Modeling Headway in Heterogeneous and Mixed Traffic Flow: A Statistical Distribution Based on a General Exponential Function
This work addresses a domain-specific problem for traffic engineering and autonomous vehicle research by improving headway modeling, though it is incremental as it modifies an existing function rather than introducing a new paradigm.
The authors tackled the problem of accurately modeling headway distributions in heterogeneous and mixed traffic flows by proposing a novel distribution based on a modified exponential function with a real number base, which outperformed six existing distributions on five open datasets, showing strong performance on highways and decent results in urban conditions.
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.