Extending travel-time based models for dynamic network loading and assignment, to achieve adherence to first-in-first-out and link capacities

An important class of models for macroscopic dynamic network loading (DNL) and dynamic traffic assignment (DTA) is based on treating link travel times as a function of link occupancy. However, these models suffer from some problems or deficiencies namely (a) the link outflows can violate first‐in‐first‐out (FIFO), (b) the link outflows can exceed the link outflow capacities, (c) the link inflows can exceed the link inflow capacities, and (d) the link occupancies can exceed the link occupancy capacities. In this paper we introduce methods to overcome each of these problems. To remove problems (a) and (b) we extend the link travel‐time model to better reflect behaviour when traffic flow is varying over time. To remove problems (c) and (d) we introduce more substantial changes in the model, to introduce capacities, spillback and queues compatible with the model. These extensions strengthen the realism, behavioural basis and usability of the link travel‐time model and the DNL and DTA models that are based on it. They have no obvious adverse implications or side effects and require little additional computational effort. The original model is a special case of the new/extended model: the above extensions are activated if and only if any of the problems (a)–(d) arise, otherwise the new model reduces to the original model.