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Challenges in using the Kingman Equation for Prediction and Validation

  • This paper discusses the application of the Kingman formula as a means for verification and validation of a production simulation framework. It turns out that this approach generates more questions than answers. This leads to a more in-depth analysis of the Kingman equation properties and the need for refinement of the resulting quantities for the practitioner. First, the one-stage queueing problem and its properties are analyzed. Then a discrete simulation model is implemented utilizing an industry standard factory simulation framework. A puzzling outcome is the observation that the simulation results match the Kingman approximation reasonably well at lower levels of utilization at which the Kingman equation itself is not very accurate, but they don’t match well at high levels of utilization at which the equation is more accurate. Alternative implementation means lead to similar results. It turns out that only one approach chosen utilizing the Lindley equation generates reasonable results, leaving the suggestion of accumulation of rounding errors as a source of the mismatch with all other approaches. The Kingman formula is applicable to general distribution patterns. Four common such patterns are employed and the results are compared to the Kingman equation, proving the point. The paper finishes with recommendations for simulation verification, it advises against the use of stochastic phenomena models like the Kingman formula, it does however strongly advise for verification means in general, based on the experienced gathered during the course of the studies discussed herein.

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Metadaten
Author:Andreas Rükgauer, Gernot Fabeck
URN:urn:nbn:de:bvb:863-opus-19067
Document Type:Working Paper
Language:English
Year of publication:2020
Publishing Institution:Hochschule für Angewandte Wissenschaften Würzburg-Schweinfurt
Release Date:2021/04/13
Tag:Production; Simulation; Statistics; Stochastics
Pages/Size:21
Institutes and faculty:Fakultäten / Fakultät Wirtschaftswissenschaften
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 519 Wahrscheinlichkeiten, angewandte Mathematik
Licence (German):License LogoCreative Commons - CC BY-NC-SA - Namensnennung - Nicht kommerziell - Weitergabe unter gleichen Bedingungen 4.0 International
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