The effect of unequal constrained at branching point on phase diagrams

Abstract

The effect of unequal constrained at branching point on phase diagrams is investigated by a totally asymmetric simple exclusion process (TASEP). At the junction point, the chosen rates of the two branches are r 1/2 and r 2/2, respectively. Based on simple mean field theory and Monte Carlo simulations, the phase diagrams and density profiles attached to the ratio n (n = r 1/r 2) and r 2 are investigated. When the chosen rates are under the unequal constrained condition, there are two thresholds r2c1=22−n+n2−2−n+n22−1+n2n1+n2 and r2c2=21+n−2n1+n2, leading to the obvious difference of phase diagrams. Additionally, the area functions and saturation point pairs of current, n and r 2 are given to predict the alterations of the phase boundaries. An optimal parameter n = r 2 = 0.8 is found to ensure the probability of traffic congestion reaches the minimum level in our model. All outcomes of theory and simulations related to density profiles and phase diagrams are in good agreement.