## 3 Analysis  
### Model Calibration  
To calibrate the simulation model, four types of distributions were investigated. The first distribution is the average speed. In this case, vehicles have a fixed speed of 48 km/h. This speed was decided based on the actual average speed obtained from the field data. The second distribution is the incremental speed: in this case, speeds started at 30 km/h then increased by 1 km until reaching 72 km/h. These are the limits collected from the actual data. The third distribution is uniform speed distribution. In this case, speeds vary based on a rectangular distribution. The values between the maximum and minimum vehicle speeds have the same probability. The fourth distribution is the normal distribution. In this case, vehicle speeds are set according to a truncated normal distribution. The truncation sets the minimum and maximum speeds to match the actual data. The truncation isused as a safegu against unreasonable values. The average and variance of the distribution are 48 and 8.8 km/h, respectively.  
Table 2 provides a comparison between the actual data and simulation results. It is worth noting that the results of each category (average, incremental, uniform, and normal) are the average of three simulation runs. It was found that the mean gap distance for all runs is less than that of the actual data. This result suggested that the model is underestimating the gap. Furthermore, the standard deviation of the simulation runs is larger than that of the actual data suggesting the simulation run data is more spread out than the actual data. This outcome suggests that the fit between the simulation data and actual data is not accurate. The data range, however, is similar to the actual data for most simulation runs.  
To determine which simulation runs closely fit the actual data, the gap data obtained from the simulation runs were ranked from highest to lowest and plotted against the actual data. Figure 3 illustrates that most of the runs underestimate the actual data. That is, the gap determined by the simulation is much narrower than that determined by pedestrians in reality. Visual inspection suggests that the normal distribution is the closest fit. The figure also illustrates the average error across all points, absolute error (modulus of average errors), and the confidence interval of the average error.  
To enhance the fit, the speed in the normal distribution runs was multiplied by a positive factor. This factor accounts for the underestimation of the simulation. Figure 4 illustrates the results of introducing different factors of 1.25, 1.5, and 1.75. In reality, the factored runs simulate a pedestrian who is overestimating the vehicle speed as it approaches. The figure also illustrates the error of the factored simulations. As shown in the figure, from the absolute error, the normal distribution runs with a factor of 1.5 gave the best results, followed by a factor of 1.25. The results indicate that pedestrians include a risk factor ranging from 1.25 to 1.5 to the speed of the vehicle speeds before deciding to cross or not.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & \multicolumn{4}{c}{**Simulation**} \\ \cline{3-6}  & & **Actual** & **Average** & **Incremental** & **Uniform Speed** & **Normal Speed** \\  & & & **Speed** & **Speed** & **Distribution** & **Distribution** \\  & & & **(kph)** & **(kph)** & **(kph)** & **(kph)** \\ \hline \multirow{3}{*}{
\begin{tabular}{c} Gap \\ Distance (m) \\ \end{tabular} } & Mean & 70.9 & 60.0 & 63.4 & 66.0 & 66.4 \\  & Std. Deviation & 17.2 & 23.5 & 23.5 & 24.4 & 24.2 \\ \cline{1-1}  & Minimum & 30.5 & 30.1 & 28.4 & 23.4 & 26.5 \\ \cline{1-1}  & Maximum & 119.6 & 118.7 & 118.6 & 118.5 & 118.6 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Descriptive statistics for the gap distance acquired from actual data and simulation results.  
Figure 3: _Cont._