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.

翻译：现有车头时距分布在准确反映异质交通（不同类型车辆）与混合交通（人工驾驶车辆与自动驾驶车辆）中多样化行为与特征方面的能力有限，导致拟合优度不尽如人意。为解决这些问题，我们通过修改指数函数得到一种新型车头时距分布。该模型未采用欧拉数（e）作为指数函数的底数，而是使用实数底数以提升对观测车头时距建模的灵活性。然而，所提函数本身并非概率函数。我们通过归一化处理计算概率并推导出闭式方程。本研究利用包含五个公开数据集（highD、exiD、NGSIM、Waymo和Lyft）的综合实验评估所提分布的性能，并在混合与异质交通流条件下与六种现有分布进行对比。结果表明，所提分布不仅能捕捉车头时距分布的基本特征，还能提供具有物理意义的参数以描述观测车头时距的分布形态。在高速公路异质流（即连续交通流）条件下，所提分布优于其他候选分布。在城市道路条件（即间断交通流）下，包括异质与混合交通场景，所提分布仍能取得良好效果。