Kinetic segregation in a multilane highway traffic flow

A traffic model is presented to study the segregation of cars on a multilane highway. When a fast (slow) car overtakes (is overtaken by) a slow (fast) car, the fist (slow) car shifts to the outer (inner) lane. The traffic kinetics on a multilane highway is described in terms of Boltzmann-like kinetic equations. The segregation of cars between lanes is studied by deriving the velocity distribution on each lane from the kinetic equations. The discrete versions of the kinetic equations are presented to solve numerically these equations. The time evolutions of velocity distributions on the lanes are calculated by numerical method. The velocity distributions on two-lane, three-lane, four-lane and five-lane highways in a steady state are also derived numerically. It is shown that the slower cars gather on the inner lanes, the faster cars gather on the outer lanes and then a segregation occurs by changing lanes.