A Marginal Utility Day-to-day Traffic Evolution Model

Most deterministic day-to-day traffic evolution models, either in continuous-time or discrete-time space, have been formulated based on a fundamental assumption on driver route choice rationality where a driver seeks to maximize her/his marginal benefit defined as the difference between the perceived route costs. The notion of rationality entails the exploration of the marginal decision rule from economic theory, which states that a rational individual evaluates his/her marginal utility, defined as the difference between the marginal benefit and the marginal cost, of each incremental decision. Seeking to analyze the marginal decision rule in the modeling of deterministic day-to-day traffic evolution, this paper proposes a modeling framework which introduces a term to capture the marginal cost to the driver induced by route switching. The introduced term describes the “shadow price” of shifting routes, which helps to explain the behavioral tendency of the driver perceiving the cost-sensitivity to link/route flows. After developing a formulation of the marginal utility day-to-day model, its theoretical properties are analyzed, including the relationship between the stable flow pattern and user equilibrium, the invariance property, and the law of diminishing marginal utility. Numerical examples are used to demonstrate the effectiveness of the proposed model and compare it to its counterpart without the marginal cost.