On-Line Scheduling Algorithm for the Gravitational Task Model

Some applications for real-time scheduling have target demands in addition to the commonly used starttime and deadline constraints: a task should be executed at a target point in time for maximum utility, but can execute around this point, albeit at lower utility. Examples for such applications include control and media processing.In this paper, we present a scheduling algorithm for the gravitational task model that we proposed in~\cite{Guerra:ECRTS08,Guerra:Kluwer09}.This model allows tasks to express their utility as a function of the point of execution and the target point.The proposed scheduler is divided into $2$ phases: ordering and timing. The former uses a heuristic to order the jobs in the ready queue and the latter schedules the execution based on the equilibrium~\cite{Guerra:ECRTS08,Guerra:Kluwer09}.The new ordering heuristic accounts for both acceptance ratio and utility accrual, hence achieving better results than the scheduler proposed in~\cite{Guerra:ECRTS08,Guerra:Kluwer09}. Besides, the scheduler proposed here uses a heuristic for the ordering phase of complexity $O(n \times log (n))$ and a timing phase of complexity $O(n)$.These complexities represent a significant reduction compared to previous work.Moreover, this paper contains an analysis of the complexity of the proposed scheduler and an evaluation through simulation.