A topology-based bounded rationality day-to-day traffic assignment model

Abstract

This paper analyzes the day-to-day adjustment process of users’ behaviors in a transport network which is affected by relevant alterations such as disruptions due to critical events which cause the impossibility to use one or more links. For representing the progressive adjustment of the flows on the network to reach a new equilibrium, a day-to-day discrete-time model is proposed, based on the idea that people are bounded rational in their choices, i.e. they often do not behave according to the optimal solution but they accept solutions they consider satisfying. Users, in their choice process, are influenced by the topological similarity between the route they are currently using and others. This means that they tend to prefer the solutions that are more similar to the one they are already using. In parallel, users exhibit a myopic behavior, i.e., they tend to overestimate the goodness of a route if, when using it, they suddenly experience a significant reduction in travel time compared to what they are used to. In the paper it is shown that such route choice behaviour implies that the steady state of the system corresponds to a Bounded Rational User Equilibrium, i.e., a state that does not diverge from the user equilibrium more than a certain value which increases when the relative importance given to the topological similarity grows. The model also assumes that these biases vanish, at least with respect to those routes that are most frequently used by users, after a sufficient amount of time. Under certain conditions, it is then shown that the steady state can eventually collapse into a User Equilibrium. The effectiveness of the proposed model is assessed via simulation results in which two test networks are analyzed in detail to show the evolution of the users’ behaviour in a transport network after a disruption.