An approach to modelling time-varying flows on congested networks

In mathematical programming models of time-varying flows on traffic networks (dynamic traffic assignment) a key component is the model of flow behaviour within individual links. However, to maintain tractability in these models, time-varying link flows tend to be modelled in very simple ways. Here we try to model link flows more flexibly, so that the trip time of a vehicle on a link is influenced by the flow rate when the vehicle enters the link, the flow rate when the vehicle exits from the link, and knock-on effects from traffic ahead on the link. We concentrate on congestion along links, but the model can be extended, for example by dividing each link into a travel link followed by a queue 'link'. We also concentrate on a system optimising model but outline how this can be extended to user equilibrium. We consider the properties of the model, and find that the first-in-first-out (FIFO) property of road traffic holds unless there is a sharp increase in inflows to a link followed by a sharp decrease. We also investigate the "holding back" of flows, a phenomenon associated with intertemporal network optimisation models in general. We apply the model to simple network examples. The model has the advantage of being linear and having a special structure which may be exploited to develop more efficient solution techniques.