  We study deterministic discrete time exclusion type spatially heterogeneous
particle processes in continuum. A typical example of this sort is a traffic
flow model with obstacles: traffic lights, speed bumps, spatially varying local
velocities etc. Ergodic averages of particle velocities are obtained and their
connections to other statistical quantities, in particular to particle and
obstacles densities (the so called Fundamental Diagram) is analyzed rigorously.
The main technical tool is a "dynamical" coupling construction applied in a
nonstandard fashion: instead of proving the existence of the successful
coupling (which even might not hold) we use its presence/absence as an
important diagnostic tool.
