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Analysis of semi-open queueing networks using lost customers approximation with an application to robotic mobile fulfilment systems
Citation Link: https://doi.org/10.15480/882.4053
Publikationstyp
Journal Article
Date Issued
2022-06
Sprache
English
Institut
TORE-DOI
Journal
Volume
44
Issue
2
Start Page
603
End Page
648
Citation
OR Spectrum 44 (2): 603-648 (2022-06)
Publisher DOI
Scopus ID
ArXiv ID
Publisher
Springer
Peer Reviewed
true
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.
Subjects
Semi-open queueing network
Backordering
Lost customers
Product form approximation
Robotic mobile fulfilment system
Warehousing
DDC Class
004: Informatik
330: Wirtschaft
510: Mathematik
Funding(s)
Funding Organisations
Ecopti GmbH (Paderborn, Germany)
Beijing Hanning Tech Co., Ltd. (Beijing, China)
Publication version
publishedVersion
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Name
Otten, Krenzler, Xie, Daduna, Kruse, Analysis of semi-open queueing networks using lost customers approximation with an application.pdf
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2.34 MB
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Adobe PDF