ANALYTICAL APPROACH TO TRAFFIC JAMS

The traffic-flow problem in two dimensions is formulated as a three-state model on a square lattice in terms of Pauli operators. Using a Pock-space representation of the master equation we get the Liouvillian for the problem with asymmetric exclusion. Three different realizations, symmetric, right-before-left model and an exchange model will be analysed within the mean-field approximation (MFA). The resulting kinetic equations for the average occupation number of cars in the upward and sideward directions are coupled. The average velocity can be calculated in MFA. It results in a jamming transition that depends on the total concentration of cars.