# A Microscopic On-Ramp Model Based on Macroscopic Network Flows
## 3 Results and Discussion
If the average within these sections lies above 3 s, it indicates a safe, conflict-free area. In this case, the section is colored gray. The real traffic data exhibited the lowest MTTCs and therefore the riskiest traffic scene. In the traffic simulated with the new model, the entry and main lane displayed the most dangerous area, but there was little to no disturbance on the two passing lanes. In the traffic simulated with the IDM, only the first 20 m long sections on both the on-ramp and the main lane showed low average MTTCs, while the rest of the analyzed stretch remained safe. Figure 4: Left: average MTTC capped at 3s for real traffic data (**top**), the new flow-based model (**center**), and IDM (**bottom**). Sections with larger MTTC are colored gray. Right: distribution of longitudinal lane change positions from the entry lane to the main lane for real traffic data (**top**), the new flow-based model (**center**), and IDM (**bottom**). Figure 5 (left) shows the average MTTCs of the lanes: We computed the average over 20 m long sections on the considered on-ramp scenario combining all lanes. Comparing the two models, we see that only three out of 15 sections have average MTTCs that are less than 3 s in the case of the IDM model, and thus, generally safe driving behavior is assumed. The new flow-based model predicted results that are more similar to the observed traffic scene in the data locally involving riskier driving behavior. Compared to real traffic, the new model exhibited multiple locations at which a lower MTTC was pronounced. Figure 5 (right) shows the total number of sections that had an average MTTC between 0-1.5 s, 1.5-2 s, 2-2.5 s, 2.5-3 s, and above 3 s. While the distribution of average MTTC achieved by the flow-based model differs from the one of the real traffic data, this is mainly because of the small number of conflicts on the passing lanes that the model predicted. Figure 4 (right) visualizes the changes from the entry lane to the main lane with respect to their location in the 20 m long sections on the considered on-ramp. In the simulations of the IDM model, vehicles preferably change to the main lane as soon as possible. While a large part of the vehicles also changed very early in the simulation results of the flow-based model, more changes occurred toward the end of the on-ramp, which is closer to the observed behavior in the data. To investigate how the macroscopic calibration would affect the microscopic model, we conducted simulations varying the maximum density of segment 2, with \(\rho_{max}^{2}\). Figure 6 shows that the deviation between the real traffic data and simulated traffic with respect to the mean velocity and density on the main lane was smallest when the calibrated value of \(\rho_{max}^{2}\) was used. A larger \(\rho_{max}^{2}\) had only a minor impact on the deviation, while a smaller  
Figure 5: Left average MTTC across all lanes with respect to their longitudinal section capped at 3 s for real traffic data (**top**), the new flow-based model (**center**), and IDM (**bottom**). Right: histogram of longitudinal sections with respect to their MTTC for real traffic data (**top**), the new flow-based model (**center**), and IDM (**bottom**). \(\rho_{max}^{2}\) led to a significant increase in the deviation, as congestion was predicted in the first half of the considered time span. This indicates that our macroscopic calibration has been suitable to obtain a valid microscopic model.