MaTE: Macroscopic Traffic Estimator for Enhanced Traffic Flow and Travel Time Prediction

By Soham NandiReviewed by Susha Cheriyedath, M.Sc.Feb 7 2024

In an article recently submitted to the arxiv* server, researchers introduced a macroscopic traffic estimator (MaTE), addressing the challenge of estimating traffic flow and travel time in areas with limited sensor coverage. Leveraging data-driven models and spatiotemporal data, MaTE used macroscopic flow theory, ensuring interpretability and adherence to flow conservation. By incorporating logit-based stochastic traffic assignment, neural networks, and destination choice models, MaTE achieved accurate estimations, outperforming benchmarks in travel time prediction.

*Important notice: arXiv publishes preliminary scientific reports that are not peer-reviewed and, therefore, should not be regarded as conclusive, guide clinical practice/health-related behavior, or treated as established information.

Background

Accurate estimation of traffic flow and travel time is vital for optimizing transportation systems in smart cities. Previous research has applied various machine learning (ML) techniques to enhance parameter estimation, focusing on speed, traffic volume, and congestion. However, challenges persist in out-of-sample estimation, particularly in network links without direct measurements. Existing data-driven models, such as spatial kriging, often require substantial data and lack interpretability and theoretical consistency, hindering their application in planning interventions like road closures or capacity improvements.

Traditional model-based approaches, like the four-step model, offer interpretability but struggle with scalability and may not capture the intricate relationship between traffic flow and travel time. This paper introduced the MaTE to address these gaps. MaTE leveraged macroscopic flow theory, computational graphs, and multi-source spatiotemporal data to estimate traffic flow and travel time in links without historical measurements. It incorporated neural networks and polynomial kernels to enrich the mapping of traffic flow to travel times, surpassing the limitations of existing models.

MaTE introduced layers for trip generation and destination choices, enhancing the model's interpretability and applicability to real-world scenarios. The proposed model extended the computational graph framework, providing a comprehensive solution for network-wide estimation, especially in areas with limited sensor coverage, and contributed to bridging the gap between data-driven and model-based methodologies.

Formulation

The MaTE model was introduced to address challenges in estimating traffic flow and travel time in transportation networks. The formulation incorporated learnable parameters such as auxiliary link flow parameters, feature-specific parameters in route choice utility functions, and performance function parameters. Assumptions include time-varying travel behavior, stochastic user equilibrium with logit assignment (SUELOGIT), and observable, time-invariant path and destination sets. The model's architecture included a neural performance function that captured traffic flow interactions, enhancing its representational capacity. The formulation involved variables such as link flows, travel times, path flows, path utilities, and more.

To optimize the model, a loss function was defined as a weighted sum of link flow loss, travel time loss, and equilibrium loss. The optimization problem sought to minimize this loss function while adhering to network flow constraints and ensuring the model's parameters satisfied fundamental properties. The importance of normalizing components to handle differences in data scale and coverage was emphasized. The model offered a comprehensive approach for estimating traffic parameters, bridging gaps between data-driven and model-based methodologies in transportation planning.

Solution Algorithm

Initialization involved setting model parameters based on domain knowledge, and the forward pass computed various variables and the loss function. The backward pass calculated gradients and the parameters were updated using a gradient-based method. The training process iterated through forward and backward passes until a termination criterion was met. Notably, the initialization strategy impacted convergence, with prior knowledge guiding parameter starting values. The forward pass involved a series of computations, including path flows, utilities, and link flows.

The backward pass used automatic differentiation tools for gradient computation. During training, all parameters were learned, while during inference, link flow parameters were adjusted to maintain a consistent relative gap. The algorithm exhibited properties ensuring its effectiveness, such as providing valid logit-based stochastic traffic assignment solutions. Additionally, the algorithm could solve the SUELOGIT problem and produce consistent solutions in diverse equilibrium conditions.

Numerical Experiments

In the numerical experiments, the MaTE algorithm was evaluated for estimating network flows and travel times using synthetic data from the Sioux Falls transportation network. The algorithm applied to a 24-node, 76-link network demonstrated its capability to converge to a SUELOGIT solution. Performance comparisons with a benchmark TVODLULPE model showed that MaTE achieved similar accuracy in reproducing traffic flow and travel time while incorporating more flexible link performance functions and a trip generation model.

The study included in-sample analyses, revealing the convergence and accuracy of the models, and out-of-sample evaluations, indicating the impact of performance function choices and the generation step on estimation performance. Overall, MaTE exhibited promising results in traffic estimation tasks, emphasizing its potential for transportation network modeling. The experiments assessed the algorithm's robustness and effectiveness in reproducing realistic traffic scenarios, laying the groundwork for its practical applications.

Large Scale Implementation

The authors described the implementation and evaluation of MaTE, which is applied to a large-scale transportation network in Fresno, California. The network comprised 1,789 nodes and 2,413 links covering major roads and highways. The model was trained using travel time and link flow data collected in October 2019 and tested with data from October 2020. MaTE was compared to another model, TVODLULPE, focusing on interpretability and performance. The model specifications involved parameters associated with link flows, utility functions, generation functions, and origin-destination (O-D) estimations.

MaTE's parameters were considered interpretable, and the model was trained using ML algorithms with an emphasis on real-world settings. The in-sample performance was evaluated using metrics such as mean squared error (MSE) and median absolute percentage error (MDAPE). Additionally, the out-of-sample performance was assessed through k-fold cross-validation, showing that MaTE outperformed data-driven benchmarks in estimating traffic flow and travel time, especially in out-of-sample scenarios.

Conclusion

In conclusion, the MaTE model, introduced for network-wide traffic flow and travel time estimation, leveraged neural networks and incorporated layers for trip generation and route choices. Demonstrating superior performance over data-driven benchmarks, MaTE was proven consistent with traffic assignment principles.

Real-world application in a large-scale transportation network showcased MaTE's effectiveness in out-of-sample predictions, outperforming regression kriging. While the authors suggested MaTE as a reliable tool for transportation planning, future research should explore its performance in diverse networks, consider model-based benchmarks, and extend its architecture to address additional aspects of traffic conditions and behaviors.

*Important notice: arXiv publishes preliminary scientific reports that are not peer-reviewed and, therefore, should not be regarded as conclusive, guide clinical practice/health-related behavior, or treated as established information.