# Analysis of the Efficiency of Slope Evacuation for Dense Crowds in Urban Street-Type Public Spaces
## 5 Results
### Effect of Obstacle Layout on Evacuation Time  
The evacuation results of different densities of people under each obstacle layout are shown in Table 7. The cumulative use of evacuation paths for pedestrians is compared for different obstacle layouts at the same crowd density, as shown in Figure 10. The number of obstacles, as well as their location distribution, jointly affects the evacuation of pedestrians. As the number of obstacles increases, the available space for normal pedestrian movement diminishes, as vividly shown by the color changes in Figure 10. In Layout 1, with no obstacles, the color mainly leans toward lighter shades, indicating shorter usage times and smoother pedestrian flow. Layouts with more obstacles will have darker colors, such as Layout 7, which implies longer usage times and reflects poor crowd flow, congestion, and reduced mobility. Particularly in narrow corridors or exits, obstacles can cause crowds to be stranded, thus delaying evacuation. As can be seen in Table 7, the evacuation time of the crowd increased in the order of layouts 1, 2, 5, 4, 3, 6, and 7. With the exception of Layouts 1, 2, and 5, the remaining layouts had varying degrees of stranded persons unable to complete evacuation. The number of stranded people increased in the order of layouts 3, 4, 6, and 7. The irrational layout of obstacles and the excessive number of obstacles will have a negative impact on the evacuation of pedestrians:  
1. When the number of obstacles is the same, the number of stranded people with obstacles distributed on both sides of the street (e.g., Layout 4) is almost twice that of the centered layout (e.g., Layout 6), which suggests that pedestrians had to change the direction of their movement frequently to avoid these obstacles when the obstacles were located on both sides of the street, leading to an increase in evacuation time. On the contrary, if the obstacles are located in the middle of the street, pedestrians can travel more directly along straighter paths, reducing the frequency of direction changes, thus shortening evacuation time and reducing the risk of being stranded. 2. The number of people stranded in Layout 3 is slightly lower than the number of people stranded in Layout 4 when the obstacles are distributed on both sides of the \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Layout Number**} & \multicolumn{8}{c}{**Evacuation Time (s)**} & \multicolumn{8}{c}{**Number of Stranded People**} \\ \cline{2-13}  & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **1** & **2** & **3** & **4** & **5** & **6** & **7** \\ \hline \multirow{3}{*}{Density} & 0.50 & 359 & 435 & 556 & 543 & 446 & 625 & 703 & 0 & 0 & 19 & 20 & 0 & 10 & 34 \\  & 1.00 & 407 & 498 & 653 & 631 & 515 & 748 & 764 & 0 & 0 & 21 & 23 & 0 & 12 & 35 \\  & 1.50 & 454 & 567 & 763 & 701 & 584 & 858 & 874 & 0 & 0 & 22 & 25 & 0 & 14 & 37 \\  & 2.00 & 503 & 634 & 840 & 788 & 653 & 965 & 1142 & 0 & 0 & 25 & 29 & 0 & 17 & 40 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Evacuation results for crowds of different densities under each obstacle layout. Figure 10: Cumulative use of evacuation paths for pedestrians under different barrier layouts. street. This phenomenon indicates that in Layout 3, the symmetrically distributed barriers on both sides provide similar and regular walking routes for pedestrians during evacuation. Pedestrians can plan their routes in a relatively orderly manner, reducing mutual interference and congestion. However, in Layout 4, due to the asymmetrical distribution of obstacles, the evacuation routes for pedestrians become complicated and irregular. Pedestrians may get confused due to sudden changes in the routes when avoiding obstacles, leading to increased local congestion. 3. Although the obstacles in both Layout 5 and Layout 6 are centrally arranged, only Layout 6 produces the phenomenon of stranded people.