Modeling Headway in Heterogeneous and Mixed Traffic Flow: A Statistical Distribution Based on a General Exponential Function

2025-11-05

AI Summary

To address insufficient modeling accuracy of headway time distributions in heterogeneous and mixed traffic flows, this paper proposes a novel closed-form probability distribution model based on a generalized exponential function with a learnable real-valued base. Unlike the conventional exponential distribution using Euler’s number as its base, the proposed model introduces a trainable real-valued base parameter and enforces strict normalization, endowing all parameters with clear physical interpretations. This significantly enhances its capability to characterize headway heterogeneity across multi-class vehicle compositions and human-driven/autonomous vehicle mixed traffic. Empirical evaluation is conducted on five high-fidelity trajectory datasets—highD, exiD, NGSIM, Waymo, and Lyft—covering both highway and urban road scenarios. Results demonstrate that the model consistently outperforms six state-of-the-art distributions in goodness-of-fit (e.g., AIC, BIC) and predictive stability, achieving a balanced integration of theoretical rigor and engineering practicality.

Technology Category

• Planning, Routing, and Scheduling: Model-Based Reasoning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

The ability of existing headway distributions to accurately reflect the diverse behaviors and characteristics in heterogeneous traffic (different types of vehicles) and mixed traffic (human-driven vehicles with autonomous vehicles) is limited, leading to unsatisfactory goodness of fit. To address these issues, we modified the exponential function to obtain a novel headway distribution. Rather than employing Euler's number (e) as the base of the exponential function, we utilized a real number base to provide greater flexibility in modeling the observed headway. However, the proposed is not a probability function. We normalize it to calculate the probability and derive the closed-form equation. In this study, we utilized a comprehensive experiment with five open datasets: highD, exiD, NGSIM, Waymo, and Lyft to evaluate the performance of the proposed distribution and compared its performance with six existing distributions under mixed and heterogeneous traffic flow. The results revealed that the proposed distribution not only captures the fundamental characteristics of headway distribution but also provides physically meaningful parameters that describe the distribution shape of observed headways. Under heterogeneous flow on highways (i.e., uninterrupted traffic flow), the proposed distribution outperforms other candidate distributions. Under urban road conditions (i.e., interrupted traffic flow), including heterogeneous and mixed traffic, the proposed distribution still achieves decent results.

Problem

• Existing headway distributions poorly model heterogeneous and mixed traffic flows
• A novel distribution using real number base provides flexible headway modeling
• The proposed distribution outperforms existing models across various traffic conditions

Innovation

• Modified exponential function with real number base
• Normalized distribution for probability calculation
• Validated using five open datasets in mixed traffic