Abstract In the context of dynamic traffic assignment (DTA), the network loading map represents a traffic flow model. Assuming that an iterative DTA microsimulator is given, this article discusses several techniques for the linearization of the network loading map. The practical context of this work is the problem of calibrating travel demand from traffic counts: The simulated travel demand is mapped on simulated traffic counts through the network loading map, and hence a linearization of this map provides directional information for the adjustment of the demand such that real-world traffic counts can be reproduced to a reasonable degree. The proposed linearization techniques rely on recursive regressions that are fitted to the traffic flow model during the iterations of the DTA microsimulator. It is demonstrated that this approach performs substantially better than the usually deployed proportional assignment in that it even functions in congested conditions.