Balanced sequences and optimal routing

The objective pursued in this paper is two-fold. The first part addresses 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 given rate? The second objective of the paper is to use this construction in the framework of optimal routing in queuing networks. We show under rather general assumptions that the optimal deterministic routing in stochastic event graphs is such a sequence.

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