## 4 Results and Discussions
### Spatial-Temporal Patterns Analysis  
While the significance of merging behavior in the context of traffic flow and safety has been well established, ongoing research continues to explore the intricacies of driver interactions within these dynamic scenarios. It is crucial to delve deeper into this complex facet of highway operation to address its implications for traffic management, safety, and the integration of autonomous vehicles. We will consider both spatial and temporal dimensions and divide the real merging scenario into limited merging patterns. These merging patterns are analyzed in detail across two dimensions: time duration and spatial location movement of the merging vehicles. The relevant terminology used in this study will then be defined. 1. Temporal dimension: the driving behavior is examined over a specific spatial duration, beginning with the moment they enter the ramp, followed by their merging maneuvers, and ending with the completion of the merge. Merging duration is also considered. 2. Spatial dimension: this study focuses on the geographical distribution of merging speed, the characteristics of the LV and the RV, the merging distance (ratio), and high-risk merging scenarios. 3. Heterogeneity: the heterogeneity of merging behavior here encompasses various combinations of ego vehicle and surrounding vehicles. For example, when the ego vehicle is a car, the alongside vehicle may be either a car or a truck. Furthermore, we examine the differences between the merging patterns. Specifically, scenario1 involves an alongside vehicle accelerating to prevent the ego vehicle from cutting in, while scenario2 entails the alongside vehicle reducing its speed to facilitate smooth merging for the ego vehicle. Whether there exists a significant difference in driving speed of the ego vehicle between these two scenarios will be further investigated. The analysis process in existing studies exhibits a higher degree of subjectivity, and the rules for selecting variables are not clearly stated. Instead of immediately applying commonly used algorithms from previous studies, we propose dividing the scenarios based on changes in the relative position of the vehicle with its surroundings. These algorithms require determining input variables, and their outcomes are somewhat influenced by the dataset or hyperparameters. This gives rise to the challenge of inadequate trajectory extraction and vehicle matching details, as well making it difficult for other researchers' to replicate these study results. However, the fundamental division method used in this study is universally applicable and remains unaffected by variations in data, algorithms, or hyperparameters. Based on the aforementioned three types of surrounding vehicles, we can categorize eight merging scenarios as shown in Table 4. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Merging Patterns**} & **Rear Vehicle (RV)** & **Lead Vehicle (LV)** \\  & **Situation** & **Situation** \\ \hline A & None & None \\ B & None & Exist \\ C & None & Exist (rear to lead) \\ D & Exist & None \\ E & Exist & Exist \\ F & Exist & Exist (rear to lead) \\ G & Exist (lead to rear) & None \\ H & Exist (lead to rear) & Exist \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Merging Patterns. 1. Merging Pattern A: There are no vehicles within the threshold range of the target vehicle. The merging behavior of vehicles in this pattern is less restricted and is influenced by the driver's own driving style and vehicle type. 2. Merging Pattern B: There is a LV and no RV. When a vehicle exists ahead in the target lane, the merging vehicles will maintain a certain distance from the vehicle ahead and then merge. 3. Merging Pattern C: The merging vehicle fails to assert its right-of-way against the adjacent vehicle, resulting in the merging vehicle being positioned behind the alongside vehicle. At the moment of merging, there is no RV. 4. Merging Pattern D: The merging vehicles cut in front of the RV. There is a RV and no LV at the merging moment.