# Optimal Control of Multiclass Fluid Queueing Networks: A Machine Learning Approach

arXiv: https://arxiv.org/abs/2307.12405 · HTML: https://mlsanity.com/paper/2307.12405/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 67 references that are in the map.
- First posted on arXiv 23 Jul 2023.

## Builds on (most cited first, 9 of 9)

- [Programmatically Interpretable Reinforcement Learning](https://mlsanity.com/paper/1804.02477/) (2018)
- [Verifiable Reinforcement Learning via Policy Extraction](https://mlsanity.com/paper/1805.08328/) (2018)
- [Queueing Network Controls via Deep Reinforcement Learning](https://mlsanity.com/paper/2008.01644/) (2020)
- [Online Mixed-Integer Optimization in Milliseconds](https://mlsanity.com/paper/1907.02206/) (2019)
- [The Voice of Optimization](https://mlsanity.com/paper/1812.09991/) (2018)
- [CoCo: Online Mixed-Integer Control via Supervised Learning](https://mlsanity.com/paper/2107.08143/) (2021)
- [Queue-Learning: A Reinforcement Learning Approach for Providing Quality of Service](https://mlsanity.com/paper/2101.04627/) (2021)
- [Learning to Optimize Computational Resources: Frugal Training with Generalization Guarantees](https://mlsanity.com/paper/1905.10819/) (2019)
- [Revised SCLP-simplex Algorithm with Application to Large-Scale Fluid Processing Networks](https://mlsanity.com/paper/2103.04405/) (2021)

## Built on by (most cited first, 1 of 1)

- [Optimal Control of Fluid Restless Multi-armed Bandits: A Machine Learning Approach](https://mlsanity.com/paper/2502.03725/) (2025)

## Abstract (arXiv)

We propose a machine learning approach to the optimal control of multiclass fluid queueing networks (MFQNETs) that provides explicit and insightful control policies. We prove that a piecewise constant optimal policy exists for MFQNET control problems, with segments separated by hyperplanes passing through the origin. We use Optimal Classification Trees with hyperplane splits (OCT-H) to learn an optimal control policy for MFQNETs. We use numerical solutions of MFQNET control problems as a training set and apply OCT-H to learn explicit control policies. Furthermore, we show that both the theoretical results and the proposed algorithm extend to robust MFQNETs with uncertain service and arrival rates. We report experimental results with up to 33 servers and 99 classes that demonstrate that the learned policies achieve 100% accuracy on the test set. While the offline training of OCT-H can take days in large networks, the online application takes milliseconds.