Impact of effective injection rates on density and phase diagram at the branching point

Abstract

In this paper, the effects of different effective injection rates at the branching point on density profiles and phase diagram have been investigated by theoretical calculation and computer simulation. At the branching point, a single-lane is divided into two sub-lanes. The variables p and q which satisfy p+q = 1 and p [Formula: see text] q are used to describe the percent of currents which enter two sub-channels, respectively. With different effective injection rates, the phase diagram includes three regions and two transition lines. Obviously, the sub-lane 2 is always in the low-density (LD) phase because the small p leads to fewer particles moving through sub-lane 2. However, sub-lane 3 is easy in the high-density (HD) phase (namely, traffic jam) because of the large q. In addition, the current of lane 1 is often in the maximal current (MC) when entrance rate [Formula: see text] [Formula: see text] 0.5. With the increase of variable q, the regions of LD/LD/LD and MC/LD/LD phases shrink dramatically while the region of the HD/LD/HD phase only expands. This result implies that the changes of the phase diagram are determined by the variable q, meanwhile, the large q will likely lead to traffic congestion.