# Smart Pedestrian Crossing Management at Traffic Light Junctions through a Fuzzy-Based Approach
## 4 Performance Evaluation
### Simulation Model
It is necessary to consider specific global parameters or for a single arm to study a road intersection concerning capacity and flows. These parameters, described in Tables 6 and 7, must be evaluated both regarding their maximum and average values. To correctly evaluate the acceptable time gap for the pedestrian crossing to be safe, it is necessary to focus the analysis on the pedestrian's point of view. The pedestrian population must be treated very differently from the vehicular one. Pedestrians do not have rigidly channeled paths. Their speed may vary according to age and physical conditions. Moreover, they can cross-track their trajectories randomly and have almost instantaneous acceleration/deceleration profiles. Consequently, it is necessary to evaluate the heterogeneous nature of the pedestrian population preliminarily. Furthermore, it is natural to think that a pedestrian will modify his/her attitude if he/she is in a hurry compared to when he/she is relaxed, varying his/her speed. For instance, concerning pedestrians, in [36], a walking speed of 3.9 ft/s (i.e., 1.2 m/s) is recommended, with the speed reduced to 3.1 ft/s (i.e., 1 m/s) if the percentage of elderly pedestrians exceeds 30%. Moreover, pedestrian speeds at crosswalks on intersections and on-road trunks have been studied in [37]. The results show that there are slower average speeds at road trunks. In [38], it is suggested to lower the walking speed of the pedestrian to 3.5 ft/s (i.e., 1.1 m/s). Nonetheless, it is also stated that speeds even lower may be appropriate in some instances. In fact, the variability of the speed of the pedestrian is a determining factor when it comes to problems related to crossing because it is directly proportional to the time required to overcome a certain distance. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Units of Measurement** \\ \hline Vehicle flow & veh/h \\ Queue length & m \\ Delay & s \\ Speed variation & m/s or km/h \\ Acceleration variation & m/s\({}^{2}\) or km/h\({}^{2}\) \\ Stop number & unit \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Descriptive parameters of vehicular flows. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**O/D**} & \multicolumn{8}{c}{**Arcs**} \\ \cline{2-10}  & \multicolumn{2}{c}{**1-3**} & **1-4** & **2-1** & **2-3** & **2-4** & **3-1** & **3-4** & **4-1** & **4-1** \\ \hline \multirow{4}{*}{**Nodes**} & 1 & 1 & 1 & \(-1\) & 0 & 0 & \(-1\) & 0 & \(-1\) & 0 \\ \cline{2-10}  & 2 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 \\ \cline{2-10}  & 3 & \(-1\) & 0 & 0 & \(-1\) & 0 & 1 & 1 & 0 & \(-1\) \\ \cline{2-10}  & 4 & 0 & \(-1\) & 0 & 0 & \(-1\) & 0 & \(-1\) & 1 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Incidence matrix associated with the analyzed nodes/arcs. This indicator has been used and developed to assign the frequency and severity of critical events between vehicles and pedestrians when crossing the road. The study of this indicator is based on the fact that critical times and distance intervals are identified as a function of vehicle speed. As a consequence, it has been evaluated, experimentally, that many drivers do not adapt their speed to the limit imposed and do not consider pedestrians who are near a potential danger. Moreover, it has been observed that out of four drivers, only one stops or slows down to let the crossing of the pedestrian who is forced, in many cases, to perform this action very quickly. Post-Encroachment Time (PET) [39] is conventionally defined as the time between the first road user leaving the common spatial zone (in a two-road user encounter) and the second road user arriving at it. The Time To Collision (TTC) [40] is defined as the time to collision of two road users if they keep their directions and velocities. In the performance evaluation of the solution introduced in this paper, the minimum TTC during the pedestrian-vehicle conflicts is used as one of the surrogate safety measures.