This contribution presents a derivation of the steady-state distribution of velocities and
distances of driven particles on a onedimensional periodic ring, using a Fokker-Planck formalism. We will compare two different situations: (i) symmetrical interaction forces fulfilling Newton’s law
of “actio = reactio” and (ii) asymmetric, forwardly directed interactions as, for example
in vehicular traffic. Surprisingly, the steady-state velocity and distance distributions
for asymmetric interactions and driving terms agree with the equilibrium distributions of
classical many-particle systems with symmetrical interactions, if the system is large enough.
This analytical result is confirmed by computer simulations and
establishes the possibility of approximating the steady state
statistics in driven many-particle systems by Hamiltonian systems. Our finding is also
useful to understand the various departure time distributions of queueing systems as a possible
effect of interactions among the elements in the respective queue [Physica A 363, 62 (2006)].
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion 05.10.Gg Stochastic analysis methods 47.70.-n Reactive and radiative flows 89.40.-a Transportation