# Vehicular Visible Light Communication for Intersection Management +
## 4 V2X Cooperative System Evaluation
### Queuing System: Dynamic Traffic Signal Phasing  
A highly congested traffic scenario will be strongly connected. To determine the delay, the number of vehicles queuing in each cell at the beginning and end of the green time is determined by V2V2I observation, as illustrated in Figure 10.  
The same four traffic flows were considered. One is coming from west (W) but with seven vehicles approaching the crossroad: five \(a_{i}\) vehicles with straight movement and three \(c_{i}\) vehicles with left turn only. In the second flow, three \(b_{i}\) vehicles from east (E) approach the intersection with left turn only. In the third flow, \(e\) vehicle, oncoming from south (S), has right-turn approach. Finally, in the fourth flow, \(f\) vehicle coming from north goes straight. Road request and response segments, offer a binary (turn left/straight or turn right) choice. According to the simulated scenario, each car represents a percentage of traffic flow. We have assumed that the intersection is approached by 540 cars per hour, of which 80 percent are coming from the east or west. Then, 50% of cars will turn left or right at the intersection and the other 50% will continue straight. There is only one episode per scenario and the cars cycle in the same order every time. In the PoC, we have assumed that \(a_{1}\), \(b_{1}\), and \(a_{2}\), make up the top three requests, followed by \(b_{2}\), \(a_{3}\), and \(c_{1}\) in the fourth, fifth and sixth places, respectively. In the seventh, eighth and ninth request places are \(b_{3}\), \(e\) and \(a_{3}\), respectively, followed in tenth place by \(c_{2}\). The penultimate request is \(a_{5}\), and the last one is \(f\). So, \(t_{a1}<t_{b1}<t_{a2}<t_{b2}<t_{a3}<t_{c1}<t_{b3}<t_{e}<t_{a4}<t_{c2}<t_{a5}<t_{f}\). The following parameters are therefore needed to model the queuing system: The initial arrival time (\(t_{0}\)) and velocity (v) in each the occupied section. The initial time is defined as the time when the vehicles leave the previous section (queue, request or message distances) and move along the next section, \(q_{i}\) (\(t\), \(t^{\prime}\)). The service time is calculated using vehicle speed and distance of the section. The number of service units or resources is determined by the capacity of the section, \(n(q_{i}\) (\(x\), \(y\), \(\delta\), \(t\))) and vehicle speed which depends on the number of request services, and on the direction of movement along the lane \(q_{i}\) (\(x\), \(y\), \(\delta\), \(t\)). To each driving Vehicle, \(x_{i}\), is assigned the unique time at which it must enter the intersection, \(t^{\prime\prime}[x_{i}]\). The phase flow of the PoC intersection is shown in Figure 11 according to the phasing diagram. In this diagram, the cycle length is composed of 5 of the 7 phases contemplated (see Figure 5a) and divided in 16 time sequences. The exclusive pedestrian phase contains the \"\(0\)\", \"\(1\)\" and \"\(16\)\" sequences. The cycle's top synchronism starts with sequence \"\(1\)\". The first, second, third, and fourth phases contain sequences between \"\(2\)\" and \"\(15\)\" and control traffic flow. The matrix of states allows the user to view, enter, or modify the division of an intersection into states, as shown in Figure 12.  
The matrix shows the durations of the states for a given cycle. It is important to note that each element in this matrix represents how the light is lit for each state of the traffic light (if it is selected, then the light is green). Columns represent the duration of the states in the different arms of the intersection, from cycle minimum [fluid traffic] to cycle maximum [dense traffic]. For a medium traffic scenario, three distinct cycles are considered based on the higher volume traffic in the request directions (N-S, W-E straight or left). The column on the right of the matrix is called the column of fixed times. A fixed time is filled in when a state has the same duration for all the cycles of the lighting plan. The durations of movable states can be entered for any state at a dynamic time.