## 4 Simulation and Analysis of HCPN Based TSP Model
### Case Study  
This section briefly discusses the application of the HCPN-based TSP control model based on several simulation-based experiments. These data can be used to analyze the capability of providing a method for improving the efficiency of the transit vehicle at intersection. A single intersection (Figure 1) project is generated in VISSIM [36], a commonly used microscopic traffic simulation software. Three kinds of signal control algorithm are implemented in the experiment, such as the fixed time method (FX), conventional TSP algorithm (CTSP) in [6; 10], and the proposed HCPN-based TSP control model (PNTSP). The length of each road connecting the intersection is set to 500 m. The traffic flows on each road are basically the same, with values of 900, 1200 and 1500 vehicle per hour (vph), respectively. The cycle length at the intersection is 122 s. What needs to be specially explained is that the indexes  
\begin{table}
\begin{tabular}{c c} \hline
**Different** & **Possible State Sequences (Node#)** & **Uniqueness** \\
**Scenario** & & \\ \hline
1 & 1, 2, 5, 9, 13,... 98, 104, 110, 116, 122, 128, 134, 140, 146,... 194,... 388,... 580,... 872, 1 & YES \\ \hline
2 & 1, 2, 5, 9, 13,... 98, 104, 110,... 132,... 725, 735,... 823,... 868, 877, 885,... 859, 868 & NO \\ \hline
3 & 1, 2, 5, 9, 13,... 98, 104, 110,... 132,... 725, 735,... 848,... 868, 877, 885,... 859, 868 & NO \\ \hline
4 & 1, 2, 5, 9, 13,... 98, 104, 110, 116, 122, 128, 134, 140, 146,... 725, 735,... & NO \\ \hline
5 & 1, 2, 6, 12, 16, 20, 25, 31,... 217,... 409,... 602,... 868, 877, 885,... 859, 868 & NO \\ \hline \end{tabular}
\end{table}
Table 4: Possible state sequences of TSP control system.  
such as the number of transit stops and transit delays are only counted from the road from eastbound to westbound while the total delay of social vehicles is based on statistics on four connecting roads.  
Simulation-based results are shown in Table 5. The data in column FX serves as a baseline for comparison. Obviously, no matter what kind of traffic flow conditions and what kind of transit ratio are configured, CTSP and PNTP methods can achieve a better performance than the FX method for  
Figure 4: Partial state spaces of the transit signal priority control HCPN model.  
both the number of transit stops and the transit delay time, although the rate of improvement will decrease as traffic flow increases. In addition, according to the indictor of the total delay of social vehicle, the PNTSP method shows better performance over the CTSP method. That is to say, it keeps the FX method's performance, while the total delay of social vehicles derived from the CTSP method increased by about 20%. The reason for this is that the traditional method mainly predicts traffic flow based on historical data, and then greatly adjusts the phase and duration of signal control, leading to additional delay for vehicles on other connecting roads. The proposed method, by its very nature, is a reactive fixed timing approach. Therefore, when using this method, the transit vehicles have the least impact on social vehicles. At the same time, it also extends the service time for the transit vehicles in a specific green light period and assigns the service time for transit vehicles in a particular red light period. Based on the simulation results, it can be concluded that the proposed HCPN-based TSP control model provides transit vehicles with more accuracy and better effectiveness at the intersection.