## 1 Introduction
### Related Research  
To accurately match GPS coordinates to the correct links on a map, common methods involve using geometric and topological algorithms, as mentioned by [PERSON] in 2009 [PERSON] (2009). These methods are essential for map matching, which refers to aligning raw GPS points to the nearest road or path on a map. Geometric algorithms focus on minimizing the distance between the GPS points and the road network, while topological algorithms take into account the connectivity and shape of the road segments. The combination of both methods improves accuracy, especially in complex urban environments or areas with closely spaced roads. While point-to-point matching is straightforward and fast, it is also sensitive to errors. Point-to-curve matching, which calculates the nearest GPS coordinates to the road network and uses a buffer, is the most prevalent method. Other notable algorithms include the segment-based algorithm Velaga (2009), the probabilistic algorithm Velaga (2009), the fuzzy logic-based algorithm Velaga (2009), and the genetic algorithm Velaga (2010). However, these require spatial searches and are distinct from the focus of this study, which is on point-to-area matching and handling large volumes of data. These distinctions highlight the unique challenges and methodologies necessary for effectively managing and analyzing vast spatial datasets in contemporary geographic information systems. Individual traffic surveys using GPS sensors have been successfully applied to highways Velaga (2010) and signalized intersections Velaga (2010) according to research Velaga (2010). Additionally, logistics data based on location-based services have been collected for route guidance services Velaga (2010). GPS data have also been utilized in supporting urban and transportation planning at a macro level Velaga (2010), reflecting travel speed patterns on road networks at a meso level Velaga (2010), and for updating network structures, attributes, and exploring driving routes at a micro level Velaga (2010). This research distinguishes itself by encompassing all three levels--macro, meso, and micro--using large-scale GPS-based data for a comprehensive analysis of road network information. This approach integrates extensive datasets across different scales to provide a more holistic understanding of traffic dynamics and infrastructure management, differing significantly from studies focused solely on individual levels. The data from moving objects such as vehicles are continuously updated due to their dynamic nature, necessitating indices that facilitate the rapid provision of location-based services [13]. Commonly used indexing techniques include tree-based methods, such as the R-Tree [14], and grid-based methods [15]. The R-Tree technique is particularly notable for its use of the Minimum Boundary Rectangle (MBR) to classify data based on two-dimensional spatial characteristics. First introduced by [PERSON] in 1984 (Gut84) and further refined (NS98), this technique efficiently handles spatial data by organizing objects in a hierarchical structure, making it well-suited for dynamically changing data like vehicle positions. However, there is no existing case study using indexing for GPS data that include speed for linear-based analysis, which is the focus of this research. Indexing techniques for the spatial matching of moving objects demonstrate significantly faster speeds compared to conventional map-matching techniques, making them highly suitable for application in this research. By optimizing the indexing methods for real-time traffic data analysis, this study aims to enhance the accuracy and speed of matching GPS data to road networks, thereby improving the effectiveness of traffic management systems. To enhance search speeds for spatial information in big data, there are techniques that convert global latitude and longitude coordinates into a single number, including the base-32 geocoding method proposed by [PERSON] [16].