We study the totally asymmetric exclusion process on a ring in discrete time with the backward-ordered sequential update and particle-dependent jumping probabilities. Using our recent exact analytical expression for the generating function of the finite time transition probabilities, we find the average velocity per one particle at all stages of evolution. Evolution of small systems towards the steady state is demonstrated explicitly. © 2008 Polish Scientific Publishers PWN, Warszawa.
Poghosyan, V. S., & Priezzhev, V. B. (2008). The relaxation dynamics of the tasep with particle-dependent hopping probabilities on a ring. Reports on Mathematical Physics, 61(2), 239–246. https://doi.org/10.1016/S0034-4877(08)80012-2