Physics of Nucleation on Roads

Although the experimental situation on freeways is rather complex, we believe that some general features of traffic flow exist which can be described by relatively simple models. Dynamical models for car cluster formation based on stochastic methods (master equation, Langevin equation, Fokker-Planck-equation) have not been extensively exploited so far in traffic theory. It is the aim of the present contribution to present a stochastic description of jam formation in synchronized traffic using master equation approach. The main and central point is to construct the transition probabilities for the jump processes to condensate one free car to a car cluster or to evaporate the first congested car into free flow. This method allows us to interpret the phase transitions between different states of traffic flow in analogy to aggregation phenomena in metastable and unstable systems like supersaturated van der Waals gases.