On deterministic developments of traffic stream models

Classical deterministic (or "mechanical") developments of traffic stream models from car-following models are criticized on the following basis. The evaluation of the constant of integration for initial conditions corresponding to speed zero and headway equal to the reciprocal of jam density ignores large numbers of possibly relevant solutions of the underlying car-following model. Some undesirable consequences, particularly the restriction to temporally and spatially constant flow conditions, of viewing traffic stream models as being deterministic consequences of car-following models are also noted. It is suggested that an approach to traffic stream models via kinetic models possibly would be more appropriate and useful.