This paper proposes an approach-proportion-based variational inequality (VI) formulation for the
multi-class dynamic traffic assignment problem with physical queues using the concept of intersection movements . To solve the problem, an extragradient method that only requires mild
assumptions for convergence is developed. A car-truck interaction paradox, stating that allowing
trucks traveling in a network or increasing the demand of trucks traveling in a network could improve the network performance for cars, in terms of total car travel time, is discussed. Numerical
examples are set up to illustrate the importance of considering multiple vehicle types and their
interaction in a dynamic traffic assignment model and the effects of various parameters on the
occurrence of the paradox.