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Approximate Approach to Compute Characteristics of Inhomogeneous TASEP with Open Boundaries

Marina V. Yashina, Alexander G. Tatashev

Abstract

A discrete-time totally asymmetric simple exclusion process on a lattice with open boundaries is considered. There are particles of different types. The type of a particle is characterized by the probability that a particle moves to a vacant site and the probability that a particle occupying the rightmost site departs the system. An approximate approach to compute the particle flow rate and density in sites is proposed. A version of the approach is proposed for an analogous continuous-time process. The accuracy of the approximation is estimated. The approach can be used in traffic models and models of statistical physics.

Approximate Approach to Compute Characteristics of Inhomogeneous TASEP with Open Boundaries

Abstract

A discrete-time totally asymmetric simple exclusion process on a lattice with open boundaries is considered. There are particles of different types. The type of a particle is characterized by the probability that a particle moves to a vacant site and the probability that a particle occupying the rightmost site departs the system. An approximate approach to compute the particle flow rate and density in sites is proposed. A version of the approach is proposed for an analogous continuous-time process. The accuracy of the approximation is estimated. The approach can be used in traffic models and models of statistical physics.

Paper Structure

This paper contains 9 sections, 35 equations.

Table of Contents

  1. 1. Introduction
  2. 2. Description of inhomogeneous process
  3. 3. Ergodicity of the system
  4. 4. Description of homogeneous process
  5. 5. Approximate approach
  6. 6. Estimation of approximation accuracy
  7. 7. Continuous-time inhomogeneous process
  8. 8. Conclusion
  9. References