Balanced sequences and optimal routing

The objective pursued in this paper is two-fold. The first part addresses t he fallowing combinatorial problem: is it possible to construct an infinite sequence wet n letters where each letter is distributed as "evenly" as pos sible and appears with a given rate? The second objective of the gaper is t o use this construction in the framework of optimal routing in queuing netw orks. We show under rather general assumptions that the optimal determinist ic routing in stochastic event graphs is such a sequence.