Shock Wave Relation Containing Lane Change Source Term for Two-Lane Traffic Flow

The shock wave relation for two-lane traffic flow with lane changes has been formulated. The post-shock condition is obtained by adding a source term which accounts for the lane changes to the continuity equation. The shock velocity, and the corresponding post-shock conditions are obtained from matching relation between the lanes. The source term is affected by the transverse velocity for the lane change. If the lane to which cars intend to change is not crowded and lane change is permitted without restriction, the source term linearly increases with increasing the transverse velocity. However, if the lane change motion is limited due to crowded traffic, the lane change rate is decreased; the traffic flow gets involved in more complicated shock wave dynamics. In any case, shock polar analysis eases the derivation and the comprehension of the matched shock relation.