B. Gaujal and E. Hyon. Optimal routing policies in two deterministic queues. Reseaux et systemes repartis - Calculateurs Paralleles, 13(6):601--633, 2001.  Home/Search   Document Not in Database   Summary   Related Articles

....This optimal policy appears to be a Sturmian sequence, which density can be computed from the decomposition in ceiled continuous fractions of the service times of all the nodes involved. A similar problem where the network of queues in tandem is replaced by single queues is addressed in [5]. The main difference here is the need to study the output process, which is an essential component to the global study of a network of queues. Henceforth, we focus particularly on the output process of a deterministic queue when the input is Sturmian. This allows to compute the average ....

.... ; fn ) if m = f i 1 f i 2 . If m is finite, the number of times a factor f j appears in this factorization is denoted jmj f j . This number is not the number of times the factor f j appears in m, but depends on the factorization. This induces Theorem 6 ( x,y) factor decomposition,[5]) Let 0 1 be such that = hl(1) l(n) i. We define two sequences, fx(i) g i 0 and fy(i) g i 0 , as follow : x(0) 1, y(0) 0 and for i 1 x(i) x(i 1) y(i 1) y(i) x(i 1) y(i 1) Thus for all nonnegative i, the upper mechanical word m ....

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B. Gaujal and E. Hyon. Optimal routing policies in two deterministic queues. Reseaux et systemes repartis - Calculateurs Paralleles, 13(6):601--633, 2001.

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