# A Novel Traffic Analysis Zone Division Methodology Based on Individual Travel Data
## 3 Traffic Subdivision Methods
### Optimal Modeling of Traffic Cell Segmentation  
According to the principle of TAZ division, the proportion of trips within a TAZ and the difference in travel density between TAZs should be as small as possible. Therefore, the optimization of TAZ division in this study is a multiobjective optimization problem. The purpose of the objective function is to minimize the difference between the travel density of each TAZ and the average travel density of the area, and to minimize the proportion of trips within the TAZ, as shown in Equation (12). Based on the spatiotemporal discretized travel data, spatial grid attribute data are constructed for the traffic subdivision model.  
\[min\frac{\sum_{j=1}^{K}(A_{v}-\frac{q_{j}}{a_{j}})}{K},TP_{j} \tag{12}\]  
Figure 4: Aggregation rules for single traffic analysis zone.  
\[A_{v}=\frac{\sum_{j=1}^{K}\frac{q_{j}}{a_{i}}}{K} \tag{13}\]  
In Equation (12), \(A_{v}\) is the average travel density within the area, which can be calculated by Equation (10), \(q_{j}\) is the total trips in the \(j\)-th cell, \(a_{j}\) is the area of the \(j\)-th cell, \(K\) is the total number of cells, and \(TP_{j}\) is the proportion of trips in the area when aggregated with the \(j\)-th grid.  
Travel similarity constraint: Based on the travel time similarity coefficient \(\rho\) between cells, the \(\rho_{ij}\) between the cell \(i\) to be aggregated and its adjacent cell \(j\) must not be lower than the threshold \(\rho^{*}\), as shown in Equation (14).  
\[\rho_{ij}\geq\rho^{*} \tag{14}\]  
Travel intensity constraint: The final travel intensity in each TAZ should be greater than 70% of the average travel quantity. This can control the statistical accuracy of the TAZ, which ensures the homogeneity of the travel intensity of all TAZs. After each aggregation, a judgment is made regarding whether the requirements are met, and if they are not, the aggregation will continue.  
\[T_{i}>avg(T_{j})\times 70\% \tag{15}\]  
Constraint on the proportion of trips within the TAZ: The travel proportion within each TAZ should be minimal and should not exceed the threshold \(TP^{*}\) to avoid excessive travel within some TAZs and loss of geographic accuracy during aggregate analysis.  
\[TP_{i}<TP^{*} \tag{16}\]  
Constraints on the TAZ area: Too large a TAZ area will increase the proportion of trips in the TAZ, which will cause the loss of geographic information; however, too small a TAZ area will reduce the statistical accuracy of the TAZ and increase the workload in the investigation, analysis, and forecasting. Therefore, in order to ensure balance between the geographic information and statistical accuracy, the area of the TAZ formed should be within a reasonable range, as shown in Equation (17).  
\[a^{top}\leq A_{i}\leq a^{bot} \tag{17}\]  
Constraint on TAZ shape: In order to ensure that the TAZ is a convex polygon, the inner angle \(\alpha\) of the polygon formed by the outermost cell centroids is calculated according to the angle discrimination method to determine whether it is less than 180\({}^{\circ}\), as shown in Equation (18).  
\[a_{i}\leq 180^{\circ} \tag{18}\]