Multi-class time reliability-based congestion pricing model based on a degradable transportation network

• We propose a traffic assignment model according to day-to-day capacity degradations.
• Robust effective path travel time is employed to capture travelers’ path choice behaviors.
• Contractive safety margin is adopted to approximate the actual margin along the path.
• A time reliability-based congestion pricing model is formulated.
• The pricing model reflects the robustness of travelers’ economic benefit.

In this study, we present a multi-class time reliability-based user equilibrium model with elastic demand, which is based on a degradable transportation network. Due to the uncertainties in the path travel time induced by random capacity degradation, the model captures the path choice behaviors of travelers in the form of the robust effective path travel time and there is no need for a known travel time probability distribution. By including the heterogeneous degrees of risk aversion among travelers, the equilibrium model can be transformed into an equivalent variational inequality (VI) problem. We also propose a heuristic solution algorithm to solve the VI problem. By taking the VI model as a constraint, a multi-class time reliability-based congestion pricing model is formulated as a mathematical programming with equilibrium constraints problem, which can be solved using the sensitivity analysis-based conjugate sub-gradient projection method. Two numerical examples are provided to illustrate the applications of the proposed models and to demonstrate the efficiency of the solution algorithms.