# A Microscopic On-Ramp Model Based on Macroscopic Network Flows
## 3 Results and Discussion  
To evaluate the proposed model, we compared real traffic data on the on-ramp (see Trajectory data) to simulations conducted with the new flow-based model, as well as simulations conducted with the IDM; see Model Implementation. Our analyses focused on the spatial variations of traffic dynamics and therefore considered temporal averages of key quantities with respect to the position on the on-ramp setting. To achieve this, we divided the road longitudinally into 5 m long sections. First, we analyzed the (longitudinal) velocities along the on-ramp. Figure 3 (left) shows that due to limited accuracy of the calibration, both models overestimated the velocities of real traffic. The models, however, accurately represented the fact that the velocities on the on-ramp lane are smaller than on the through lanes. Comparing both models, we found that the variance in velocity between the lanes, which in the data ranged from 52.65 km/h on the entry lane to 72.02 km/h on the second passing lane, was better represented by the new model predicting a range from 64.28 km/h to 82.66 km/h. Unlike the IDM, it assumed that the largest difference in average velocity was between the on-ramp and the main lane (from 64.28 km/h to 77.54 km/h), while in the data, only a minor difference (52.65 km/h to 56.40 km/h) was observed. The largest difference in average velocities in the data was observed between the main lane and the first passing lane (from 56.40 km/h to 67.05 km/h), which was also the case in the simulations by the IDM, predicting a jump from 73.25 km/h to 81.36 km/h. These different model results might occur because the new model does not explicitly include differences between the through lanes. In reality, these speed differences occur not only due to the on-ramp, but they also occur due to different desired speeds of the individual vehicles. This heterogeneity was not considered in our simulations. In terms of acceleration, Figure 3 (right) shows that both models predicted larger absolute accelerations compared to the data. This means that the observed behavior that drivers adapt their speed to the forthcoming on-ramp and therefore avoid large accelerations was not reflected in both models. In other words, both models tend to predict aggression regarding acceleration and reactive, i.e., less anticipatory, driver behavior. Since our model is derived from a macroscopic model, not explicitly accounting for acceleration, additional model assumptions in the future might achieve more realistic accelerations. Furthermore, we note that our model was only calibrated on the macroscopic scale and that  
Figure 3: Average longitudinal velocities (**left**) and accelerations (**right**) for real traffic data (**top**); the new flow-based model (**center**) and IDM (**bottom**). the IDM was used with SUMO's default values. Detailed microscopic calibration, which has not been realized in this analysis due to its large computational cost and complexity, could be helpful to find a suitable balance between the two acceleration terms in Equation (9) and therefore obtain more realistic accelerations. Figure 3 (right) also shows that in the results of our model, the vehicles on the through lanes decelerated significantly in front of the on-ramp section to allow vehicles from the right to merge. This phenomenon can also be observed in real traffic data, but to a smaller extent. Moreover, the IDM produced large negative accelerations at the end of the on-ramp lane, because vehicles stop and wait for a suitable gap if they have not found one before. Our proposed model does not show this unrealistic behavior. In the real traffic data and the traffic simulated with the considered models, no accident occurred, which calls for further measures to evaluate the traffic safety evaluation. With the help of Surrogate Safety Measures, areas with higher collision risk can be identified. Figure 4 (left) shows the average MTTC values under 3 s within a given 20 m long section (see the Model Evaluation section for details).