## 5 Results and Analysis
### Mechanism of the Nonlinear Effect of Built Environment Factors on Ridership
#### 5.4.3 Road Network Density  
Figure 10a-c show the partial dependence of road network density on total passenger flow and inbound and outbound passenger flow in the morning peak on weekdays, which shows the nonlinear effect of accessibility on them.  
For total passenger flow and outbound passenger flow, road and rail transport have a complementary effect when the road network density is \(\geq\)30 km/km\({}^{2}\) (as shown in Figure 10a,c). This indicates that the accessibility of the last kilometre is effectively improved by roads that are connected by walking or cycling. The high density network of side streets and secondary roads significantly reduces the walking/cycling connection distance and extends the catchment area of the metro station.  
For inbound passenger flow, there is a significant negative correlation between the density of the road network and the density of the road network between 0 and 13 as the density of the road network increases. When the network density is close to 0, the metro attracts up to 1300 passengers; when the network density increases to 13, the inbound passenger flow drops to zero. This indicates that at this stage, the city's rail system is not yet fully developed, and urban residents tend not to choose the metro as a mode of travel.  
When the network density reaches between 22 and 24, the impact pattern shifts to an inverted U-shaped curve, with a brief peak at about 23. This means that when the network density reaches a more developed level, it attracts more residents who do not normally use the railways to reach the metro stations via short connections, thus increasing the number of metro passengers. However, once the road network density exceeds 24, the excessive passenger flow will cause traffic congestion, which, in turn, inhibits more people from choosing the metro for travelling, leading to a decline in passenger flow. This phenomenon reveals the importance of rational planning of road network density in enhancing the efficiency of public transport.  
Figure 9: The nonlinear influence of accessibility on total ridership and inbound and outbound ridership. (**a**) On total ridership; (**b**) on inbound ridership; (**c**) on outbound ridership.  
Therefore, in areas with a road network density of \(\geq\)30 km/km\({}^{2}\), the service area of metro stations should be expanded by strengthening the construction of pedestrian and cycling connections to enhance accessibility in the 'last kilometre'. For areas with a road network density between 0 and 13, this indicates that the current rail system is not yet mature and that urban residents tend not to choose the metro as a mode of travel, so priority should be given to the development of infrastructure facilities, the gradual increase in the number of metro routes and frequency of service, and the improvement of ground transportation conditions to attract passengers. When the road network density reaches 22 to 24, the metro passenger flow can be significantly increased by optimising short-distance connections, but we must be alert to the traffic congestion that may be caused by a road network density of more than 24, which requires us to find the optimal road network density balance point in our planning, to avoid new congestion caused by overdevelopment, and to ensure efficient operation of the public transport system and quality of service.