# A Novel Traffic Analysis Zone Division Methodology Based on Individual Travel Data
## 4 Case Validation and Analysis  
Based on the constructed TAZ aggregation model, the TAZ within the Fourth Ring Road in Beijing was delineated using GIS data of the bus network and bus card data collected on a working day in March 2016. During the delineation process, the number of TAZs was varied between 240 and 340, with an increment of five TAZs per scheme, resulting in a total of 21 different TAZ delineation schemes. Figure 8 illustrates the changes in macro-indicators for each scheme. As the number of TAZs increases, the area of each TAZ decreases, and the proportion of trips within each TAZ shows a decreasing trend. Moreover, the average trip proportion within each area remains below 10%, and the variation coefficient of travel density decreases. When the number of TAZs is around 285 to 290, these indicators reach a relative balance. To evaluate and select the optimal TAZ delineation scheme, the macro-indicator matrix  
Figure 8: Macro-indicators of the TAZ scheme. Figure 7: Unaggregated grids in the aggregation model. for all schemes was calculated, with the results shown in Table 1, and the proximity of each scheme to the ideal solution was determined using the TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) evaluation method, as shown in Table 2.  
In Table 1, the normalized macro-indicator matrix for all TAZ delineation schemes is presented. This matrix includes the key performance indicators for each scheme, such as the area of each TAZ, the trip proportion within each TAZ, and the travel density variation coefficient. These values were normalized to ensure they could be compared on the same scale across different TAZ schemes. Table 2 shows the proximity of each scheme to the ideal solution, calculated using the TOPSIS method. The proximity value reflects how close each scheme is to the ideal solution, with higher values indicating better overall performance. The scheme with the highest proximity value (285 TAZs) was selected as the optimal delineation scheme for this study. TOPSIS, proposed by [PERSON] and [PERSON] in 1981 [PERSON] and [PERSON] (1981), is a widely used method for multicriteria decision analysis. The method begins by normalizing the original data matrix and determining the ideal and worst solutions (represented by the ideal and worst vectors). The proximity of each evaluation object to the ideal solution is calculated by measuring the Euclidean distance to both the ideal and worst solutions. This method is commonly used to select the best solution based on its closeness to the ideal solution and its distance from the worst solution. The results indicate that when the number of TAZs is 285, the proximity to the ideal solution is the highest, yielding the best TAZ delineation effect. When the number of TAZs is too large or too small, the proximity is lower, indicating poorer overall performance. Therefore, 285 TAZs were selected as the optimal TAZ delineation scheme for the area within Beijing's Fourth Ring Road. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Number of TAZ** & **Travel Density** & **Average Area** & **Average Travel** \\
**Division Schemes** & **Variation Coefficient** & **Average Area** & **Proportion in the TAZ** \\ \hline  
\hline \hline \end{tabular}
\end{table} 
Table 1: Normalized matrix of macro-indicators. By applying the TOPSIS comprehensive evaluation method, the optimal number of traffic districts within the Fourth Ring Road area of Beijing was determined to be 285, with the division results shown in Figure 9, where different colors represent different traffic districts. The distribution of the areas of all traffic districts when the study area was divided into 285 traffic districts is shown in Figure 10a. The areas are primarily distributed within the range of [0.5 km\({}^{2}\), 2.5 km\({}^{2}\)], accounting for more than 95% of the total number of traffic districts.