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

Dmitry Efrosinin1,2, Vladimir Vishnevsky3, Natalia Stepanova4

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

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|July 8, 2023
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Summary
This summary is machine-generated.

This study introduces a novel approach using simulation and neural networks to optimize scheduling in complex queueing systems with switching costs. The method effectively finds optimal control policies, proving robust across various service time distributions.

Keywords:
Markov decision problemheterogeneous queuesneural networkoptimal schedulingqueue simulationsimulated annealing

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Area of Science:

  • Operations Research
  • Computer Science
  • Applied Mathematics

Background:

  • Traditional queueing theory often assumes homogeneous processes or Markovian models for parallel queue systems.
  • Calculating optimal scheduling policies with switching costs and arbitrary distributions is computationally challenging.

Purpose of the Study:

  • To develop and validate a method combining simulation and neural networks for optimal scheduling in parallel queue systems.
  • To address the complexity arising from switching costs and non-standard inter-arrival and service time distributions.

Main Methods:

  • A multi-layer neural network is employed for scheduling decisions, guided by simulated annealing for optimization.
  • The neural network is trained on heuristic policies, with optimization targeting the minimization of a simulation-calculated average cost function.
  • Markov decision problems are used to verify the optimality of the proposed scheduling policy.

Main Results:

  • The simulation-neural network approach effectively determines optimal deterministic control policies for routing and scheduling.
  • The optimized scheduling policy demonstrates statistical insensitivity to the specific shapes of inter-arrival and service time distributions, provided their first moments are consistent.
  • The method proves effective for general queueing systems, including resource allocation problems.

Conclusions:

  • The integration of simulation and neural networks offers a powerful solution for complex scheduling problems in queueing theory.
  • The findings suggest that optimal scheduling policies in such systems are primarily influenced by the average rates rather than the detailed distributions of arrival and service times.