Optimal stable real-time scheduling of a flexible manufacturing system modelled as a switched server system

We study a flexible manufacturing system modelled as a switched server system. This system consists of one server and n buffers. We give a precise solution for an optimization problem. Moreover, we study dynamics of the optimal closed-loop system and prove that the switched server system with n buffers has (n-1)! locally asymptotically stable limit cycles. Furthermore, we prove that any trajectory of this system is attracted by one of these limit cycles.