Equilibrium traffic flow of a mixture of cars with different properties

Statistical mechanics of a disordered system of cars on a single-lane road is developed. Behaviour of cars is defined by conditional probability of car velocity depending on the distance and velocity of the car ahead. A system consisting of different cars is modelled by a system of two types of cars differing in maximal velocity or efficiency of brakes. Starting from conditional probabilities and using principle of maximum entropy, probability densities of car velocities and headways are calculated. It is shown that the first-order phase transition between free flow and congested traffic may be driven by number of fast cars in a system of slow cars, and, as a rule, admixture of cars of superior qualities does not increase but decreases the total flow. In the system of cars with poor brakes platoons of cars of the same velocity are formed. They are dissolved by a small addition of cars with good brakes. Application of principle of maximum entropy was justified by comparing the results with steady state properties of an equivalent kinetic model.
Comment: 17 pages, 11 figures