The paper presents a large-scale stochastic road traffic assignment model for the Copenhagen Region. The model considers several classes of passenger cars (different trip purposes), vans and trucks, each with its own utility function on which route choices are based. The utility functions include distributed coefficients (Error Components) estimated on SP-data in a mixed logit model. This was compared with a traditional nested logit model. A number of alternative formulations of EC were tested, and the resulting distributions of value of times are discussed. In application, the different classes and types of vehicles influence all the speed-flow relationships on links within an equilibrium framework. Sub-models for intersections and roundabouts describe queues and geometric delays.