Automated analysis of real-time scheduling using graph games

In this paper, we introduce the powerful framework of graph games for the analysis of real-time scheduling with firm deadlines. We introduce a novel instance of a partial-observation game that is suitable for this purpose, and prove decidability of all the involved decision problems. We derive a graph game that allows the automated computation of the competitive ratio (along with an optimal witness algorithm for the competitive ratio) and establish an NP-completeness proof for the graph game problem. For a given on-line algorithm, we present polynomial time solution for computing (i) the worst-case utility; (ii) the worst-case utility ratio w.r.t. a clairvoyant off-line algorithm; and (iii) the competitive ratio. A major strength of the proposed approach lies in its flexibility w.r.t. incorporating additional constraints on the adversary and/or the algorithm, including limited maximum or average load, finiteness of periods of overload, etc., which are easily added by means of additional instances of standard objective functions for graph games.