## 3 Network Dynamic Evolution and Empirical Analysis
### The Model on the WBH
#### 3.1.2 Model Calibration and Empirical Analysis  
The MFD of each subregion on the two days in Figures 5 and 7 is calibrated by empirical data. Generally, a congested branch will appear in the MFD where the average flow decreases as the density increases, and the density corresponding to the maximum flow \(q_{ic}\) is the critical density \(k_{ic}\). For each network subregion of the WBH (Figure 5a) and subregion 3 of the OW (Figure 7a), no congested branch appears. The scatters on the MFD are all distributed within the critical density. Therefore, according to previous literature [31], the critical density of the MFD without a congested branch is calibrated as 30 veh/km/lane in this paper. The proportional relationship between the exit flow from the boundary and the flow inside the area appears to be a constant linear proportional trend after 6:00. The calibration results are listed in Table 2. The jam density \(k_{j}\) is calculated as the average vehicle length of 5.2 m and the minimum headway distance of 1.95 m, \(k_{b}=140\) veh/km/lane. The free-flow speed is the average value of the space-mean speed at night (0:00-5:00), that is \(v_{i}=20\) km/h. The reason for the low free-flow speed is that the travel time included delays such as signal waiting and queuing at intersections. Moreover, the network of the study area includes different grades of roads, and the design speeds of sub-arterial roads and branches are lower than 40 km/h. There are also disturbances from non-motor vehicles and pedestrians that cause an increase in travel time. The space-mean average speed is the average of all vehicles on the network, and all these factors cause lower average speed.  
The calibrated model is used to simulate the evolution of the network state. Taking the average density at 7:00 of the network as the initial density, the initial densities of the network evolution are (4,6,10) veh/km/lane on the WBH, and are (24,19,4) veh/km/lane on the OW. Figure 10 shows the network evolution process over time on the WBH and the OW. Figure 10(a1) is the evolutions of subregions 1 and 2, and Figure 10(a2) is subregions 2 and 3 on the WBH, and Figure 10(b1,b2) are the evolutions on the OW. The blue line is the simulation result of the model, and the scatters are the empirical data. Points A and B represent the initial state and final state of the simulation, respectively. On the WBH, the state converges to a free-flow state in subregions 1 and 2, while it evolves to congestion in subregion 3. On the OW, both states in subregions 1 and 2 evolve to congested state over time. The simulation results are consistent with the ground truth, indicating that the model can reflect the actual evolution of the network. Compared with the OW, the traffic flow in the city center decreases on the WBH, the transfer ratio from subregion 2 to subregion 1 (\(P_{21}\)) decreases, and the congestion has not occurred in subregion 1. The transfer ratio  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline
**Model** & \(k_{1c}\) & \(k_{2c}\) & \(k_{3c}\) & \(q_{3c}\) & \(P_{12}\) & \(P_{21}\) & \(P_{23}\) & \(P_{32}\) & \(P_{3A}\) & \(P_{3E}\) \\
**Parameters** & **(veh/km/lane)** & **(veh/km/lane)** & **(veh/km/lane)** & **(veh/h/lane)** & **(veh/h/lane)** & **\(P_{12}\)** & \(P_{21}\) & \(P_{23}\) & \(P_{32}\) & \(P_{3A}\) & \(P_{3E}\) \\ \hline WBH & 30 & 30 & 30 & 454 & 0.5 & 0.55 & 0.6 & 0.51 & 0.2 & 0.12 \\ OW & 27.66 & 27.29 & 30 & 380 & 0.32 & 0.68 & 0.2 & 0.6 & 0.18 & 0.12 \\ \hline \end{tabular}
\end{table}
Table 2: Parameters calibration of the model on the weekday before the holiday and the ordinary weekday.  
\(P_{23}\) and the external inflow ratio \(P_{3A}\) increase, leading to an increase in the traffic flow in subregion 3, and the network becomes congested.