## 6 Instance Validation
### User Choice Behavior Fitting
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Travel Mode** & **Variant** & **Coefficient** & \begin{tabular}{c} **Standard** \\ **Deviation** \\ \end{tabular} & \(p\)**-Value Test** \\ \hline \multirow{3}{*}{\begin{tabular}{c} Parking \\ Reservation \\ \end{tabular} } & dependability & 0.036 & 0.347 & 0.042 \\  & convenience & 1.275 & 0.451 & 0.050 \\  & travel time & \(-\)2.336 & 0.680 & 0.010 \\ \hline \multirow{3}{*}{\
\begin{tabular}{c} Conventional \\ Parking \\ \end{tabular} } & dependability & 0.495 & 0.481 & 0.030 \\  & convenience & 1.453 & 0.575 & 0.009 \\  & travel time & \(-\)2.287 & 0.615 & 0 \\ \hline \multirow{3}{*}{
\begin{tabular}{c} Other Travel \\ Modes \\ \end{tabular} } & dependability & 1.807 & 0.935 & 0.033 \\  & convenience & 1.957 & 0.863 & 0.023 \\ \cline{1-1}  & travel time & \(-\)0.883 & 0.772 & 0.025 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Travel mode attribute parameters. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Selection** & \begin{tabular}{c} **Reservation** \\ **Time** \\ \end{tabular} & **Cost** & **Preferences** & **Constant Term** \\ \hline \multirow{3}{*}{\
\begin{tabular}{c} Conventional \\ Parking \\ \end{tabular} } & - & \(-\)0.428 & 2.220 & \(-\)3.447 \\ \hline \multirow{3}{*}{
\begin{tabular}{c} Other Travel \\ Modes \\ \end{tabular} } & - & \(-\)0.278 & 2.639 & \(-\)15.06 \\ \cline{1-1} \cline{2-5}  & 17:00–18:00 & \(-\)0.637 & 1.910 & 0 \\  & 18:00–19:00 & \(-\)0.626 & 2.057 & \(-\)1.006 \\  & 19:00–20:00 & \(-\)0.541 & 1.920 & \(-\)1.809 \\  & 20:00–21:00 & \(-\)0.719 & 2.210 & 0.090 \\  & 21:00–22:00 & \(-\)0.341 & 1.914 & \(-\)5.730 \\  & 17:00–19:00 & \(-\)0.422 & 2.340 & 0.127 \\  & 18:00–20:00 & \(-\)0.392 & 2.357 & \(-\)0.521 \\  & 19:00–21:00 & \(-\)0.444 & 2.118 & 0.130 \\  & 20:00–22:00 & \(-\)0.240 & 2.052 & \(-\)4.016 \\  & 17:00–20:00 & \(-\)0.383 & 1.059 & 1.902 \\  & 18:00–21:00 & \(-\)0.264 & 1.509 & \(-\)1.373 \\  & 19:00–22:00 & \(-\)0.330 & 1.765 & \(-\)0.289 \\  & 17:00–21:00 & \(-\)0.425 & 1.459 & 3.869 \\  & 18:00–22:00 & \(-\)0.425 & 2.147 & 0.970 \\  & 17:00–22:00 & \(-\)0.667 & 20.754 & \(-\)26.157 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Attribute parameters of each selected branch. Parking reservations  
The calibrated utility model for a user choosing to travel by reserved parking is:  
\[ \begin{split} V_{i(a)}=0.149(\text{age})&+0.121(\text{ income})+0.021(\text{purpose})+0.085(\text{distance})\\ &+0.036(\text{dependability})+1.275(\text{convenience})\\ &-2.336(\text{travel time})\end{split}  \tag{26}\]  
Similarly, the probability of a user choosing a specific appointment time slot can be calculated. The utility of the appointment time layer selection branch is taken as an example for the 18:00-19:00 time slot:  
\[V_{l}=-0.626(\text{cost})+2.057(\text{preferences})-1.006 \tag{27}\]  
Based on the pooled attributes of the user group for this mode of travel, estimated for age, income, trip purpose, and distance, the pooled utility function for users who choose to reserve a parking lot for parking is as follows:  
\[ \begin{split} V_{1}=-1.826&+0.593\ln(\exp(2.057-0.6 37w_{1})+\exp(1.736-0.626w_{2})\\ &+\exp(0.495-0.541w_{3})+\exp(3.036-0.719w_{4})\\ &+\exp(-3.179-0.341w_{5})+\exp(3.328-0.422w_{12})\\ &+\exp(2.694-0.392w_{23})+\exp(2.778-0.444w_{34})\\ &+\exp(-1.671-0.24w_{45})+\exp(2.961-0.383w_{123})\\ &+\exp(0.702-0.264w_{234})+\exp(2.359-0.33w_{345})\\ &+\exp(6.301-0.425w_{1234})+\exp(4.835-0.425w_{2345})\\ &+\exp(15.351-0.667w_{12345}))\end{split}  \tag{28}\]  
Traditional parking in the neighborhood  
The probabilistic utility of a user choosing to park in the traditional way in a neighboring parking lot is calculated. The calibrated user utility model is:  
\[ \begin{split} V_{2}=0.149(\text{age})&+0.121(\text{ income})+0.021(\text{purpose})+0.085(\text{distance})\\ &+0.495(\text{dependability})+1.453(\text{convenience})\\ &-2.287(\text{travel time})+2.22(\text{preferences})-0.428( \text{fee})\\ &-3.447\end{split}