Modelling road traffic assignment as a day-to-day dynamic, deterministic process: a unified approach to discrete- and continuous-time models.

We consider the modelling of road transport systems as a day-to-day dynamic, deterministic process. The main contribution is to present a unified treatment of discrete-time and continuous-time approaches, with these two classes of approaches having been developed in two parallel streams of research which have had little connection made between them. In doing so, we aim to clarify the usefulness of these alternative approaches. We pay particular attention to: the specification of such models, the conditions which characterise the various forms of emergent behaviour, and the relationship between the model assumptions and real-world phenomena. The proposed framework is heavily focused, in the first instance, on a probabilistic approach to user choice modelling, though we also review and analyse the limiting case of deterministic choice model.