Statistical Approach to Traffic Flow
Statistical mechanics of a small system of cars on a single-lane road is developed. The system is characterized by a conditional probability of a velocity of a car for a given velocity and distance of the car ahead. Distribution of car velocities for various densities of a group of cars is derived as well as probabilities of density fluctuations of the group for various velocities. Free-flow phase, congested phase, and formation of platoons of cars were found.
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