Switched Server Systems Whose Parameters are Normal Numbers in Base 4

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 with 3 buffers (tanks), a server, filling rates $$\rho _1=\rho _2=\rho _3=\frac{1}{3}$$ parameters $$d_1, d_2, d_3>0$$ whose $$\omega $$ -limit set is fractal set. In this article, we give an explicit large subset for which the corresponding have no More precisely, Poincaré map each system has finite The approach use to study topological dynamics family piecewise $$\lambda -affine contractions includes maps as particular case.