Cluster mean-field analysis for spontaneous symmetric breaking in a bidirectional two-lane system with narrow entrances and parallel update

¹ School of Engineering Science, University of Science and Technology of China - Hefei 230026, PRC
² MOE Key Laboratory for Urban Transportation Complex Systems Theory and Technology, Beijing Jiaotong University - Beijing 100044, PRC

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

Received: 6 January 2017
Accepted: 11 March 2017

Abstract

This paper carries out a cluster mean-field analysis for spontaneous symmetric breaking in a two-lane asymmetric exclusion process with narrow entrances and parallel update. We demonstrate that the asymmetric low-density/low-density phase does not exist, based on a current minimization principle. With the increase of the cluster number in the cluster mean-field analysis, an exponential decay of the boundary between asymmetric high-density/low-density phase and symmetric low-density phase as well as the bulk density in the symmetric low-density phase has been observed, which enables us to predict the phase boundary and the bulk density in the exact solution. The predicted results are in agreement with simulations.