1 research outputs found
Kinetics of Clustering in Traffic Flows
We study a simple aggregation model that mimics the clustering of traffic on
a one-lane roadway. In this model, each ``car'' moves ballistically at its
initial velocity until it overtakes the preceding car or cluster. After this
encounter, the incident car assumes the velocity of the cluster which it has
just joined. The properties of the initial distribution of velocities in the
small velocity limit control the long-time properties of the aggregation
process. For an initial velocity distribution with a power-law tail at small
velocities, \pvim as , a simple scaling argument shows that the
average cluster size grows as n \sim t^{\va} and that the average velocity
decays as v \sim t^{-\vb} as . We derive an analytical solution
for the survival probability of a single car and an asymptotically exact
expression for the joint mass-velocity distribution function. We also consider
the properties of spatially heterogeneous traffic and the kinetics of traffic
clustering in the presence of an input of cars.Comment: 18 pages, Plain TeX, 2 postscript figure