Optimal Parking Pricing in Many-to-One Park-and-Ride Network with Parking Space Constraints

This paper investigates an optimal parking pricing problem in a many-to-one (multiple origins to one destination) park-and-ride (P + R) network, taking into account practical parking space constraints. The proposed problem aims to minimize the total travel cost by setting optimal parking fees at P + R terminals. The problem is formulated as a bilevel programming model that comprises an upper-level problem of determining optimal parking fees and a lower-level problem of characterizing commuters’ travel equilibrium of departure time and path choices. For the lower-level problem, a user equilibrium model is developed to address the commuting patterns with and without parking space constraints in the many-to-one P + R network. In the commute equilibrium analysis, extra earlier departure times, defined by slack variables, are introduced to examine the conditions in which commuters need to compete for limited parking spots. Meanwhile, the parking spot ending time is used to describe how commuters from different origins compete with one another for the limited parking spots at the destination. Finally, numerical experiments show that the methods proposed in this study are effective in managing the P + R facilities.