Spreading of Traffic Jam in a Traffic Flow Model

A cellular automaton (CA) model is presented to simulate the traffic jam induced by a traffic accident. The spreading of jamming cars induced by a car crash is investigated by computer simulation. An analogy is proposed between the crystal growth and the traffic-jam spreading. The scaling behavior of the traffic-jam spreading is studied. It is shown that the number N of jamming cars scales as N ≈ t 2.34±0.03 for p above the dynamical jamming transition p c =0.35 and N ≈ t 1.07 below p c where t is the time and p is the density of cars. The time constant t s , which is the time required for all cars to stop, scales as t s ≈ p -1.07±0.03 for p < p c . The following scaling form is found: p -1 N ≈( p 1.07 t ) 1.07 for p < p c .