Use Cases of Machine Learning in Queueing Theory Based on a GI / G / K System

Dmitry Efrosinin (), Vladimir Vishnevsky, Natalia Stepanova and Janos Sztrik
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Dmitry Efrosinin: Institute for Stochastics, Johannes Kepler University Linz, 4040 Linz, Austria
Vladimir Vishnevsky: V. A. Trapeznikov Institute of Control Sciences, Moscow 117997, Russia
Natalia Stepanova: Institute for Stochastics, Johannes Kepler University Linz, 4040 Linz, Austria
Janos Sztrik: Department of Informatics and Networks, Faculty of Informatics, University of Debrecen, 4032 Debrecen, Hungary

Mathematics, 2025, vol. 13, issue 5, 1-36

Abstract: Machine learning (ML) in queueing theory combines the predictive and optimization capabilities of ML with the analytical frameworks of queueing models to improve performance in systems such as telecommunications, manufacturing, and service industries. In this paper we give an overview of how ML is applied in queueing theory, highlighting its use cases, benefits, and challenges. We consider a classical G I / G / K -type queueing system, which is at the same time rather complex for obtaining analytical results, consisting of K homogeneous servers with an arbitrary distribution of time between incoming customers and equally distributed service times, also with an arbitrary distribution. Different simulation techniques are used to obtain the training and test samples needed to apply the supervised ML algorithms to problems of regression and classification, and some results of the approximation analysis of such a system will be needed to verify the results. ML algorithms are used also to solve both parametric and dynamic optimization problems. The latter is achieved by means of a reinforcement learning approach. It is shown that the application of ML in queueing theory is a promising technique to handle the complexity and stochastic nature of such systems.

Keywords: GI / G / K queueing system; performance analysis and optimization; machine learning; dynamic programming; reinforcement learning; deep Q -learning (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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