# Research of Park and Ride Parking Spaces Tiered Pricing Methodology Based on Subway Ride Distance
## 3 Results and Discussion
### Prediction of Effectiveness  
Here, we assess the practical impact of implementing a tiered pricing scheme in P&R facilities by predicting two factors: the proportion (\(\delta\)) of subway commuters based on the distance traveled using P&R facilities and the average revenue (\(Wp\)) per parking session. This evaluation aims to validate the effectiveness of tiered pricing for P&R facilities. In the survey section, 244 respondents who have utilized P&R facilities were asked about the distance they traveled by subway during their last P&R trip. The distribution of subway travel distances for P&R trips is illustrated in Figure 5.  
All travelers are categorized into three groups: short-distance subway ride P&R travelers, medium-distance subway ride P&R travelers, and long-distance subway ride P&R travelers. Figure 5 reveals that short-, medium-, and long-distance subway commutes using P&R facilities constitute 19.7%, 56.5%, and 23.8% of all P&R travel, respectively. These data are utilized as the \(\theta g_{j}\) value under the fixed pricing strategy. Based on the marginal effect analysis in the previous section, we can ascertain the probabilities of respondents choosing P&R modes with varying parking fees. And from the statistics of the results of the fixed pricing scenario questions in the questionnaire, we can obtain the probability of the P&R trip choice for short-, medium-, and long-distance subway rides under the fixed pricing and tiered pricing modes, as shown in Table 6.  
Calculated by Equation (5), the proportions of the potential demand of P&R travelers for each distance of subway ride are depicted in Figure 6. It is evident that the largest potential user group is medium-distances subway ride P&R users, accounting for 57% of the overall total. The long-distance and short-distance subway ride P&R users exhibit a similar proportion, constituting approximately 21% and 22% of the total, respectively. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Near-Distance** & **Medium-Distance** & **Long-Distance** \\ \hline Fixed pricing & 25.8\% (\(P_{S1}\)) & 28.0\% (\(P_{S2}\)) & 33.6\% (\(P_{S3}\)) \\ Tered pricing & 12.0\% (\(P_{S1}\)) & 30.4\% (\(P_{S2}\)) & 41.3\% (\(P_{S3}\)) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Probability of P&R mode choice for travelers according to subway ride distance. Figure 5: Distribution of P&R travel subway ride distance statistics. Figure 6: Percentage of potential demand for subway ride distance. Calculated by Equation (6), the proportions of different distance subway ride P&R users under the tiered pricing strategy are displayed in Figure 7. It is notable that following the implementation of tiered pricing, the proportion of short-distance subway ride P&R users is the lowest, accounting for less than 10% of the total. In Figure 8, a comparison between the proportions of P&R travelers based on the subway ride distance traveled under fixed and tiered pricing strategies is presented. It is evident that following the implementation of tiered pricing, there is a decrease of over 10% in the proportion of short-distance subway ride P&R users. Simultaneously, there is an increase in the proportions of medium- and long-distance subway ride P&R users. This indicates that the implementation of tiered pricing effectively frees up over ten percent of P&R parking spaces for use by medium- and long-distance subway ride P&R users. In analyzing the composition of P&R facility users on the basis of exploring the P&R facility revenue under the tiered pricing strategy, Equation (7) can be used to predict the  
Figure 8: Comparison chart of the percentage of users of fixed pricing and tiered pricing strategies. Figure 7: Percentage of subway ride distance users across the tiered pricing strategy. parking revenue.