Stability of switched server systems with finite buffer capacity

Under the service-time-limited scheduling policy (STLSP), any solution to the switched server system asymptotically converges to a unique periodic solution. Though, the STLSP restricts the service time for each buffer, it does not consider the constraints on the buffer capacity. However, the buffer capacity is finite for most of real-world problems. Motivated by this problem, this paper generalizes the STLSP, and considers the execution of the STLSP with the constraints on the buffer capacity. We give the checking condition of feasible initial states, which guarantees that the solution to the switched server system under the STLSP asymptotically converges to the periodic solution while satisfying the constraints on the buffer capacity. Furthermore, for the switched server system with two buffers under the STLSP, we give the expression of the set of all feasible initial states. The simulation analysis validates our methods.