0000000000846525
AUTHOR
Julia Tolmacheva
Stochastic approach to highway traffic
We analyze the characteristic features of jam formation on a circular one-lane road. We have applied an optimal velocity model including stochastic noise, where cars are treated as moving and interacting particles. The motion of N cars is described by the system of 2 N stochastic differential equations with multiplicative white noise. Our system of cars behaves in qualitatively different ways depending on the values of control parameters c (dimensionless density), b (sensitivity parameter characterising the fastness of relaxation), and α (dimensionless noise intensity). In analogy to the gas-liquid phase transition in supersaturated vapour at low enough temperatures, we observe three differ…
Applications to Traffic Breakdown on Highways
During the last years researches into properties of vehicle ensembles on highways form a new branch of physics, called physics of traffic flow. On macroscopic scales the vehicle ensembles exhibit a wide class of phenomena like phase separation and phase transformations widely met in physical systems. Due to the steadily increasing traffic volume in cities and on highways, the mathematical modelling of these phenomena has attracted a great interest. Particularly, the topic of car—following has become of increased importance in traffic engineering and safety research.