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

Research output: Journal contributionsJournal articlesResearchpeer-review

Authors

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.

Original languageEnglish
JournalOR Spectrum
Volume44
Issue number2
Pages (from-to)603-648
Number of pages46
ISSN0171-6468
DOIs
Publication statusPublished - 06.2022

Bibliographical note

Ruslan Krenzler and Sonja Otten are funded by the industrial project “Robotic Mobile Fulfillment System”, which is financially supported by Ecopti GmbH (Paderborn, Germany) and Beijing Hanning Tech Co., Ltd. (Beijing, China).

    Research areas

  • Backordering, Lost customers, Product form approximation, Robotic mobile fulfilment system, Semi-open queueing network, Warehousing
  • Business informatics
  • Informatics

Recently viewed

Projects

  1. Biogasanlagen

Publications

  1. What does it mean to be sensitive for the complexity of (problem oriented) teaching?
  2. A Column Generation Approach for Bus Driver Rostering Problems
  3. Intellectual Property Issues in Space Contracts
  4. Erratum to "Generic functions of railway stations-A conceptual basis for the development of common system understanding and assessment criteria" [Transp. Policy 18 (2010) 446-455]
  5. The Influence of Robots’ Emotion Expressions on the Uncanny-Valley-Effect
  6. Effect of yttrium addition on lattice parameter, Young's modulus and vacancy of magnesium
  7. Informatik
  8. Wavlet analysis for rotor fault diagnosis with rub-impact of rotor systems
  9. (De)Composing Public Value
  10. Editorial introduction to the special issue on crises at work
  11. Same but different? Measurement invariance of the PIAAC motivation-to-learn scale across key socio-demographic groups
  12. Path dependence and technological expectations in transport policy
  13. Bird's Response to Revegetation of Different Structure and Floristics-Are "Restoration Plantings" Restoring Bird Communities?
  14. Grain size statistics, composition and provenance of fragmental particles in some Apollo 14 breccias
  15. Introduction
  16. Variation in short-term and long-term responses of photosynthesis and isoprenoid-mediated photoprotection to soil water availability in four Douglas-fir provenances
  17. Smelling like resin
  18. Boundaryless working hours and recovery in Germany
  19. Climate change as an element of sustainability communication
  20. The professional identity of gameworkers revisited
  21. Erratum zu
  22. Gathering Voices, Feeling Relations
  23. Publicum
  24. Was wissen Grundschulkinder über den Computer als Schreibwerkzeug?
  25. The economic value of soil carbon
  26. The Effect of Solid Solute and Precipitate Phase on Young's Modulus of Binary Mg–RE Alloys
  27. Liniennetzpläne
  28. Expectations of Health Tourists in Germany - Illusions and Reality.
  29. A Questionnaire Assessing Discomfort in Automation – The Disco-Scale
  30. Mapping relative risk for biodiversity from the application of pesticides, focusing on pollinators
  31. Fehler und Versuch. Parteispenden und ihre Regulierung
  32. Cyberspace
  33. Thermodynamic formulation of models for multiscale crystal plasticity at large deformation