Integrated traffic-transit stochastic equilibrium model with park-and-ride facilities

• An integrated traffic-transit stochastic equilibrium model is proposed.
• Travelers are allowed to change from car to transit at park-and-ride facilities.
• The integrated model considers traffic and passenger congestion.
• An MSA algorithm is proposed to calculate the Integrated Stochastic Equilibrium.
• The model is tested with data from a real city.

We propose an Integrated Stochastic Equilibrium model that considers both private automobile traffic and transit networks to incorporate the interactions between these two modes in terms of travel time and generalized costs. In addition, in the general version of the model, travelers are allowed to switch from personal vehicles to mass transit at specific locations in a park-and-ride scheme. The assignment for traffic equilibrium is based on the Markovian Traffic Equilibrium model of Baillon and Cominetti (2008), whereas the equilibrium of the transit network is represented by the Stochastic Transit Equilibrium model of Cortés et al. (2013). Stochastic travel decisions are made at the node level, thereby avoiding the enumeration of routes or strategies and incorporating various perception and uncertainty issues. We propose a Method-of-Successive-Averages algorithm to calculate an Integrated Stochastic Equilibrium and conduct numerical experiments to highlight the effect of stochasticity on equilibrium flows and travel times. Our experiments show that higher stochasticity implies greater dispersion of equilibrium flows and longer expected travel times. Results on a real network with mode combination and park and ride facilities provide insights regarding the use of park and ride in terms of number and location, potential modal share of the combined mode option under different circumstances, and travel time impact due to the implementation of such park and ride facilities in a real setting.