The reaction time of drivers and the stability of traffic flow

In this work, a condition for any traffic flow model is proposed: the consistency condition. An expression for the reaction time of drivers as a function of traffic density is derived from this condition. The changes introduced in the Payne model by the adoption of this expression for the reaction time are investigated. A comparison analysis of the resulting Payne model with others proposed by several authors and with the Simple Continuum Model is carried out. This analysis leads to the conclusion that the results of the Payne model are almost identical to those given by the Simple Continuum Model. Finally, the stability of traffic flow is studied by linearizing the Payne model and the car-following models modified by the adoption of the new formulation for the reaction time. The analysis shows that the inclusion of stochastic terms in the models would be necessary to explain instability phenomena in traffic flow.