# Machine-Learned Prediction Equilibrium for Dynamic Traffic Assignment

arXiv: https://arxiv.org/abs/2109.06713 · HTML: https://mlsanity.com/paper/2109.06713/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 58 references that are in the map.
- First posted on arXiv 14 Sep 2021.

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

- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [WaveNet: A Generative Model for Raw Audio](https://mlsanity.com/paper/1609.03499/) (2016)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [GMAN: A Graph Multi-Attention Network for Traffic Prediction](https://mlsanity.com/paper/1911.08415/) (2019)
- [Graph Neural Network for Traffic Forecasting: A Survey](https://mlsanity.com/paper/2101.11174/) (2021)
- [A Network Game of Dynamic Traffic](https://mlsanity.com/paper/1705.01784/) (2017)
- [Dynamic Flows with Adaptive Route Choice](https://mlsanity.com/paper/1811.07381/) (2018)
- [The Price of Anarchy for Instantaneous Dynamic Equilibria](https://mlsanity.com/paper/2007.07794/) (2020)

## Built on by (most cited first, 2 of 2)

- [Learning from user's behaviour of some well-known congested traffic networks](https://mlsanity.com/paper/2508.14804/) (2025)
- [Once-for-All: Scalable Simultaneous Forecasting via Equilibrium State Estimation](https://mlsanity.com/paper/2606.13285/) (2026)

## Abstract (arXiv)

We study a dynamic traffic assignment model, where agents base their instantaneous routing decisions on real-time delay predictions. We formulate a mathematically concise model and define dynamic prediction equilibrium (DPE) in which no agent can at any point during their journey improve their predicted travel time by switching to a different route. We demonstrate the versatility of our framework by showing that it subsumes the well-known full information and instantaneous information models, in addition to admitting further realistic predictors as special cases. We then proceed to derive properties of the predictors that ensure a dynamic prediction equilibrium exists. Additionally, we define varepsilon-approximate DPE wherein no agent can improve their predicted travel time by more than varepsilon and provide further conditions of the predictors under which such an approximate equilibrium can be computed. Finally, we complement our theoretical analysis by an experimental study, in which we systematically compare the induced average travel times of different predictors, including two machine-learning based models trained on data gained from previously computed approximate equilibrium flows, both on synthetic and real world road networks.