## 4 Simulation and Calibration
### Data Processing and Analysis  
Microscopic simulation models contain may parameters that describe traffic flow characteristics. The proposed model of this paper was calibrated by regional average traffic flow speed, volume, and occupancy. Travel time detectors were set in the entrance and exit of each arterial to collect average travel time of traffic flow passing through the arterial. The arterial average speed is obtained by the distance of travel time detectors dividing the average travel times of each arterial. The regional average speed is defined as the mean value of arterial average speed in the network. Traffic flow detectors were set in the middle of road segment between two intersections to collect traffic volume and occupancy. The regional average flow and regional average occupancy are defined as the mean value of traffic volume and occupancy collected by traffic flow detectors in the network respectively. Different time interval of traffic data will show out different accuracy and performance in regional traffic flow managing and controlling. In this paper, traffic data was collected at 5 s intervals, 10 s interval and 15 s interval with and without sudden fire disasters in the simulation network respectively as to identify the catastrophe border of traffic flow. Because of VISSIM's stochastic nature, multiple runs must be conducted for each parameter set to reduce the stochastic variability. The required number of runs was determined by running the model 10 times initially, then calculating the minimum sample size on the basis of the traffic data output mean values and standard deviation, assuming a Student \(t-\)distribution [32]. After 10 iterations were completed, 230 groups of regional traffic flow parameters in each scenario and each collecting interval were calculated and extracted as sample datasets for further analysis. The datasets used for further analysis are shown in Figures 4-6. Figure 4: Dataset of regional average flow in different collecting time intervals with and without sudden fire disasters. The process of catastrophe border identification for urban high-density area under sudden fire disasters based on simulation datasets can describe as following step. Step 1: Data normalization processing. To highlight the characteristics of traffic flow data and identify the sudden jump of catastrophe border more easily, the sample datasets are performed normalization processing. The normalization processing method is as follows:  
\[\text{X}=\text{speed-speed at capacity} \tag{13}\]  
\[\text{Y}=(\text{flow-capacity})/100 \tag{14}\]  
\[\text{Z}=\text{occupancy-maximum occupancy at maximum flow} \tag{15}\]  
The capacity in the formula is the statistical capacity, and the maximum flow is collected in each interval based on the extracted data from simulation model by muti-running the simulator. The critical value extracted from simulation in different time intervals is shown as Table 3.  
Figure 5: Dataset of regional average occupancy in different collecting time intervals with and without sudden fire disasters. Figure 6: Dataset of regional average speed in different collecting time intervals with and without sudden fire disasters. Step 2: Data displayed in three-dimensional panel. After normalization processing, the traffic flow parameters in different traffic conditions can be converted into the corresponding variables in the cusp model of catastrophe theory, respectively. Then, three datasets of traffic flow data after normalization processing are displayed in a three-dimensional panel to indicate the transition from stable state to instable state of traffic flow, as shown in Figures 7-9. In Figures 7-9, the red pentagon in the figures represents the traffic flow data without a sudden fire disaster situation, and the black circle represents the traffic flow data with sudden fire disasters.