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Jamming transitions induced by a slow vehicle in traffic flow on a multi-lane highway

We study the current–density diagram for when a slow vehicle is introduced in multi-lane traffic flow. We extend the conventional optimal velocity model to the multi-lane traffic by taking into account the lane changing. The dynamical state of the traffic changes with increasing density. The dynamical phase transitions occur at certain densities. It is found that there are four distinct states for the two-lane traffic flow including a slow vehicle: (1) the free traffic at a low density, (2) the jammed traffic at an intermediate density, (3) the homogeneous traffic with different occupancies on the first and second lanes, at increasing density furthermore, and (4) the congested traffic with the same occupancy on the first and second lanes at a high density. Traffic state (2) is divided into two dynamic states for the three-lane and four-lane traffic. In addition, traffic state (3) is divided into two dynamic states for the four-lane traffic. The dependence of the current on the velocity of a slow vehicle is derived numerically and analytically.