The modeling of multimodal choice in a railway-highway system with single park-and-ride service on a linear travel corridor is studied. Commuters choose either auto or railway to travel directly from home to city center or drive to the park-and-ride facility and transfer to railway transit service. Both the traffic congestion on the highway and the crowding on rail transit are considered. The highway capacity is assumed to be stochastic to take into account travel time reliability for use of the auto mode. Commuters are assumed to be distributed uniformly along the corridor. A linear complementarity system to model commuters' mode choice along the corridor and to solve the spatial equilibrium travel pattern is proposed. 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.
Wang, D. Z. W. & Du, B. (2013). Reliability-Based Modeling of Park-and-Ride Service on Linear Travel Corridor. Transportation Research Record, 2333 16-26.