Evolutionary Analysis on the Dynamical Systems of Travel Behavioral Decision-Making

The road traffic flow evolutionary patterns of metropolitan areas evolve slowly through a complex multi-dimensional travel decision-making behavior (including travel mode, departure time and route choice joint decision-making). How to forecast the long run evolutionary trend of traffic flow on the entire network? Does the traffic evolution track converge to equilibrium? If it can, what´s the condition should be satisfied? And what´s the relationship between trip costs and traffic flow evolutionary patterns? In order to answer these related questions, this paper aims at the general travel behavioral decision-making process, a novel dynamical systems formulation of the traffic assignment problem using evolutionary game theory is proposed. The assumptions on drivers´ behavior in multi-dimensional travel choice are supposed to be fairly general and reasonable. And the stable properties of this dynamical system on its equilibrium points are investigated using Lyapunov method in a general network. It shows that the evolutionary dynamical system exist only one solution on the condition that the traveler population satisfies some hypotheses which individual´s trip payoff satisfy some constraint conditions. These means that there maybe exist inherent motive power which drive the traffic flow evolve to some stable patterns from long run view point. It can improve our understandings to urban traffic flow evolution process and provide significant reference for relevant management section.