# Smart Pedestrian Crossing Management at Traffic Light Junctions through a Fuzzy-Based Approach
## 4 Performance Evaluation
### Simulation Results
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Traffic Light Cycle 84 s**} & \multicolumn{4}{c}{**Traffic Light Cycle 94 s**} \\ \hline \multirow{2}{*}{**Arcs**} & _Speed ped_ & **dm** & \multirow{2}{*}{**QLEN AVG**} & _QLEN AVG_ & _STOPS_ & _Speed ped_ & **dm** & \multirow{2}{*}{**QLEN AVG**} & _QLEN AVG_ & _STOPS_ \\  & **(m/s)** & **(m/s2)** & & & & & & \\ \hline
1-3 & 1.1 & 6.3 & 1.4 & 0.73 & 1.01 & 6.1 & 2.19 & 0.91 \\
1-4 & 1.51 & 5.9 & 1.67 & 0.75 & 1.02 & 5.4 & 2.19 & 0.96 \\
2-1 & 1.05 & 6.1 & 2.01 & 0.52 & 1.05 & 5.9 & 2.32 & 0.39 \\
2-3 & 2.36 & 5.2 & 1.91 & 1.23 & 1.3 & 5 & 1.68 & 0.96 \\
2-4 & 1.63 & 6.7 & 1.01 & 0.41 & 1.3 & 6.3 & 1.78 & 0.29 \\
3-1 & 1.44 & 5.6 & 4.78 & 1.54 & 1.2 & 5 & 6.5 & 2.86 \\
3-4 & 0.98 & 5.9 & 1.78 & 2.28 & 0.62 & 5.6 & 1.5 & 4.11 \\
4-1 & 0.72 & 6 & 1.15 & 0.84 & 0.71 & 6 & 1.73 & 0.61 \\
4-3 & 1.72 & 5.7 & 1.15 & 0.56 & 1.01 & 5.1 & 1.73 & 0.42 \\ \hline \multicolumn{2}{c}{**Total for**} & \multirow{2}{*}{1.39} & \multirow{2}{*}{5.93} & \multirow{2}{*}{1.87} & \multirow{2}{*}{0.98} & \multirow{2}{*}{1.02} & \multirow{2}{*}{5.60} & \multirow{2}{*}{2.40} & \multirow{2}{*}{1.28} \\ \multicolumn{2}{c}{**intersection**} & & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Obtained distribution of pedestrians without the proposed fuzzy-based solution. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Traffic Light Cycle 84 s**} & \multicolumn{4}{c}{**Traffic Light Cycle 94 s**} \\ \hline \multirow{2}{*}{**Arcs**} & _VEHS_ & _QLEN AVG_ & _QLEN MAX_ & _STOPS_ & _VEHS_ & _QLEN AVG_ & _QLEN MAX_ & _STOPS_ \\ \hline
1-3 & 100 & 12.04 & 95.16 & 0.67 & 100 & 22.18 & 67.21 & 0.41 \\
1-4 & 151 & 14.02 & 88.11 & 0.43 & 152 & 16.37 & 88.64 & 0.68 \\
2-1 & 145 & 1.99 & 60.12 & 0.32 & 145 & 1.05 & 42.13 & 0.43 \\
2-4 & 63 & 1.05 & 20.24 & 0.39 & 63 & 0.57 & 21.87 & 0.25 \\
2-3 & 36 & 0.66 & 12.15 & 0.71 & 35 & 0.69 & 21.34 & 0.74 \\
3-1 & 144 & 39.73 & 89.59 & 0.87 & 92 & 45.38 & 87.15 & 1.59 \\
3-4 & 98 & 35.05 & 100.32 & 1.54 & 62 & 71.25 & 88.84 & 2.98 \\
4-1 & 72 & 4.02 & 75.17 & 0.81 & 71 & 3.56 & 81.23 & 0.66 \\
4-3 & 172 & 6.08 & 80.76 & 0.58 & 171 & 2.09 & 66.76 & 0.55 \\ \hline \multicolumn{2}{c}{**Total for**} & \multirow{2}{*}{981} & \multirow{2}{*}{12.73} & \multirow{2}{*}{100.32} & \multirow{2}{*}{0.70} & \multirow{2}{*}{891} & \multirow{2}{*}{18.13} & \multirow{2}{*}{88.84} & \multirow{2}{*}{0.92} \\ \multicolumn{2}{c}{**intersection**} & & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Obtained distribution of flows with the proposed fuzzy-based solution. Figure 7: Queue length in the arms with the static traffic light cycle: (**a**) 84 s; (**b**) 94 s.  
The pedestrian flow has been analyzed in the various traffic light cycles through the variation of the parameters described in Table 7. Precisely, a similar variation of the stops and average stops for the two cycles analyzed has been measured, as shown in Figure 9. Furthermore, as shown in Figure 10, there is a similarity in the values of NORMSPEEDAVG, an increase of less than 5% of the parameter SPEEDTODESTAVGand an increase of 8-10% of the parameter SPEEDAVGduring the traffic cycle from 84 s to that of 94 s. These values arise from the pedestrian green times, i.e., 49 s for the cycle of 84 s and 64 s for that of 94 s respectively. The results obtained through the application of the fuzzy-based approach are almost similar to those with the static management of the traffic light cycle. In fact, the goal of the FLC is not to significantly increase the speed of pedestrians, but to dispose of their influx through a smart management of the traffic light phases. An analysis has been made regarding the density of pedestrian flows. More in detail, the average flow in the direction of the destination, obtained from the product between the current speed and the total current density, has been evaluated, taking into account the static potential in the position of each pedestrian.