  The rotor-router model is a popular deterministic analogue of random walk. In
this paper we prove that all orbits of the rotor-router operation have the same
size on a strongly connected directed graph (digraph) and give a formula for
the size. By using this formula we address the following open question about
orbits of the rotor-router operation: Is there an infinite family of
non-Eulerian strongly connected digraphs such that the rotor-router operation
on each digraph has a single orbit?
  It turns out that on a strongly connected digraph the stationary distribution
of the simple random walk coincides with the frequency of vertices in a rotor
walk. In this common aspect a rotor walk simulates a random walk. This gives
one similarity between two models on (finite) digraphs.
