Discrete Time TASEP in Heterogeneous Continuum

We study discrete time totally asymmetric exclusion process (TASEP) describing collective random walk of countable particle configurations in heterogeneous continuum. A typical example of this sort is a traffic flow model with obstacles: traffic lights, speed bumps, spatially varying local velocities etc. Ergodic properties of such systems are studied, in particular we obtain the so called Fundamental Diagram: dependence of average particle velocities on particles and obstacles densities and jump probabilities. 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. This techniques allows to reduce the calculation of the average velocity to the similar problem for an auxiliary lattice zero-range process.