Berlin 2005 – scientific programme
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AKSOE: Physik sozio-ökonomischer Systeme
AKSOE 8: Poster Session
AKSOE 8.4: Poster
Monday, March 7, 2005, 14:00–15:30, Poster TU E
Stochastic Description of Traffic Breakdowns — •Jevgenijs Kaupužs1 and Reinhard Mahnke2 — 1Univ. Latvia, LV–1459 Riga, Latvia — 2Inst. of Physics, Univ. Rostock, D–18051 Rostock
We analyse 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. From the probabilistic point of view we investigate a quite classical dynamical system given by stochastic differential equations, i. e. ordinary differential equations with multiplicative noise. Based on this Langevin approach the distributions of vehicular velocity difference as well as headway distances are calculated and discussed.
In analogy to the gas-liquid phase transition in supersaturated vapour at low enough temperatures, we observe three different regimes of traffic flow. There are the free flow regime (like gaseous phase) at small densities of cars, the coexistence of a jam and free flow (like liquid and gas) at intermediate densities, and the homogeneous dense traffic (like liquid phase) at large densities.
[1] J. Kaupužs, H. Weber, J. Hinkel, R. Mahnke, Application to Traffic Breakdown on Highways, In: Progress in Industrial Mathematics at ECMI 2002, Springer, Berlin, pp. 133 – 138, 2004
[2] R. Mahnke, J. Kaupužs, Phys. Rev. E 59, 117, 1999
[3] P. E. Kloeden, E. Platen, Numerical Solution of Stochastic Differential Equations, Springer, Berlin, 1992