## 1 Introduction
### Related Research  
Numerous studies have analyzed the spatial and temporal patterns of traffic accidents. [PERSON] [2] analyzed the spatial and temporal patterns of traffic accidents based on seasons, investigated characteristics related to accident severity, and used Geographic Information System (GIS) and spatial statistical techniques to visualize and analyze the locations and frequencies of accidents, including analyzing the frequencies and trends of traffic accidents in winter and summer. [PERSON] and [PERSON] [3] used the Global Positioning System to accurately record accident locations, analyzed the data using ArcGIS to identify traffic accident patterns, and proposed preventive measures based on the findings. [PERSON] [4] predicted accident patterns on mountain roads by considering geographical factors and seasonal changes using the kernel density estimation (KDE) technique to derive areas of high accident density. [PERSON] [5] found that secondary accidents primarily occur within a specific time and distance following an initial accident and that the frequencies and locations of secondary accidents vary based on the severity of, time of day of, and traffic volume at the time of the initial accident, emphasizing the significant economic impact of secondary accidents and  
Figure 1: Comparison of traffic deaths between OECD countries. the need for effective traffic management strategies to reduce them. [PERSON] [6] proposed a method to identify secondary accidents using the theory of traffic shockwaves based on the data of 10,762 accidents on California state highways in 2012. By calculating the speed of the shockwave based on the traffic flow and density at the site of the initial accident, he defined and filtered accidents occurring within the reach of the shockwave as secondary accidents by estimating the impact range of the initial accident in real time using the shockwave speed. [PERSON] [7] developed a two-step procedure for automatically identifying secondary accidents in large-scale highway systems. First, potential secondary accidents were identified based on the initial accident and traffic flow data using variables such as the time and location of the accident and traffic density. The accuracy of the identified potential secondary accidents was enhanced by applying shockwave theory and queuing models for verification. [PERSON] [8] dynamically identified secondary accidents using a speed-contour-map-based approach using various sensor technologies. The shockwave-based approach identifies secondary accidents using traffic flow theory, and recent studies have developed a data-based analysis framework to propose methods for automatically identifying secondary accidents. [PERSON] [9] collected traffic accident data and modeled the locations and timings of secondary accidents using statistical techniques and machine learning. By analyzing the temporal progression and spatial distribution following an initial accident, he derived patterns of secondary accident occurrences, revealing that secondary accidents tend to occur within a specific time frame after an initial accident within the impact area. Spatially, secondary accidents occur more frequently in areas with high traffic densities, and various factors, such as the severity of the initial accident, traffic volume, and time of day, influence the likelihood of occurrence of secondary accidents. Studies have used techniques such as hotspot analysis, kernel density estimation, spatial autocorrelation, geographically weighted regression, and spatial join to visualize spatial distributions through heat maps; however, improvements in data processing speed and accuracy based on range are needed. Static space-time-threshold-based approaches are simple but lack flexibility, which can lead to misidentification, whereas queuing-model-based approaches can provide more accurate impact areas but heavily depend on the number and quality of predictors.