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Regular version of the site

Article

Discrete Time TASEP in Heterogeneous Continuum

Markov Processes and Related Fields. 2012. Vol. 18. P. 531-552.

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.