Dynamic traffic assignment (DTA) has been a topic of substantial research during the past decade. Although DTA is gradually maturing, many aspects still need improvement, especially regarding its formulation and solution capabilities under the transportation environment affected by advanced transportation management and information systems. It is necessary to develop a set of DTA models to acknowledge the fact that the traffic network itself is probabilistic and uncertain, and different classes of travelers respond differently under an uncertain environment given different levels of traffic information. The aim of this research is to advance the state of the art in DTA modeling in the sense that the proposed model captures the travelers' decision making among discrete choices in a probabilistic and uncertain environment, in which both probabilistic travel times and random perception errors that are specific to individual travelers are considered. Travelers' route choices are assumed to be made with the objective of minimizing perceived disutilities at each time. These perceived disutilities depend on the distribution of the variable route travel times, the distribution of individual perception errors, and the individual traveler's risk-taking nature at each time instant. The integrated DTA model is formulated through a variational inequality approach. Subsequently, the solution algorithm for the formulation is discussed, and experimental results are given to verify the correctness of solutions obtained.