  This paper studies optimal scheduling and resource allocation under allowable
over-scheduling. Formulating an optimisation problem where over-scheduling is
embedded, we derive an optimal solution that can be implemented by means of a
new additive increase multiplicative decrease (AIMD) algorithm. After
describing the AIMD-like scheduling mechanism as a switching system, we show
convergence of the scheme, based on the joint spectral radius of symmetric
matrices, and propose two methods for fitting an optimal AIMD tuning to the
optimal solution derived. Finally, we demonstrate the overall optimal design
strategy via an illustrative example.
