Journal of Statistical Physics

, Volume 161, Issue 4, pp 843–858 | Cite as

On the Blockage Problem and the Non-analyticity of the Current for Parallel TASEP on a Ring

  • Benedetto Scoppola
  • Carlo Lancia
  • Riccardo Mariani


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 \(\varepsilon \) 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 \(\varepsilon = 0\).


Parallel TASEP Blockage problem Current 

Mathematics Subject Classification

60J10 37B15 60K30 



We wish to thank Elisabetta Scoppola for useful discussions.


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Benedetto Scoppola
    • 1
  • Carlo Lancia
    • 1
  • Riccardo Mariani
    • 1
  1. 1.Dipartimento di MatematicaUniversità degli Studi di Roma Tor VergataRomeItaly

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