# Traffic estimation in unobserved network locations using data-driven macroscopic models

arXiv: https://arxiv.org/abs/2401.17095 · HTML: https://mlsanity.com/paper/2401.17095/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 37 references that are in the map.
- First posted on arXiv 30 Jan 2024.

## Builds on (most cited first, 4 of 4)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Correlating sparse sensing for large-scale traffic speed estimation: A Laplacian-enhanced low-rank tensor kriging approach](https://mlsanity.com/paper/2210.11780/) (2022)
- [Estimating multi-class dynamic origin-destination demand through a forward-backward algorithm on computational graphs](https://mlsanity.com/paper/1903.04681/) (2019)
- [Statistical inference of travelers' route choice preferences with system-level data](https://mlsanity.com/paper/2204.10964/) (2022)

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

- [Scalable Dynamic Origin-Destination Demand Estimation Enhanced by High-Resolution Satellite Imagery Data](https://mlsanity.com/paper/2506.22499/) (2025)

## Abstract (arXiv)

This paper leverages macroscopic models and multi-source spatiotemporal data collected from automatic traffic counters and probe vehicles to accurately estimate traffic flow and travel time in links where these measurements are unavailable. This problem is critical in transportation planning applications where the sensor coverage is low and the planned interventions have network-wide impacts. The proposed model, named the Macroscopic Traffic Estimator (MaTE), can perform network-wide estimations of traffic flow and travel time only using the set of observed measurements of these quantities. Because MaTE is grounded in macroscopic flow theory, all parameters and variables are interpretable. The estimated traffic flow satisfies fundamental flow conservation constraints and exhibits an increasing monotonic relationship with the estimated travel time. Using logit-based stochastic traffic assignment as the principle for routing flow behavior makes the model fully differentiable with respect to the model parameters. This property facilitates the application of computational graphs to learn parameters from vast amounts of spatiotemporal data. We also integrate neural networks and polynomial kernel functions to capture link flow interactions and enrich the mapping of traffic flows into travel times. MaTE also adds a destination choice model and a trip generation model that uses historical data on the number of trips generated by location. Experiments on synthetic data show that the model can accurately estimate travel time and traffic flow in out-of-sample links. Results obtained using real-world multi-source data from a large-scale transportation network suggest that MaTE outperforms data-driven benchmarks, especially in travel time estimation. The estimated parameters of MaTE are also informative about the hourly change in travel demand and supply characteristics of the transportation network.