# Smart Pedestrian Crossing Management at Traffic Light Junctions through a Fuzzy-Based Approach
## 4 Performance Evaluation  
### Simulation Model  
The traffic light junction has been implemented through the use of Vissim micro-simulation software [34], which is based on the car model defined by [PERSON] [35]. In the first phase, the geometric road diagram has been implemented by inserting strings and nodes that are part of a transport graph. In general, the nodes of a road network are identified by the intersection of the roads constituting the system to be analyzed. The analysis of supply/demand has further been implemented by considering the Origin/Destination (O/D) attributes with particular reference to the percentages of maneuvers made from one node to another. The graph nodes match at the origin or destination of the displacement. Of them, the source/destination centroids corresponding to the beginning/end maneuver for each intersection arm have been highlighted. In the case of pedestrian flow, they correspond to the beginning/end of crossing for each arm of the urban road intersection. The arcs of the graph are characterized by a principal direction, corresponding to Direction 1-3, and a secondary one, corresponding to Lines 2-4, as noted above. Any network can be described as a matrix with rows as the set of origins and the columns as the set of destinations. The number of rows and columns would match the number of nodes in the network. Conventionally, the horizontal rows of a matrix are recognized as a set of origin nodes, and the vertical columns of the matrix are specified as a set of destination nodes. Every cell entry in the matrix can be utilized to register data on the connection between a pair of nodes. Every single node is well connected to other nodes in a network and, as a consequence, can be accessed. However, this evaluation is not reasonable in a more complex network involving a more significant number of nodes and also alternative routes. More in detail, given a graph-oriented \(G(N,A)\), with \(|N|=n\) and \(|A|=m\), \(G\) is a matrix \(M\) of size \(n\times m\) composed of \((0,1,-1)\) as follows. Each row is associated with a node of \(N\), while each column is associated with an arc of \(A\). Specifically, the \(M\) column associated with the arc \(uv\in A\) will have exactly a value of \(-1\) at the line associated with the node \(u\), while it will have \(+1\) at the line associated with node \(v\), and 0 in all other rows. \(M\) is called incidence matrix (arcs-nodes) of \(G\). The incidence matrix associated with the analyzed nodes/arcs, referring to possible maneuvers, is shown in Table 5. The cells of the matrix have a value of one if the node is a departure in the arc; on the contrary, it is \(-1\) if it is the destination, and zero if the node does not exist in the arc. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Rule** & **Time of the Day** & **Pedestrians Number** & **Traffic Light Phase** \\ \hline
1 & Critical & Low & Medium \\
2 & Critical & Medium & Medium \\
3 & Critical & High & High \\
4 & Not Critical & Low & Low \\
5 & Not Critical & Medium & Medium \\
6 & Not Critical & High & High \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Inference rules. The mathematical investigation of traffic-related phenomena is based on code theory. Traffic is then modeled as a stochastic process. For instance, a process defines the arrival times of vehicles entering a specific passage, and another defines the time taken to make a route. The qualitative classification of congestion is usually carried out on a six-letter scale (from A-F) referring to Levels Of Service (LOS), as defined in the Highway Capacity Manual [36]. These levels are used in transport engineering as a quick way to describe traffic levels on roads or crossroads. Since collisions between pedestrians and vehicles have a much higher potential for mortality than other types of accidents, in the last few years, a growing sensitivity in understanding and predicting the causes of these types of accidents is spreading.