  We propose a bridge between the theory of exactly solvable models and the
investigation of traffic flow. By choosing the activities in an apropriate way
the dimer configurations of the Kasteleyn model on a hexagonal lattice can be
interpreted as space-time trajectories of cars. This then allows for a
calculation of the flow-density relationship (fundamental diagram). We further
introduce a closely-related cellular automaton model. This model can be viewed
as a variant of the Nagel-Schreckenberg model in which the cars do not have a
velocity memory. It is also exactly solvable and the fundamental diagram is
calculated.
