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At the intersection of two unidirectional traffic flows a stripe formationinstability is known to occur. In this paper we consider coupled time evolutionequations for the densities of the two flows in their intersection area. Weshow analytically how the instability arises from the randomness of the trafficentering the area. The Green function of the linearized equations is shown toform a Gaussian wave packet whose oscillations correspond to the stripes.Explicit formulas are obtained for various characteristic quantities in termsof the traffic density and comparison is made with the much simpler calculationon a torus and with numerical solution of the evolution equations.

Stripe formation instability in crossing traffic flows