An Analysis of Totally Clairvoyant Scheduling

Abstract

Traditional scheduling models assume that the execution time of a job in a periodic job-set is constant in every instance of its execution. This assumption does not hold in real-time systems wherein job execution time is known to vary. A second feature of traditional models is their lack of expressiveness, in that constraints more complex than precedence constraints (for instance, relative timing constraints) cannot be modeled. Thirdly, the schedulability of a real-time system depends upon the degree of clairvoyance afforded to the dispatcher. In this paper, we shall discuss Totally Clairvoyant Scheduling, as modeled within the E-T-C scheduling framework (Subramani, 2002). We show that this instantiation of the scheduling framework captures the central issues in a real-time flow-shop scheduling problem and devise a polynomial time sequential algorithm for the same. The design of the polynomial time algorithm involves the development of a new technique, which we term Mutable Dynamic Programming. We expect that this technique will find applications in other areas of system design, such as Validation and Software Verification. We also introduce an error-minimizing performance metric called Violation Degree and establish that optimizing this metric in a Totally Clairvoyant Scheduling System is NP-Hard.