Approximating G(t)/GI/1 queues with deep learning

TL;DR

This paper introduces a neural network-based method called MBRNN for fast, accurate estimation of the transient distribution in G(t)/GI/1 queues, outperforming traditional simulation in speed while maintaining high accuracy.

Contribution

The paper presents a novel Moment-Based Recurrent Neural Network approach that efficiently predicts queue distributions using limited moments, extending deep learning applications in queueing theory.

Findings

MBRNN requires only the first four moments of inter-arrival and service times.

The method achieves less than 3% error in mean customer count over time.

MBRNN analyzes hundreds of systems in a fraction of a second.

Abstract

In this paper, we apply a supervised machine-learning approach to solve a fundamental problem in queueing theory: estimating the transient distribution of the number in the system for a G(t)/GI/1. We develop a neural network mechanism that provides a fast and accurate predictor of these distributions for moderate horizon lengths and practical settings. It is based on using a Recurrent Neural Network (RNN) architecture based on the first several moments of the time-dependant inter-arrival and the stationary service time distributions; we call it the Moment-Based Recurrent Neural Network (RNN) method (MBRNN ). Our empirical study suggests MBRNN requires only the first four inter-arrival and service time moments. We use simulation to generate a substantial training dataset and present a thorough performance evaluation to examine the accuracy of our method using two different test sets. We show that even under the configuration with the worst performance errors, the mean number of customers over the entire timeline has an error of less than 3%. While simulation modeling can achieve high accuracy, the advantage of the MBRNN over simulation is runtime, while the MBRNN analyzes hundreds of systems within a fraction of a second. This paper focuses on a G(t)/GI/1; however, the MBRNN approach demonstrated here can be extended to other queueing systems, as the training data labeling is based on simulations (which can be applied to more complex systems) and the training is based on deep learning, which can capture very complex time sequence tasks. In summary, the MBRNN can potentially revolutionize our ability to perform transient analyses of queueing systems.