Modal equilibrium of a tradable credit scheme with a trip-based MFD and logit-based decision-making

The literature about tradable credit schemes (TCS) as a demand management system alleviating congestion flourished in the past decade. Most proposed formulations are based on static models and thus do not account for the congestion dynamics. This paper considers elastic demand and implements a TCS to foster modal shift by restricting the number of cars allowed in the network over the day. A trip-based Macroscopic Fundamental Diagram (MFD) model represents the traffic dynamics at the whole urban scale. We assume the users have different OD pairs and choose between driving their car or riding the transit following a logit model. We aim to compute the modal shares and credit price at equilibrium under TCS. The travel times are linearized with respect to the modal shares to improve the convergence. We then present a method to find the credit charge minimizing the total travel time alone or combined with the carbon emission. The proposed methodology is illustrated with a typical demand profile from 7:00 to 10:00 for Lyon Metropolis. We show that traffic dynamics and trip heterogeneity matter when deriving the modal equilibrium under a TCS. A method is described to compute the linearization of the travel times and compared against a classical descend method (MSA). The proposed linearization is a promising tool to circumvent the complexity of the implicit formulation of the trip-based MFD. Under an optimized TCS, the total travel time decreases by 17% and the carbon emission by 45% by increasing the PT share by 24 points.