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

TL;DR

This paper introduces a novel headway distribution model based on a generalized exponential function, improving the fit for heterogeneous and mixed traffic flows by capturing observed behaviors more accurately.

Contribution

It proposes a flexible, normalized exponential-based distribution that better models diverse traffic headways, validated across multiple real-world datasets.

Findings

Outperforms existing distributions in highway heterogeneous traffic.

Provides meaningful parameters describing headway distribution shape.

Achieves decent fit in urban mixed traffic conditions.

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.