The objective pursued in this paper is two-fold. The first part gives an overview of the following combinatorial problem: is it possible to construct an infinite sequence over $n$ letters where each letter is distributed as «evenly» as possible and appears with a fixed rate? The second objective of the paper is to relate this construction to the framework of optimal routing in queueing networks. We show under rather general assumptions that the optimal deterministic routing in several event graphs is such a sequence.