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

arXiv: https://arxiv.org/abs/2407.08765 · HTML: https://mlsanity.com/paper/2407.08765/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 36 references that are in the map.
- First posted on arXiv 11 Jul 2024.

## Builds on (most cited first, 6 of 6)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [Multivariate goodness-of-Fit tests based on Wasserstein distance](https://mlsanity.com/paper/2003.06684/) (2020)
- [Sample Efficient Reinforcement Learning in Mixed Systems through Augmented Samples and Its Applications to Queueing Networks](https://mlsanity.com/paper/2305.16483/) (2023)
- [Learning Queuing Networks by Recurrent Neural Networks](https://mlsanity.com/paper/2002.10788/) (2020)
- [When to arrive at a queue with earliness, tardiness and waiting costs](https://mlsanity.com/paper/1709.03374/) (2017)

## Built on by (most cited first, 4 of 4)

- [Analyzing homogenous and heterogeneous multi-server queues via neural networks](https://mlsanity.com/paper/2504.01052/) (2025)
- [Supervised Learning for the (s,S) Inventory Model with General Interarrival Demands and General Lead Times](https://mlsanity.com/paper/2601.12900/) (2026)
- [A Learning-Based Superposition Operator for Non-Renewal Arrival Processes in Queueing Networks](https://mlsanity.com/paper/2603.11118/) (2026)
- [DynaSchedBench: Calibrated Dynamic Scheduling Benchmarks and Observability Paradox in LLM-based Scheduling Agents](https://mlsanity.com/paper/2605.27566/) (2026)

## Abstract (arXiv)

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.