Totally asymmetric simple exclusion processes on two intersected lanes

¹ School of Engineering, Anhui Agricultural University - Hefei 230036, China
² Anhui Province Engineering Laboratory of Intelligent Agricultural Machinery Equipment, Anhui Agricultural University - Hefei 230036, China
³ School of Engineering Science, University of Science and Technology of China - Hefei 230026, China
⁴ MOE Key Laboratory for Urban Transportation Complex Systems Theory and Technology, Beijing Jiaotong University - Beijing, 100044, China
⁵ School of Automotive and Transportation Engineering, Hefei University of Technology - Hefei 230009, China

^(a) jiangrui@bjtu.edu.cn (corresponding author)

Received: 3 September 2019
Accepted: 24 November 2019

Abstract

This paper carries out a cluster mean field analysis for spontaneous symmetry breaking in a two-lane totally asymmetric exclusion processes with an intersection. We find that the boundaries of the asymmetric phase are determined by differences of upstream segment densities and downstream segment flow rates of two lanes. The spontaneous symmetry breaking phenomenon exists when the interaction of particles is strong enough. The critical values, beyond which the phenomenon disappears, are identified through simulation and analysis, and they are in excellent agreement. The analytical results of the asymmetric phase boundaries are closer to simulation ones than those of simple mean field analysis. The analytical results of density profiles and the simulation ones are also in excellent agreement.