  We generalize a recently introduced traffic model, where the statistical
weights are associated with whole trajectories, to the case of two-way flow. An
interaction between the two lanes is included which describes a slowing down
when two cars meet. This leads to two coupled five-vertex models. It is shown
that this problem can be solved by reducing it to two one-lane problems with
modified parameters. In contrast to stochastic models, jamming appears only for
very strong interaction between the lanes.
