Day-to-day traffic dynamics considering social interaction: From individual route choice behavior to a network flow model

- Travelers' day-to-day route choice behavior with social interaction is modeled.
- The evolution of network flow is deduced based on the route choice model.
- Network flow equilibrium under the effect of social interaction is proved.
- Some individual-level factors exert no influence on the evolution of network flow.
- Individuals' behaviors are not necessarily invariable under network flow equilibrium.

Social interaction is increasingly recognized as an important factor that influences travelers' behaviors. It remains challenging to incorporate its effect into travel choice behaviors, although there has been some research into this area. Considering random interaction among travelers, we model travelers' day-to-day route choice under the uncertain traffic condition. We further explore the evolution of network flow based on the individual-level route choice model, though that travelers are heterogeneous in decision-making under the random-interaction scheme. We analyze and prove the existence of equilibrium and the stability of equilibrium. We also analyzed and described the specific properties of the network flow evolution and travelers' behaviors. Two interesting phenomena are found in this study. First, the number of travelers that an individual interacts with can affect his route choice strategy. However, the interaction count exerts no influence on the evolution of network flow at the aggregate-level. Second, when the network flow reaches equilibrium, the route choice strategy at the individual-level is not necessarily invariable. Finally, two networks are used as numerical examples to show model properties and to demonstrate the two study phenomena. This study improves the understanding of travelers' route choice dynamics and informs how the network flow evolves under the influence of social interaction.