Controllability of switched server systems with service-time and queue constraints on buffers

The service-time-limited (STL) scheduling policy with lower and upper service-time adjustable factors, admits service-time constraints on buffers, but does not bring queue constraints on buffers. However, the buffer capacity is finite for most of real-world problems. Motivated by this problem, this paper considers the execution of the STL scheduling policy with finite buffer capacity. First, the notion of controllability of the state in safety region is introduced, meaning that the solution to switched server systems with controllable initial state remains in safety region forever, and asymptotically converges to a periodic solution. Furthermore, a sufficient condition for determining factors ensuring the state is controllable, is presented, which establishes the relation between controllability of the state and upper service-time adjustable factors in the STL scheduling policy. The simulation results illustrate our results.