# An Efficient Parallelization of Microscopic Traffic Simulation
## 3 Results
### Assessment with the Bologna Scenario
Note the logarithmic scale of the simulation runtime. The 100% demand level has not been evaluated, as the SUMO simulation showed excessive congestion due to artificial deadlocks at intersections. Also, the 75% demand level resulted in heavy congestion and gridlock, which is why the SUMO waiting times are considerably higher than those of ParSim for this scenario. ParSim has no gridlock situation, but it can create artificial slow-downs in a situation where the vehicle speed is suddenly set to zero because the successive edge is momentarily occupied. This means that both simulators may show unrealistic behavior but that this behavior occurs in different situations. With SUMO, deadlocks happen at complex and congested intersections, while with ParSim, slow-down effects are more serious if vehicles run at higher speeds and occur more frequently at high vehicle densities. In order to get a clearer picture of the simulated traffic volumes, we have recorded the number of vehicles entering each edge for ParSim and SUMO. We show only results for the 25% and 50% demand level, as the SUMO starts to show gridlock phenomena for the 75% demand level that is increased even further in the 100% scenario. The total traffic volumes (the sum of vehicles entered in all edges) for off-peak and successive peak periods are shown in Figure 8. ParSim and SUMO generated comparable aggregate traffic volumes across all scenarios. At both the 25% and 50% travel demand levels, ParSim estimated lower volumes during the off-peak hour (676.07 vs. \(704.30\times 10^{3}\) veh/h at 25% demand and 1362.44 vs. \(1427.02\times 10^{3}\) veh/h at 50% demand) and slightly higher volumes during the peak hour than SUMO (836.04 vs. \(820.46\times 10^{3}\) veh/h at 25% demand and 1778.91 vs. \(1662.64\times 10^{3}\) veh/h at 50% demand). Note that trips have exactly the same start time and the same routes for both simulators. The difference in flows during a certain time window is because the speed and number of crossed edges of an individual vehicle differs in the two simulators due to interactions with other vehicles and traffic lights. To better visualize the spatial distribution, the simulated edge flows are shown for the peak-hour scenario with 50% travel demand. It can be observed in Figure 9 that edges with \begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{**Traffic Demand**} & \multicolumn{2}{c}{**Avg. Waiting Time [s]**} & \multicolumn{2}{c}{**Avg. Speed [m/s]**} \\ \cline{2-5}  & **ParSim** & **SUMO** & **ParSim** & **SUMO** \\ \hline
25\% & 51.00 & 61.27 & 17.30 & 15.45 \\
50\% & 76.65 & 98.53 & 16.88 & 14.33 \\
75\% & 121.74 & 743.78 & 15.75 & 12.88 \\ \hline \end{tabular}
\end{table} 
Table 6: Comparison of ParSim and SUMO simulation outputs. Figure 8: Aggregate traffic volumes from ParSim and SUMO across the simulation area under different travel demand thresholds. high vehicle flows are fairly similar in both ParSim and SUMO: higher traffic volumes are predominantly located along the inner ring road, the radial roads to/from the city center, and the outer ring road. In more detail, the volumes simulated by ParSim are slightly higher than those in SUMO for this scenario (Figure 8), as indicated by the greater presence of red areas with flows reaching up to 500-600 vehicles per hour. Pearson correlation coefficients (r) and mean absolute errors (MAEs) of edge-level traffic volumes simulated by ParSim and SUMO are compared during peak and off-peak hours under the 25% and 50% demand scenarios, as shown in Table 7. The results demonstrate positive (\(0<r<1\)) and strong correlations (\(r>0.8\)) [34] between the two simulation outputs. In addition, we also performed a regression analysis between the flows generated by ParSim and SUMO. Figure 10 shows the flows from both simulators for each edge as a dot; slopes and \(R^{2}\) values are also reported.