Chen, Wanying (Amanda) & De Koster, René B.M. & Gong, Yeming, 2021. "Performance evaluation of automated medicine delivery systems," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 147(C).
    3. 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.
    4. Chen, Wanying (Amanda) & De Koster, René & Gong, Yeming, 2023. "Warehouses without aisles: Layout design of a multi-deep rack climbing robotic system," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 179(C).
    5. Chen, Wanying & Gong, Yeming & Chen, Qi & Wang, Hongwei, 2024. "Does battery management matter? Performance evaluation and operating policies in a self-climbing robotic warehouse," European Journal of Operational Research, Elsevier, vol. 312(1), pages 164-181.
    6. Lamballais, T. & Merschformann, M. & Roy, D. & de Koster, M.B.M. & Azadeh, K. & Suhl, L., 2022. "Dynamic policies for resource reallocation in a robotic mobile fulfillment system with time-varying demand," European Journal of Operational Research, Elsevier, vol. 300(3), pages 937-952.
    7. 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.
    8. Lamballais, T. & Roy, D. & de Koster, M.B.M., 2017. "Inventory Allocation in Robotic Mobile Fulfillment Systems," ERIM Report Series Research in Management ERS-2017-001-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.
    9. 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.
    10. Jing Jia & Sunderesh S. Heragu, 2009. "Solving Semi-Open Queuing Networks," Operations Research, INFORMS, vol. 57(2), pages 391-401, April.
    11. Lamballais, T. & Roy, D. & De Koster, M.B.M., 2017. "Estimating performance in a Robotic Mobile Fulfillment System," European Journal of Operational Research, Elsevier, vol. 256(3), pages 976-990.
    12. 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.
    13. Sonja Otten & Ruslan Krenzler & Lin Xie & Hans Daduna & Karsten Kruse, 2022. "Analysis of semi-open queueing networks using lost customers approximation with an application to robotic mobile fulfilment systems," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 44(2), pages 603-648, June.
    14. 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.
    15. Kumar, Suryakant & Sheu, Jiuh-Biing & Kundu, Tanmoy, 2023. "Planning a parts-to-picker order picking system with consideration of the impact of perceived workload," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 173(C).

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