Three "equations of state" are required to describe the traffic fluid. The first is volume equals speed times density, and the second is the continuity of vehicles. There are at least four options for the third equation: (1) the deterministic speed-density model, (2) the equilibrium speed-density model, (3) the Payne model, and (4) the ross model. Two restrictions on the space step DX and time step DT apply to numerical integrations of all four models. There is an additional restriction on DT that applies to the last three models and a special restriction on the "anticipation" term in the Payne model.The time required to perform numerical integrations of all four models is shown to be inversely proportional to the square of the length of the smallest feature represented. A general form for the "relaxation time" in the three non-deterministic models is derived. It is argued, on the basis of experience with the ross model, that although a dependence upon speed is "correct", setting the relaxation time constant is adequate for most traffic purposes. The relationship between relaxation time and lost time at signals in the ross model is shown to be linear.
Abstract