## 2 Data Description and Network Partitioning
### Network Partitioning  
The related research reveals [27] that the heterogeneous distribution of the network traffic flow has a significant impact on the MFD. Here the network is gridded to a size of \(1\) km \(\times\) 1 km, and the density in each grid is calculated. Three days are considered, i.e., the weekday before the holiday (WBH), the day of Qingming Festival (DQF), and the ordinary weekday (OW). Figure 3 shows the comparisons in the network density distribution of these days. The traffic densities are heterogeneously distributed on the network, and the congested areas are different in location and size. On the WBH, the density in the city center is low, and the links with high densities are distributed on the suburb of the city (Figure 3a). The traffic flow on the DQF is mainly on the roads to cemeteries and its surrounding area (the west of the network in Figure 3b). On the OW, congestion is localized in the central area (Figure 3c). Therefore, it is necessary to divide the whole network into subregions with similar congestion levels, which provides a basis for further regional traffic control. Among graph segmentation methods, the normalized cut partition (Ncut) algorithm is commonly utilized due to its advantages effectiveness and robustness in the research of heterogeneous networks [28; 29]. Therefore, the whole network is partitioned based on the link densities during 7:00-8:00 with congestion by Ncut algorithm. The basic idea is to partition the whole network into some subregions first and then merge them one by one; the details of the Ncut algorithm are given in Appendix A.  
Figure 2: Schematic illustration of the locations of cameras on a link. The network densities during the peak hour are analyzed for the three days, i.e., the OW, the WBH, and the DQF. Figure 4 shows subregions by using the network partitioning on these days. The network is distinguished with different densities by partitioning. In Figure 4, the high-density area is labeled by red, the middle-density area is labeled by yellow, and the low-density area is labeled by green. The traffic density is similar within each subregion, while much distinct among different subregions. Table 1 lists the average density of each subregion and the evaluation indicators of partitioning. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Subregion** & **1** & **2** & **3** \\ \hline \multirow{2}{*}{WBH} & The mean of density (veh/km/lane) & 6.04 & 9.04 & 15.85 \\  & \(ANS_{k}\) & & 0.8218 & \\ \multirow{2}{*}{DQF} & The mean of density (veh/km/lane) & 25.02 & 40.99 & 8.51 \\  & \(ANS_{k}\) & & 0.8101 & \\ \multirow{2}{*}{OW} & The mean of density (veh/km/lane) & 41.28 & 27.81 & 6.92 \\  & \(ANS_{k}\) & & 0.6092 & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Evaluation indicators of partitioning (The evaluation indicators of partitioning is defined as the average similarity \(ANS_{k}\), it is used to the evaluate the result of partitioning and calculated by Equation (A18) in Appendix A). Figure 4: Network subregions during peak periods on: (**a**) the weekday before the holiday, (**b**) the day of Qingming Festival, (**c**) the ordinary weekday. The numbers 1, 2 and 3 in each figure are the labels of the subregion, representing subregion1, subregion 2, and subregion 3, respectively. Figure 3: Spatial–temporal distribution of network density during peak hour (7:00–8:00) on: (**a**) the weekday before the holiday, (**b**) the day of Qingming Festival, (**c**) the ordinary weekday. On the WBH and the OW, the network is partitioned into three annular subregions. The regions from the inner to the outer are labeled as subregion 1, 2, and 3. On the WBH, the high-density areas are located in the suburb (subregion 3 in Figure 4a), with an average density of 15.85 veh/km/lane, much smaller than the density (41.28 veh/km/lane) in the city center on the OW. And the average density of the two inner subregions is below 10 veh/km/lane. In contrast, on the DQF, the network is partitioned into three adjacent subregions.