Numerous statistical and data-driven modeling frameworks have estimated rear-end crashes and crash-prone events from macroscopic traffic states which are at the heart of traffic flow modelling and control. However, existing frameworks focus on critical events and exclude a vast majority of safer interactions, which are essential information with respect to identifying the trade-offs between congestion management and rear-end crash prevention.

This study proposes a flexible conflict-based framework to extract safety information from freeway macroscopic traffic state variables (i.e., speed and density) by utilizing the information from all underlying car-following interactions. Time spent in conflict ($\mathit{TSC}$) is introduced as the total time spent by all vehicles in rear-end conflicts based on a given conflict measure and a threshold to be determined flexibly. Using the NGSIM vehicle trajectory dataset, we show that the proportion of stopping distance ($\mathit{PSD}$) is more desirable than several event-based conflict measures (e.g., time to collision) for describing $\mathit{TSC}$ based on macroscopic state variables. Besides, it is shown that $\mathit{PSD}$ provides explicit safety information about the entire travel time for each macroscopic state because it applies to all car-following interactions.

This paper proposes a hybrid methodological framework combining probabilistic and machine learning models to develop the relationships between safety and macroscopic state variables within a flexible conflict-based safety assessment framework. At first, probabilistic and Machine learning models are separately developed to estimate $\mathit{PSD}$-based $\mathit{TSC}$ using only macroscopic stte variables. Each approach is evaluated comprehensively against empirical observations using the NGSIM vehicle trajectory dataset. While the machine learning approach has better predictive accuracy for a fixed rear-end conflict threshold (i.e., $\mathit{PS}{D}_{\mathit{cr}}$), the probabilistic approach has a better explaining capability and captures $\mathit{TSC}$ using flexible conflict thresholds. Utilizing the advantages of these two approaches, the proposed hybrid framework satisfactorily predicts $\mathit{TSC}$ corresponding to $\mathit{PSD}<PS{D}_{\mathit{cr}}$ for a wide range of thresholds based only on macroscopic state variables.

This paper provides an endogenous safety dimension to the fundamental relations of freeway traffic flows that can be utilized to balance freeway traffic flow efficiency and safety. For instance, control studies can utilize the proposed framework to minimize total travel time while also minimizing total time spent in conflict for crash-prone situations such as shockwaves and traffic oscillations.

许多统计和数据驱动的建模框架已经从宏观交通状态中估计了追尾碰撞和容易碰撞的事件，这是交通流建模和控制的核心。然而，现有框架专注于关键事件，排除了绝大多数更安全的交互，这些交互是确定拥塞管理和追尾事故预防之间权衡的重要信息。

本研究提出了一个灵活的基于冲突的框架，通过利用来自所有潜在跟车交互的信息，从高速公路宏观交通状态变量（即速度和密度）中提取安全信息。在冲突中花费的时间（$\mathit{TSC}$) 被引入为所有车辆在追尾冲突中花费的总时间，基于给定的冲突措施和一个灵活确定的阈值。使用NGSIM车辆轨迹数据集，我们表明停车距离（$\mathit{PSD}$) 比几种基于事件的冲突度量（例如，碰撞时间）更可取来描述 $\mathit{TSC}$基于宏观状态变量。此外，还表明$\mathit{PSD}$ 为每个宏观状态提供有关整个行程时间的明确安全信息，因为它适用于所有跟车交互。

本文提出了一种结合概率和机器学习模型的混合方法框架，以在基于冲突的灵活安全评估框架内开发安全和宏观状态变量之间的关系。首先，分别开发概率模型和机器学习模型来估计$\mathit{PSD}$-基于 $\mathit{TSC}$仅使用宏观 stte 变量。使用 NGSIM 车辆轨迹数据集根据经验观察对每种方法进行综合评估。而机器学习方法对于固定的追尾冲突阈值（即，$\mathit{聚苯乙烯}{D}_{\mathit{铬}}$)，概率方法有更好的解释能力和捕获 $\mathit{TSC}$使用灵活的冲突阈值。利用这两种方法的优点，所提出的混合框架令人满意地预测$\mathit{TSC}$ 对应于 $\mathit{PSD}<磷秒D_{\mathit{铬}}$ 适用于仅基于宏观状态变量的各种阈值。

本文为高速公路交通流的基本关系提供了一个内生安全维度，可用于平衡高速公路交通流效率和安全。例如，控制研究可以利用所提出的框架来最小化总旅行时间，同时也最小化在冲突中花费的总时间，以应对容易发生碰撞的情况，例如冲击波和交通波动。