A two phase extension of the LWR model based on the boundedness of traffic acceleration.

The outline of the paper is the following. After a brief summary of the LWR model, a first model, the bounded acceleration LWR model, is introduced, based on the idea of restricting the set of solutions of the LWR model. The limitations of this first approach, notably an inadequate treatment of initial conditions and jam dynamics, justify the introduction of the two-phase model, based on the idea that there exist two phases in traffic flow: the equilibrium (EQ) phase, in which traffic behaves as in the LWR model, and traffic acceleration is less than the upper acceleration bound A, and the (EA) phase in which traffic acceleration is exactly A, but speed (or density) are lower than they would be at equilibrium. The last sections of the paper are devoted to the analysis of the resulting model and some fundamental examples. It is shown that features such as persistent traffic jams, parallel moving traffic jams, traffic hysteresis, capacity drops, scatter of measurement points on the rhs of the fundamental diagram, are easily recaptured. (Author/publisher) For the covering entry of this conference, please see ITRD abstract No. E208120.