Microcanonical and canonical approach to traffic flow

Details Microcanonical and canonical approach to traffic flow Microcanonical and canonical approach to traffic flow

2007-03-21

arxiv.org/abs/physics/0703202v1

Physics

Physics and Society

13 pages, 8 figures, submitted to Physica A

Scientific paper

A system of identical cars on a single-lane road is treated as a microcanonical and canonical ensemble. Behaviour of the cars is characterized by the probability of car velocity as a function of distance and velocity of the car ahead. The calculations a performed on a discrete 1D lattice with discrete car velocities. Probability of total velocity of a group of cars as a function of density is calculated in microcanonical approach. For a canonical ensemble, fluctuations of car density as a function of total velocity is found. Phase transitions between free and jammed flow for large deceleration rate of cars and formation of queues of cars with the same velocity for low deceleration rate are described.

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