An exit-&ow model used in dynamic tra(c assignment

We consider the behaviour of a link exit-&ow model that has been used to model link &ows in dynamic tra(c assignment (DTA) on networks. In particular, we investigate how the model behaves when time and space (the link length) discretised and the discretisation is varied. We present numerical examples based on various in&ow patterns and exit-&ow functions and draw conclusions for applications of the model in discrete space and in discrete or continuous time. If in&ows are always less than capacity and the link is homogeneous, with no obstructions at the exit, then if the discretisation is re3ned to the continuous limit the model goes to the solution of the well-known LWR model. However, we observe, somewhat counter intuitively, that the usual continuous-time model does not give as good an approximation to the LWR solution as does the discrete-time model: for a best approximation, the discretisation of space and time should be synchronised. We also investigate the ‘dip’ in out&ows, or ‘jamming’ of out&ows, that the model displays if in&ows are permitted to exceed a capacity limit (as they sometimes do in published applications of the model) and the exit-&ow function has a downward sloping part (which has usually been assumed away in DTA applications). In that case, if the number of spatial segments is increased, or the number of time intervals is reduced, then any dip in out&ows occurs sooner and is more pronounced, and leads to earlier jamming. In the continuous limit, the jam occurs at the link entrance, preventing in&ows in excess of capacity. ? 2003 Elsevier Ltd. All rights reserved.