## 4 The Monte Carlo Simulation and Experimental Results
### The Procedure of Our Approach  
The Monte Carlo simulation is performed based on the parameter setup as shown in Table 1. Then, our dynamic adjusting model is verified three times of the uncertainty loading, length of vehicle, initial seconds, initial queued vehicles, and passing time. The column Loading represents whether the demand exceeds road capacity. For instance, the Loading of Scenario 1 is 80 which means demand is below the capacity, and vice versa. The column Length of Vehicle means that the overall length of the vehicle plus the distance between each vehicle and its unit would be meter. The seconds of traffic light green to red time can be represented by Initial Seconds. Usually, the initial seconds of the peak hour traffic would be longer than off peak one. The column Initial Queued Vehicles can be the number of vehicles in the intersection. We also provide the passing time that is the average time of vehicles passing through the intersection. In Table 2, columns 1 to 10 are given as the settings of this example and columns 11 to 16 are calculated by using Equations (1) to (8). Please note that a detailed description of each variable can be seen in Section 3.1.1. According to our simulation case, as shown in Figure 1, we have calculated the following results. The \(R_{t,i}\) shown in column 1 which represents the real length of three intersection roads in an interchange of Shen-Keng of the Formosa Freeway in Taiwan. The \(ALC_{t,i}\) shown in column 11 is obtained from (1). The \(RT_{t,i}\) shown in column 12 is obtained by using (2), which represents the ratio of the each length on intersection roads \(R_{i}\) to the average length of each vehicle. It denotes the maximum capacity of a specific intersection road to load its vehicles. The \(AR_{t,i}\) shown in column 13 is obtained from (3), which denotes the initial queued vehicles, the difference of the reaching vehicles and their reducing amount of vehicle on each intersection road. Additionally, the real time total accumulated vehicles, \(AR_{t,i}\), must less equal than the vehicles capacity of its intersection road \(RT_{t,i}\). The \(\Delta T_{t,i}\) shown in column 14 is obtained from (5), which denotes the dynamic adjusting time of green light on each intersection road by the difference of the fixed time of green light and the actual times of green light. Note that the negative value of \(\Delta T_{t,i}\) represents the protect times of the initial fixed time of  
Figure 1: The Google Map of the three intersection roads (red blocks) in an interchange of Shenkeng of the Formosa Freeway in Taiwan. green light which is not sufficient and must be increased into the next period adjusting time of the traffic light immediately. The \(S_{t+1,i}\) shown in column 15 is obtained from (6), which denotes the initial time of each traffic light minus its dynamic adjusting time of green light previous period. In addition, The \(SCW_{t,i}\) of the period \(t+1\) and \(t+2\) are obtained by inheritance from the \(AR_{t,i}\) of the period \(t\) and \(t\) + 1, respectively, as described in (7). The \(S_{t,i}\) of the period \(t+1\) and \(t+2\) are obtained by inheritance from the \(S_{t+1,i}\) of the period \(t\) and \(t+1\) as described in (8). The arrows upward and downward in \(\Delta T_{t+1,i}\), shown in column 16, which denote the comparison between \(S_{t,i}\) (column 5) and \(S_{t+1,i}\) (column 15). A detailed analysis related to the direction of arrows is shown in Table 2. Please note that the symbol \(\uparrow\) in column 16 of Table 2 represents the adjusting time greater than initial time, and vice versa. For instance, given that in simulation run 1 with \(i\)=1, the initial time \(S_{t,1}\) equals to 40 and \(S_{t+1,1}\) is 109. Then we can know \(\Delta T\) being \(\uparrow\). Also, we highlight the important information by red and black blocks in Table 2. The \(S_{t,i}\) in red block shows initial time and \(SCW_{t,i}\) means the initial queued vehicles.