Regensburg 2004 – scientific programme

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DY: Dynamik und Statistische Physik

DY 14: Solitons and Stochastic Dynamics

DY 14.5: Talk

Monday, March 8, 2004, 15:30–15:45, H2

Probabilistic Description of Traffic Flow — •Reinhard Mahnke¹, Jevgenijs Kaupužs², and Ihor Lubashevsky³ — ¹FB Physik, Univ. Rostock, D–18051 Rostock — ²Univ. Latvia, LV–1459 Riga, Latvia — ³Physics Inst., Russian Acad. Sc., Moscow, Russia

A stochastic description of traffic flow, called probabilistic traffic flow theory, is developed. The general master equation is applied to relatively simple models to describe the formation and dissolution of traffic congestions. Our approach is mainly based on spatially homogeneous systems like periodically closed circular rings without on– and off–ramps. We consider a stochastic one–step process of growth or shrinkage of a car cluster (jam). As generalization we discuss the coexistence of several car clusters of different sizes. The basic problem is to find a physically motivated ansatz for the transition rates of the attachment and detachment of individual cars to a car cluster consistent with the empirical observations in real traffic. The emphasis is put on the analogy with first–order phase transitions and nucleation phenomena in physical systems like supersaturated vapour. The results are summarized in the flux–density relation, the so–called fundamental diagram of traffic flow, and compared with empirical data. Different regimes of traffic flow are discussed: free flow, congested mode as stop–and–go regime, and heavy viscous traffic. The traffic breakdown is studied based on the master equation as well as the Fokker–Planck approximation to calculate mean first passage times or escape rates. In conclusion, the calculated flux–density relation and characteristic breakdown times coincide with empirical data measured on highways.