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Optimal allocation sequences of two processes sharing a resource. (English) Zbl 0909.68135

The author shows the relevance of the “most regular words” in the study of two processes sharing a common resource, with an external constraint on the system frequency. These words essentialy correspond to drawing a discrete straight line through the origin in the plane: they are composed with vertical and horizontal unit segments; hence they are either periodic or Sturmian characteristic words (the second case corresponds to irrational slopes). Properties of these words and applications to the initial problem are given. Some results are sketched for more than two processes, i.e., for “most regular words” on an alphabet with at least three letters.

MSC:

68R15 Combinatorics on words
11B83 Special sequences and polynomials
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