A Park and Ride (P & R) system is a set of facilities located throughout an urban area that can serve as transfer points for travelers that would like to utilize their private vehicles for one part of their journey and a more sustainable transport mode, such as public transport, for another part of the same journey. The catchment area of the facilities is identified as a fundamental element for planning a P & R system. It can be assumed to be accurately represented by several geometric shapes, such as a circle or a parabola. In that regard, a method denominated as the parabola method can be used to visualize those geometric shapes on digital maps of an urban environment. It can be implemented as a software program that integrates the variables that represent the elements of the P & R system as well as the set of equations that are used in a geographic information system (GIS) software. A significant aspect of how the parabola method is applied is its orientation as a shape, which is traditionally configured in respect to the area of major business activity or central business districts (CBDs). In fact, the research presented in this article aims to provide a new approach to the parabola’s orientation to study the P & R system’s catchment area by proposing the parabola’s orientation according to the primary access that potential users used to reach the facility. A case study that portrays the application of our method is given that is focused on the medium-sized city of Cuenca, Ecuador, where we determine which approach to the parabola’s orientation is the most suitable. In conclusion, the second approach proposed in this research reflects in a more realistic form the operation of the catchment area of the P & R system, considering a better distribution of the coverage area of the P & R system in the urban environment.
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