Optimal Scheduling in General Multi-Queue System by Combining Simulation and Neural Network Techniques

Author:

Efrosinin Dmitry12ORCID,Vishnevsky Vladimir3ORCID,Stepanova Natalia4ORCID

Affiliation:

1. Institute for Stochastics, Johannes Kepler University Linz, 4040 Linz, Austria

2. Department of Information Sciences, Peoples’ Friendship University of Russia (RUDN University), Moscow 117198, Russia

3. V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow 117997, Russia

4. Scientific and Production Company “INSET”, Moscow 129085, Russia

Abstract

The problem of optimal scheduling in a system with parallel queues and a single server has been extensively studied in queueing theory. However, such systems have mostly been analysed by assuming homogeneous attributes of arrival and service processes, or Markov queueing models were usually assumed in heterogeneous cases. The calculation of the optimal scheduling policy in such a queueing system with switching costs and arbitrary inter-arrival and service time distributions is not a trivial task. In this paper, we propose to combine simulation and neural network techniques to solve this problem. The scheduling in this system is performed by means of a neural network informing the controller at a service completion epoch on a queue index which has to be serviced next. We adapt the simulated annealing algorithm to optimize the weights and the biases of the multi-layer neural network initially trained on some arbitrary heuristic control policy with the aim to minimize the average cost function which in turn can be calculated only via simulation. To verify the quality of the obtained optimal solutions, the optimal scheduling policy was calculated by solving a Markov decision problem formulated for the corresponding Markovian counterpart. The results of numerical analysis show the effectiveness of this approach to find the optimal deterministic control policy for the routing, scheduling or resource allocation in general queueing systems. Moreover, a comparison of the results obtained for different distributions illustrates statistical insensitivity of the optimal scheduling policy to the shape of inter-arrival and service time distributions for the same first moments.

Funder

Johannes Kepler University Linz

Russian Science Foundation

Publisher

MDPI AG

Subject

Electrical and Electronic Engineering,Biochemistry,Instrumentation,Atomic and Molecular Physics, and Optics,Analytical Chemistry

Reference36 articles.

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2. Stintzing, J., and Norrman, F. (2023, May 25). Prediction of Queuing Behaviour through the Use of Artificial Neural Networks. Available online: http://www.diva-portal.se/smash/get/diva2:1111289/FULLTEXT01.pdf.

3. Nii, S., Okuda, T., and Wakita, T. (2020, January 28–30). A performance evaluation of queueing systems by machine learning. Proceedings of the IEEE International Conference on Consumer Electronics (ICCE-Taiwan), Taoyuan, Taiwan.

4. Sherzer, E., Senderovich, A., Baron, O., and Krass, D. (2022). Can machines solve general queueing systems?. arXiv.

5. Kyritsis, A.I., and Deriaz, M. (2019, January 25–27). A machine mearning approach to waiting time prediction in queueing scenarios. Proceedings of the 2019 Second International Conference on Artificial Intelligence for Industries (AI4I), Laguna Hills, CA, USA.

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