On the blockage problem and the non-analyticity of the current for the parallel TASEP on a ring

Abstract

The Totally Asymmetric Simple Exclusion Process (TASEP) is an important example of a particle system driven by an irreversible Markov chain. In this paper we give a simple yet rigorous derivation of the chain stationary measure in the case of parallel updating rule. In this parallel framework we then consider the blockage problem (aka slow bond problem). We find the exact expression of the current for an arbitrary blockage intensity $\epsilon$ in the case of the so-called rule-184 cellular automaton, i.e. a parallel TASEP where at each step all particles free-to-move are actually moved. Finally, we investigate through numerical experiments the conjecture that for parallel updates other than rule-184 the current may be non-analytic in the blockage intensity around the value $\epsilon =0$.

References in corpus (4)

• Determinant solution for the Totally Asymmetric Exclusion Process with parallel update
• Determinant solution for the Totally Asymmetric Exclusion Process with parallel update II. Ring geometry
• The mixing time for simple exclusion
• The parallel TASEP, fixed particle number and weighted Motzkin paths

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• Conditional expectation of the duration of the classical gambler problem with defects
• Localization of defects via residence time measures