  A new class of exclusion type processes acting in continuum with synchronous
updating is introduced and studied. Ergodic averages of particle velocities are
obtained and their connections to other statistical quantities, in particular
to the particle density (the so called Fundamental Diagram) is analyzed
rigorously. The main technical tool is a "dynamical" coupling applied in a
nonstandard fashion: we do not prove the existence of the successful coupling
(which even might not hold) but instead use its presence/absence as an
important diagnostic tool. Despite that this approach cannot be applied to
lattice systems directly, it allows to obtain new results for the lattice
systems embedding them to the systems in continuum. Applications to the traffic
flows modelling are discussed as well.

Dynamical Systems;Statistical Mechanics;Probability