An evolutionary game theory approach to the day-to-day traffic dynamics

The most important research topic in traffic network modeling for more than a decade has been the effort to formulate and solve more complex and realistic models, especially to support applications of ITS (Intelligent Transport System). The representation of behavioral adaptation and traveler's learning processes are of great importance to study because they describe the underlying traffic flow evolution from day-to-day perspective.; Some key issues regarding individual traveler's behavior are not well understood, for instance, travelers' stochastic inertia to change routes. This research aims to investigate the day-to-day adjustment process of travelers in order to provide insights into how a traffic flow pattern evolves over time. This problem is important, both for gaining a deeper understanding of the properties of the standard traffic equilibrium model, and for practical reasons related to the monitoring of traffic. By applying the evolutionary game theory to the traffic flow dynamics, we are able to study the individual stochastic behavior first by means of a stochastic process and thereafter obtain a unique mean day-to-day traffic flow dynamic in the aggregate level. We can explore the equivalence between the stationary link flow pattern and the deterministic/stochastic user equilibrium provided that all travelers follow certain rational learning process. The equivalence suggests that the monitoring and analysis of traffic patterns can be conducted on the level of link instead of paths with implications for ITS.; The traffic evolution can be considered as the sum of a nonlinear mean dynamic and a random motion. The random term will dominate the system motion after the mean dynamic has reached its fixed point. In continuous-time, the random term can be modeled as a Brownian motion while multivariate normal distribution in discrete-time. We propose a novel approach to directly compute the covariance matrix of the multivariate normal in discrete-time instead of the iterative method in previous literature. In this way, the exact solution of the covariance matrix can be achieved with much less computational efforts.