# Measuring Collision Risk in Mixed Traffic Flow Under the Car-Following and Lane-Changing Behavior
## 1 Introduction
When a CAV follows an HDV, it cannot achieve cooperative driving due to communication limitations, resulting in the degradation of Cooperative Adaptive Cruise Control (CACC) to Adaptive Cruise Control (ACC) mode. This degradation phenomenon has been extensively studied. For instance, [PERSON] [13] evaluated the safety impact of CACC degradation on collision risk using the TIT index, finding that sudden deceleration of the leading vehicle significantly increases collision risk. [PERSON] [14] analyzed the stability and safety of mixed traffic flow with varying CV penetration rates when connected vehicles (CVs) degrade to regular vehicles. [PERSON] [15] studied CACC vehicles' degradation into ACC mode due to communication failures, noting that this significantly raises the safety risks in mixed traffic. These studies considered the functional degradation of CAVs but did not consider the perception-reaction time (PRT) of CAVs. The PRT of intelligent vehicle systems is crucial for evaluating performance, encompassing perception time, decision time, and control time. Compared to HDVs, CAVs have a shorter PRT. Some researchers have conceptually considered time lags in PRT. [PERSON] [16] included the perception-reaction time factor and the safe time headway factor in the ACC model. [PERSON] [17] designed a new heterogeneous lattice hydrodynamic model, incorporating CAVs and HDVs, to explore the feedback control effect of delayed differences for different vehicle types. In summary, few studies have considered both the degradation of CAVs and their PRT. Based on the previous discussion, we conducted a search in Scopus to review studies published since 2017. The search used the keywords \"mixed traffic flow\", \"collision risk\", \"car-following behavior\", \"lane-changing behavior\", \"CAV degradation\", and \"perception-reaction time\", as well as their combinations. While several studies address individual factors or partial combinations, no research comprehensively considers all of them. Therefore, the primary objective of this study is to develop a new comprehensive SSM designed to quantify collision risks in mixed traffic flow. This new SSM considers the combined effects of longitudinal and lateral vehicle interactions. By comparing it with other typical SSMs, the proposed index evaluates the impacts of CAV degradation and PRT, highlighting the differences between these metrics. Through the design, validation, and application of this novel measure, we aim to address the existing research gap regarding the combined effects of CAV degradation and PRT, thereby providing a more scientific tool for the quantitative assessment of safety in mixed traffic flow. The flowchart of the proposed methodology is shown in Figure 1. The main contributions of this study are summarized as follows:  
1. We introduce a new SSM that incorporates both longitudinal and lateral factors. This metric, denoted as \(R_{\text{total}}\), is utilized to assess the risk level of mixed traffic flow;
2. The weight of each parameter within \(R_{\text{total}}\) is ascertained through numerical analysis. The validity of \(R_{\text{total}}\) is substantiated using an empirical dataset, and the risk threshold is derived;
3. \(R_{\text{total}}\) is used to assess the impact of penetration rate, PRT, and lane-changing combinations on mixed traffic flow safety, contributing to a deeper understanding of safety in mixed-traffic environments  
The structure of this paper is as follows. Section 2 provides an overview and analysis of widely used SSMs. Section 3 introduces a new SSM (\(R_{\text{total}}\)), detailing the determination of weights and thresholds and validation of its effectiveness. Section 4 optimizes the longitudinal car-following model considering CAV degradation and determines combinations of typical lateral lane-changing behaviors. It further presents the simulation experiments for risk assessment and the analysis of the results. Lastly, Section 5 summarizes the key findings of our study and outlines future research directions in this field.