Risk-Based Railroad Fare and Road Toll Under Bounded Rational Bi-Modal Equilibrium

This paper considers modal split in daily travel when there is a railroad parallel to a bottleneck-constrained road between home and a workplace. We examine the optimality and efficiency of different railroad fare and road toll (RFRT) schemes with the boundedly rational mode choice behavior of travelers. Under such behavior, commuters do not necessarily choose the mode of which the travel cost is absolutely lower than the mode of the other. A general definition of boundedly rational bi-modal equilibrium (BRBE) is presented. As the BRBE solution is not unique, the best-, worst- and average-case total travel costs under BRBE for a given RFRT scheme are proposed. The performance of each RFRT policy under different traveler levels of BR in mode choice behavior is also examined. The numerical results illustrate that system travel costs may be uncertain within the BRBE set, and the proposed RFRT schemes are able to address uncertainty due to the non-unique BRBE solution.