# A Distributed Gradient Approach for System Optimal Dynamic Traffic Assignment

arXiv: https://arxiv.org/abs/2112.14389 · HTML: https://mlsanity.com/paper/2112.14389/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Dec 2021.

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

- [From Optimization to Prediction: Transformer-Based Path-Flow Estimation to the Traffic Assignment Problem](https://mlsanity.com/paper/2510.19889/) (2025)

## Abstract (arXiv)

This study presents a distributed gradient-based approach to solve system optimal dynamic traffic assignment (SODTA) formulated based on the cell transmission model. The algorithm distributes SODTA into local sub-problems, who find optimal values for their decision variables within an intersection. Each sub-problem communicates with its immediate neighbors to reach a consensus on the values of common decision variables. A sub-problem receives proposed values for common decision variables from all adjacent sub-problems and incorporates them into its own offered values by weighted averaging and enforcing a gradient step to minimize its objective function. Then, the updated values are projected onto the feasible region of the sub-problems. The algorithm finds high quality solutions in all tested scenarios with a finite number of iterations. The algorithm is tested on a case study network under different demand levels and finds solutions with at most a 5% optimality gap.