This paper studies the modeling of multimodal choice in a railway/highway system with
continuum park-and-ride services along a linear traffic corridor. Heterogeneous commuters
choose travel mode among auto, railway and park-and-ride. Both the traffic congestion on
highway and crowding effects on rail transit are considered. The highway capacity is
assumed to be stochastic to take into account the travel time reliability on highway.
Commuters are assumed to be distributed continuously along the corridor. A linear
complementarity system is proposed to model the modal choice for heterogeneous
commuters along the corridor and solve the spatial equilibrium pattern. The formulated linear
complementarity system is transformed into a mixed integer linear program to be solved. The
modeling approach and solution algorithm are implemented in a small numerical example.
The resultant solutions show that direct rail mode is chosen by commuters living close to the
CBD and park-and-ride is chosen by those far away from the city center, while in the middle
auto mode is preferred. Furthermore, when the stochastic link capacity is considered, more
commuters choose to use park-and-ride mode for higher reliability.