13 citations · 17 across the 3 of their papers we have counts for
4 papers
Boundary singularities and boundary conditions for the Fokker-Planck equations
Ihor Lubashevsky, Rudolf Friedrich, Reinhard Mahnke +2
The boundary conditions for the Fokker-Planck equations, forward and backward ones are directly derived from the Chapman-Kolmogorov equation for M-dimensional region with boundarie…
Probabilistic Description of Traffic Breakdowns Caused by On-ramp Flow
Reinhart Kuhne, Ihor Lubashevsky, Reinhard Mahnke +1
The characteristic features of traffic breakdown near on-ramp are analyzed. To describe this phenomenon the probabilistic description regarding the jam emergence as the formation o…
Towards the fundamentals of car following theory
Ihor Lubashevsky, Peter Wagner, Reinhard Mahnke
The problem of a car following a lead car driven with constant velocity is considered. To derive the governing equations for the following car dynamics a cost functional that ranks…
Order Parameter as an Additional State Variable of Unstable Traffic Flow
Ihor A. Lubashevsky, Reinhard Mahnke
We discuss a phenomenological approach to the description of unstable vehicle motion on multilane highways that could explain in a simple way such observed self-organizing phenomen…