# Smart Pedestrian Crossing Management at Traffic Light Junctions through a Fuzzy-Based Approach
## 4 Performance Evaluation
### Simulation Results
Besides, the average pedestrian density parameter, i.e., the ratio of all pedestrians in the network to pedestrians in pedestrian areas, has also been measured. The values depicted in Figure 11 highlight an overall similarity of the two results when the traffic light cycle changes. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Traffic Light Cycle 84 s**} & \multicolumn{3}{c}{**Traffic Light Cycle 94 s**} \\ \hline \multirow{2}{*}{**Arcs**} & _Speed ped_ & **dm** & \multirow{2}{*}{_QLEN AVG_} & \multirow{2}{*}{_STOPS_} & _Speed ped_ & **dm** & \multirow{2}{*}{_QLEN AVG_} & \multirow{2}{*}{_STOPS_} \\  & **(m/s)** & **(m/s\({}^{2}\))** & & & & **(m/s)** & & \\ \hline
1-3 & 1.1 & 6.3 & 1.11 & 0.41 & 1.01 & 6.1 & 1.17 & 0.43 \\
1-4 & 1.51 & 5.9 & 1.02 & 0.81 & 1.02 & 5.4 & 1.21 & 0.62 \\
2-1 & 1.05 & 6.1 & 1.04 & 0.45 & 1.05 & 5.9 & 1.51 & 0.38 \\
2-3 & 2.36 & 5.2 & 1.88 & 1.01 & 1.3 & 5 & 1.07 & 0.81 \\
2-4 & 1.63 & 6.7 & 1.12 & 0.33 & 1.3 & 6.3 & 1.08 & 0.31 \\
3-1 & 1.44 & 5.6 & 2.83 & 1.08 & 1.2 & 5 & 3.34 & 1.15 \\
3-4 & 0.98 & 5.9 & 1.22 & 1.06 & 0.62 & 5.6 & 1.11 & 2.27 \\
4-1 & 0.72 & 6 & 1.03 & 0.53 & 0.71 & 6 & 1.73 & 0.52 \\
4-3 & 1.72 & 5.7 & 1.08 & 0.52 & 1.01 & 5.1 & 1.81 & 0.39 \\ \hline
**Total for** & \multirow{2}{*}{1.39} & \multirow{2}{*}{5.93} & \multirow{2}{*}{1.37} & \multirow{2}{*}{0.69} & \multirow{2}{*}{1.02} & \multirow{2}{*}{5.60} & \multirow{2}{*}{1.56} & \multirow{2}{*}{0.76} \\
**intersection** & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Obtained distribution of pedestrians with the proposed fuzzy-based solution. Figure 8: Average queue length of pedestrians. been evaluated. In fact, in research on traffic conflict techniques, TTC has been demonstrated to be a sound measure for traffic conflicts' severity. TTC is specified as the time to collision if two vehicles continue to drive at the same speed and in the same direction without any evasion behavior. The maximum value is infinite, and the minimum is 0 s (at the time the collision happens). The potential site of collision is first determined when Vehicle 1 occupies a precise position at a specific time. PET is defined as the time taken for Vehicle 2 to reach the identified site. The lower value of the TTCmin is associated with the higher risk of a collision. On the other hand, when TTC is high, but PET is small, there is no risk of rear-end collision. However, even a slight change in the motion characteristics may lead to a rear-end collision. The main difference between PET and TTC is the absence of the collision course criterion in PET. As shown in [41], since there is no requirement for the existence of collision course, PET is more useful in measuring transversal conflicts. The obtained values of TTC and PET are depicted in Figure 12. As is possible to note, even in this case, applying the FLC, the best performances are obtained compared to the use of the fixed traffic light cycle since the collision time lapse between the pedestrian and the vehicle and the pedestrian crossing compared to the one waiting to cross is increased. In general, only conflicts with a minimum TTC of less than 1.5 s are considered critical observers. Nevertheless, as can be noted in Figure 12, the TTC values exceed the value of 1.5 s through the fuzzy implementation, thus reducing the probability of accidents. Other parameters valuable for the evaluation of pedestrian safety during crossing are related to the possible types of accidents at the road infrastructure. The types of accidents examined in this paper are the following:  
* Read end;
* Crossing;
* Changing lanes. These types of collisions can be assessed through the Surrogate Safety Assessment Model (SSAM) tool [42] that employs some particular Vissim outputs to estimate the trajectories of vehicles and, consequently, their propensity to accidents. In Figure 13, an assessment of the various accidents before and after the application of the fuzzy logic is presented.