Effect of velocity-dependent friction on multiple-vehicle collisions in traffic flow

We present the dynamic model for the multiple-vehicle collisions to take into account the velocity-dependent friction force. We study the effect of the velocity-dependent friction on the chain-reaction crash on a road. In the traffic situation, drivers brake according to taillights of the forward vehicle and the friction force depends highly on the vehicular speed. The first crash may induce more collisions. We investigate whether or not the first collision induces the multiple-vehicle collisions, numerically and analytically. The dynamic transitions occur from no collisions, through a single collision and double collisions, to multiple collisions with decreasing the headway. We explore the effect of the velocity-dependent friction on the dynamic transitions and the region maps in the multiple-vehicle collisions.