Resumen de Switched Server Systems Whose Parameters are Normal Numbers in Base 4

André do Amaral Antunes, Yann Bugeaud, Benito Pires

• Switched server systems are mathematical models of manufacturing, traffic and queueing systems. Recently, it was proved in (Eur J Appl Math 31(4), 682–708, 2020) that there exist switched server systems with 3 buffers (tanks), a server, filling rates ρ1 = ρ2 = ρ3 = 1 3 and parameters d1, d2, d3 > 0 whose ω-limit set is a fractal set. In this article, we give an explicit large subset of parameters for which the corresponding switched server systems have no fractal ω-limit set. More precisely, the Poincaré map of each system has a finite ω-limit set. The approach we use is to study the topological dynamics of a family of piecewise λ-affine contractions that includes the Poincaré maps of the switched server systems as a particular case.