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

TL;DR

MaTE addresses out-of-sample traffic estimation by integrating macroscopic flow theory with differentiable data-driven components in a single computational-graph framework. It combines trip generation, destination and route choice, a neural performance function with polynomial kernels, and a relaxed equilibrium regularizer to estimate link flows and travel times across unobserved links. In synthetic experiments, MaTE achieves competitive or superior out-of-sample accuracy compared with data-driven benchmarks and yields interpretable parameter estimates; in Fresno, CA, it demonstrates network-wide scalability and superior travel-time estimation under real data. The approach offers a principled, extensible tool for planning and evaluating network interventions, with an open-source implementation to facilitate replication and adoption.

Abstract

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.

Figures (28)

• Figure 1: An illustration of MaTE. The blue elements represent the components that extend the model developed by guarda_estimating_2024.
• Figure 2: An illustration of the cross-validation strategy proposed to compute out-of-sample performance and perform model selection. The dashed line represents the model selection approach used in the current literature. The red line represents our approach.
• Figure 3: Synthetic traffic flow and travel time measurements generated in the Sioux Falls network during off-peak (orange) and peak periods (blue)
• Figure 4: Convergence of logit-based stochastic user equilibrium (SUELOGIT) model using synthetic data from the Sioux Falls network
• Figure 5: Convergence of TVODLULPE model using synthetic data from Sioux Falls network

Theorems & Definitions (10)

• Remark 1
• Remark 2
• Definition 1: STALOGIT
• Proposition 1: STALOGIT solution
• proof
• Remark 3
• Definition 2
• Proposition 2: Equilibrium solution
• proof
• Remark 4