# Research of Park and Ride Parking Spaces Tiered Pricing Methodology Based on Subway Ride Distance
## 3 Results and Discussion
### Marginal Effects Analysis  
A crucial consideration when designing P&R parking facilities with tiered pricing based on different subway ride distances is to assess the price elasticity of travelers regarding P&R parking charges. In this study, the cost of adopting the P&R mode encompasses three distinct components: P&R parking fees, expenses for subway tickets, and fuel costs. In constructing the mixed logit model, P&m has been included as an explanatory variable. The TP model's fitted outcomes for P&m demonstrate statistical significance at the 99.9% level, rendering the pursuit of further marginal effect analysis on P&m a valid endeavor. As a result, this section focuses on marginal effects of P&m, aiming to derive the P&R parking price through a reverse calculation grounded in P&m. Furthermore, we hypothesize a positive correlation between subway ride distance and total travel distance; a total travel distance of D = 4 km represents a short-distance subway ride; D = 10 km represents a medium-distance subway ride; D = 20 km represents a long-distance subway ride. Marginal effect computations for P&m are conducted individually for each of these three total travel distances. Figure 4a-c illustrate the shifting proportions of traveler preferences among P&R, private car, taxi, and PT modes for short-range D = 4 km, medium-range D = 10 km, and long-range D = 20 km trips as P&R mode varies. For a more visual comparative analysis of the changing proportions of selecting the P&R mode for various travel distances, we have integrated the choice proportion curves for the P&R mode across the three travel distances into a single graph, depicted in Figure 4d. For short-distance travel, the proportions of PT and taxi mode selections are comparable. When P&m falls between RMB 1 and 4.5, the proportion of those selecting the PT mode outweighs that of the taxi mode. Yet, as the P&m surpasses RMB 4.5, more travelers choose the taxi mode, making it the most favored option among the four travel modes. The choice proportion for the car mode remains consistently low and exhibits a low increase. This pattern is primarily attributed to the substantial parking fees charged in public parking facilities, rendering the car mode a considerably less economical choice for short-distance travel. The proportion of P&R mode selection shows a slow shift when the P&m is below RMB 0.7. At this range, approximately 60% of travelers favor the P&R mode. With the P&m surpassing RMB 0.7, the rate of decline in P&R mode selection accelerates, reaching its steepest slope at P&m = RMB 3. Following this point, as the P&m continues to increase, the decrease in P&R mode selection becomes more gradual, and beyond a P&m value of 6, the curve levels off. For short-distance travel, our objective is to minimize P&R mode selections. It is evident that when the P&m increases by RMB 1 at P&m = RMB 6, the proportion of P&R mode selection decreases by a mere 1.2%. Hence, setting the Pkm for P&R at RMB 6 is deemed suitable. According to the scenario outlined in this study, we can further compute that the optimal P&R mode short-distance subway ride parking fee would be approximately RMB 20. For medium-distance travel, the selection proportion curves for car and taxi demonstrate resemblances. This similarity can be attributed to their similar travel costs and preferences among travelers. Following a Pkm threshold of RMB 0.7, the choice proportions for both modes start increasing, and once the Pkm exceeds RMB 3, the curves plateau. Beyond a Pkm value of RMB 5, there are no further changes in the selection proportions. The proportion of choosing the P&R mode demonstrates a notable declining pattern right from the start, with the sharpest decline occurring at Pkm = RMB 1.5. After exceeding a Pkm value of RMB 5, the P&R mode's selection proportion levels off and ceases to decrease.