  This contribution presents a derivation of the steady-state distribution of
velocities and distances of driven particles on a onedimensional periodic ring.
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 [D.
Helbing et al., Physica A 363, 62 (2006)].
