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Analysis of semi-open queueing networks using lost customers approximation with an application to robotic mobile fulfilment systems

Author

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  • Sonja Otten

    (Leuphana University of Lüneburg
    Hamburg University of Technology)

  • Ruslan Krenzler

    (Leuphana University of Lüneburg)

  • Lin Xie

    (Leuphana University of Lüneburg)

  • Hans Daduna

    (Universität Hamburg)

  • Karsten Kruse

    (Hamburg University of Technology)

Abstract

We consider a semi-open queueing network (SOQN), where one resource from a resource pool is needed to serve a customer. If on arrival of a customer some resource is available, the resource is forwarded to an inner network to complete the customer’s order. If no resource is available, the new customer waits in an external queue until one becomes available (“backordering”). When a resource exits the inner network, it is returned to the resource pool. We develop a new solution approach. In a first step we modify the system such that new arrivals are lost if the resource pool is empty (“lost customers”). We adjust the arrival rate of the modified system such that the throughputs in all nodes of the inner network are pairwise identical to those in the original network. Using queueing theoretical methods, in a second step we reduce this inner network to a two-station system including the resource pool. For this two-station systems, we invert the first step and obtain a standard SOQN which can be solved analytically. We apply our results to storage and delivering systems with robotic mobile fulfilment systems (RMFSs). Instead of sending pickers to the storage area to search for the ordered items and pick them, robots carry shelves with ordered items from the storage area to picking stations. We model the RMFS as an SOQN to determine the minimal number of robots.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:orspec:v:44:y:2022:i:2:d:10.1007_s00291-021-00662-9
    DOI: 10.1007/s00291-021-00662-9
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    References listed on IDEAS

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    Cited by:

    1. Kaibo Liang & Li Zhou & Jianglong Yang & Huwei Liu & Yakun Li & Fengmei Jing & Man Shan & Jin Yang, 2023. "Research on a Dynamic Task Update Assignment Strategy Based on a “Parts to Picker” Picking System," Mathematics, MDPI, vol. 11(7), pages 1-29, March.
    2. 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.

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