MC-Fluid: simplified and optimally quantified

The fluid scheduling model allows for schedules in which an individual task may be assigned a fraction of a processor at each time instant. These assignments are subject to the constraints that no fraction exceeds one and the sum of all the assigned fractions do not exceed the sum of the computing capacities of all the processors at any instant. An algorithm, MC-Fluid, has recently been proposed for scheduling systems of mixed-criticality implicit-deadline sporadic tasks under the fluid scheduling model. MC-Fluid has been shown to have a speedup bound no worse than (1 + root 5)/2 or approximate to 1.618 for scheduling dual-criticality systems. We derive here a simplified variant of MC-Fluid called MCF, that has run-time linear in the number of tasks. We prove that this simplified variant has a speedup bound no worse than 4/3 for dual-criticality systems, and show that this implies that MC-Fluid, too, has a speedup bound no worse than 4/3. We know from prior results in uniprocessor mixed-criticality scheduling that no algorithm may have a speedup bound smaller than 4/3, allowing us to conclude that MCF and MC-Fluid are in fact speedup-optimal for dual-criticality scheduling.