## 4 Simulation and Calibration
### Data Processing and Analysis
So the model ability at different data collection interval based on cusp catastrophe theory can be seen in Table 6.  
In Table 2, the relative accuracy of catastrophe border identification at 5 s interval and 10 s interval are 89.1% and 92.7% compare to the method of capacity assessment approach (CAA) respectively, which shows that the study in this article based on cusp catastrophe theory can describe the traffic flow characteristics effectively at fine granularity data collection interval. However, the catastrophe border identification error at 15 s interval is larger, which is more than 20%. The cause of the larger error may be traffic flow parameters in coarse granularity cannot catch the traffic flow changing accurately in the simulation, and traffic flow mutation happening under sudden fire disasters always at smaller data collection interval. In the area of risk management, it gradually reaches a basic consensus that emergency traffic flow management and control can effectively reduce emergency response time and improve security in disaster relief and mitigation. Traffic flow catastrophe border identification can help engineers, planners, and emergency managers identify the approximate time or position it would take for traffic flow to manage or control in disaster-affected area. In addition, advanced traffic signal control systems can have tremendous impact on the movement of traffic flow in urban high-density areas under sudden disasters, facilitates emergency evacuation and response in disaster relief and mitigation [51; 52]. However, most of these studies have not considered the systematic integration of traffic data collection intervals when optimizing control target and signal timing [52]. The present simulation-based study tries to provide a technical understanding regarding which the data collection interval provides better results in identifying the catastrophe border. This traffic data collection interval is also suitable for integrating into advanced traffic control system in optimizing control targets and signal timing for disaster relief and mitigation, to match the changing of traffic flow in the network. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Data Collection** & \begin{tabular}{c} **Catastrophe Border** \\ **based on CCT** \\ **(pcu/lane/h)** \\ \end{tabular} & \
\begin{tabular}{c} **Catastrophe Border** \\ **based on CAA** \\ **(pcu/lane/h)** \\ \end{tabular} &
\begin{tabular}{c} **Relative** \\ **Precision** \\ **(\%)** \\ \end{tabular} \\ \hline
5 s & 439 & & 89.1 \\
10 s & 529 & 493 & 92.7 \\
15 s & 377 & & 76.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Model at different data collection intervals based on cusp catastrophe theory. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Data Collection Interval (s)** & \
\begin{tabular}{c} **Catastrophe Border** \\ **Regional Average Occupancy \(o\) (\%)** \\ \end{tabular} &
\begin{tabular}{c} **Regional Average Flow \(q\) (pcu/lane/h)** \\ \end{tabular} \\ \hline
5 & 20 & 439 \\
10 & 20 & 529 \\
15 & 20 & 377 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Catastrophe border identification at different time intervals. This paper provides the approach to identify the catastrophe border of traffic flow in urban high-density area under sudden fire disasters. However, the method and model of the present study still have many limitations. The first limitation is that model building in the simulation did not consider the traffic signal control in the intersection. Different types of signal control have different abilities to alleviate traffic congestion and disorder in high-density area under sudden disasters. The present study cannot explore catastrophe border under different types of signal timing or control model, such as fixed-time, actuated control, adaptive control and isolated signal control, arterial coordination control, or regional coordination control. The second limitation is that the present study only considers vehicle traffic flow in the network.