## 4 Regional Control Strategies Analysis
### Simulation Results  
(1) Strategy 1: decreasing \(P_{12}\) or decreasing \(P_{2A}\)  
Strategy 1 can be implemented by restricting vehicles entering subregion 2 from subregion 1 or outside. In simulations, the parameters \(P_{12}\) and \(P_{2A}\) are decreased by 5% and 10%, respectively, to compare the impacts of different control strategies. Figure 13(a1,a2) display the network state evolution of the ground truth and after decreasing \(P_{12}\). The solid blue line is the evolution with no control, and the red and green dashed lines are the evolutions when \(P_{12}\) being decreased by 5% and 10%. In the same simulation period, the evolution final points are B1, B2, and B3. The average density of subregion 2 has reduced, but the average density in subregion 1 has increased. The traffic state of subregion 1 evolves to congestion under \(P_{12}\) decreasing by 10% (green line in Figure 13(a1)). It indicates that this strategy can alleviate the congestion of subregion 2 but cause subregion 1 in congestion. The simulation results of network state evolution under decreasing \(P_{2A}\) are shown in Figure 13(b1,b2). In this strategy, traffic state of each subregion is in free-flow state under \(P_{2A}\) decreasing by 10% (green line in Figure 13b). Thus, among the two strategies, decreasing \(P_{2A}\) strategy is better.  
(2) Strategy 2: increasing \(P_{21}\) or increasing \(P_{2E}\)  
For the morning peak hours on the DQF, the outflow from subregion 2 can be increased by directing vehicles away from the region in time. In simulations, the parameters \(P_{21}\) and \(P_{2E}\) are increased by 5% and 10%, respectively. The evolutions of the network are shown in Figure 14, where the solid blue line is the evolution with no control, and the red and green dashed lines are the evolutions under the two strategies. Points B1, B2, and B3 are final points in the same simulation period. Under increasing \(P_{21}\) strategy, the average density of subregion 2 reduces with the increase in \(P_{21}\), but the traffic state of subregions 1 evolves to congestion. While under increasing \(P_{2E}\) strategy, the average density of subregion 2 decreases, and traffic states of subregions 1 and 2 are both in free-flow. Therefore, increasing \(P_{2E}\) strategy is better.  
Figure 13: The network evolution on the day of Qingming Festival: (**a1**) subregions 1 and 2, (**a2**) subregions 2 and 3 under \(P_{12}\) is decreased, (**b1**) subregions 1 and 2, (**b2**) subregions 2 and 3 under \(P_{2A}\) is decreased. The line is the simulation result of the model, and the arrow indicates the direction of system evolution. Point A represents the initial state and points B1, B2, and B3 represent final state of the simulation under different control strategies.  
In summary, when \(P_{12}\) and \(P_{2A}\) are decreased or \(P_{21}\) and \(P_{2E}\) are increased in the same proportion, controlling the external inflow or outflow ratio of subregion 2 is more effective in reducing the density of the regional network. To avoid a large amount of traffic gathering in this region in a short period, the total traffic flow can be dispersed in time, or plan detour routes for vehicles entering from outside, and implement temporary control upstream of the entrance. Since the roads connected to the cemeteries are mostly high-grade roads such as expressways and highways, the traffic flow can be limited at the entrances of expressways in actual traffic control.