Improved mean-field theory of two-dimensional traffic flow models

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Abstract
An improved mean-field theory is proposed for traffic-flow models in two dimensions, both in the absence and presence of faulty traffic lights. The present theory includes the effects of blockage of cars due to cars moving in the same direction, while previous theories included only the effects of cars moving in the perpendicular direction. In the absence of faulty lights, the theory gives a much better estimate of the critical car density, above which the traffic is in a jamming phase. In the presence of faulty lights, the theory captures all the essential features in published simulation data. It gives the correct behaviour of the velocity in the dilute limit of car density. The dependence of the critical car density on the fraction of faulty traffic lights is studied.