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Publisher DOI: 10.1007/s00291-021-00662-9
arXiv ID: 1912.01782
Title: Analysis of semi-open queueing networks using lost customers approximation with an application to robotic mobile fulfilment systems
Language: English
Authors: Otten, Sonja 
Krenzler, Ruslan 
Xie, Lin 
Daduna, Hans 
Kruse, Karsten  
Keywords: Semi-open queueing network; Backordering; Lost customers; Product form approximation; Robotic mobile fulfilment system; Warehousing
Issue Date: Jun-2022
Publisher: Springer
Source: OR Spectrum 44 (2): 603-648 (2022-06)
Abstract (english): 
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.
DOI: 10.15480/882.4053
ISSN: 1436-6304
Journal: OR spectrum 
Institute: Mathematik E-10 
Document Type: Article
Project: Robotic Mobile Fulfillment System 
Projekt DEAL 
Funded by: Ecopti GmbH (Paderborn, Germany)
Beijing Hanning Tech Co., Ltd. (Beijing, China)
Peer Reviewed: Yes
License: CC BY 4.0 (Attribution) CC BY 4.0 (Attribution)
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