## 5 Conclusions  
This work for the first time uses HCPN to design a traffic control system for a four-phase intersection dealing with priority to provide public transit passing through the intersection. Two kinds of transit priority strategies, i.e., green extension and red truncation are formalized in this work. Their analysis is performed by the state space method. Their important properties such as boundness, liveness and reversibility are verified. This helps to enhance the state of the art in traffic real-time detection and traffic management of an intersection. Future work is to design a traffic control system that is complex and close to the actual application. For example, the impact of pedestrians on the transit priority should be considered. In addition, if there are multiple transit lines overlapping at the intersection, transits on different lanes may also make a priority request at the same time; hence, how to solve these complex scenes should be considered. Also, in this work, we use a four-phase signal control system with a deterministic phase transition structure. In the future, we will explore the effect of a non-deterministic phase transition structure on TSP control strategies.  
**Acknowledgments: This paper has been supported by the National Natural Science Foundation of China under Grant No. (51278058, 61703053), the Natural Science Foundation of Shaanxi Province under Grant No. 2014Z019, China Postdoctoral Science Foundation under Grant No. 2012M521729, and the Fundamental Research Funds for the Central Universities under Grant No. 310824162021.**  
**Author Contributions: This work was conducted by [PERSON] and [PERSON] with the help of graduate student [PERSON] and [PERSON]. It was mainly drafted by [PERSON] and [PERSON], and checked and revised by  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{\
\begin{tabular}{c} **Traffic** \\ **Flows** \\ **(vph)** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Transit** \\ **Ratio** \\ **(\%)** \\ \end{tabular} } & \multicolumn{3}{c}{**Number of Transit Stop**} & \multicolumn{3}{c}{**Transit Delay (M)**} & \multicolumn{3}{c}{**Total Delay of Social Vehicle (H)**} \\ \cline{3-10}  & & & & **(Times)** & & & & & **Vehicle (H)** \\ \hline \multirow{4}{*}{900} & 1 & 1 & 1 & 1 & 0.36 & 0.36 & 0.36 & 2.87 & 3.301 & 2.871 \\  & 5 & 2 & 2 & 2 & 0.63 & 0.57 & 0.6 & 2.859 & 3.315 & 2.859 \\  & 10 & 5 & 4 & 3 & 2.42 & 2.23 & 1.5 & 2.877 & 3.279 & 2.579 \\  & 15 & 9 & 7 & 4 & 2.46 & 2.38 & 1.48 & 2.796 & 3.221 & 2.697 \\ \hline \multirow{4}{*}{1200} & 1 & 2 & 1 & 1 & 0.72 & 0.63 & 0.7 & 4.132 & 4.743 & 4.137 \\  & 5 & 3 & 3 & 3 & 0.66 & 0.62 & 0.64 & 4.062 & 4.858 & 4.046 \\  & 10 & 7 & 5 & 4 & 3.12 & 2.81 & 1.85 & 4.071 & 4.865 & 4.012 \\  & 15 & 11 & 8 & 8 & 4.52 & 3.91 & 2.9 & 4.113 & 4.944 & 4.317 \\ \hline \multirow{4}{*}{1500} & 1 & 2 & 2 & 2 & 1.08 & 1.08 & 1.06 & 6.186 & 7.612 & 6.495 \\  & 5 & 5 & 4 & 4 & 4.26 & 3.83 & 3.72 & 6.096 & 7.501 & 6.584 \\ \cline{1-1}  & 10 & 10 & 8 & 9 & 8.52 & 7.82 & 7.96 & 6.25 & 7.675 & 6.825 \\ \cline{1-1}  & 15 & 21 & 15 & 19 & 12.42 & 11.47 & 12.1 & 6.419 & 7.893 & 6.908 \\ \hline \hline \end{tabular} FX: fixed time method; CTSP: conventional TSP algorithm; PNTSP: the proposed HCPN-based TSP control model.  
\end{table}
Table 5: Statistics of simulations in VISSIM.  
[PERSON] and [PERSON]. [PERSON] and [PERSON] designed and analyzed the proposed model. [PERSON] performed the simulation. [PERSON] were responsible for the English polish and proofreading of this work.  
**Conflicts of Interest:** The authors declare no conflict of interest.