Semi-Federated Scheduling of Parallel Real-Time Tasks on Multiprocessors

Federated scheduling is a promising approach to schedule parallel real-time tasks on multi-cores, where each heavy task exclusively executes on a number of dedicated processors, while light tasks are treated as sequential sporadic tasks and share the remaining processors. However, federated scheduling suffers resource waste since a heavy task with processing capacity requirement $x + \epsilon$ (where $x$ is an integer and $0 < \epsilon < 1$) needs $x + 1$ dedicated processors. In the extreme case, almost half of the processing capacity is wasted. In this paper we propose the semi-federate scheduling approach, which only grants $x$ dedicated processors to a heavy task with processing capacity requirement $x + \epsilon$, and schedules the remaining $\epsilon$ part together with light tasks on shared processors. Experiments with randomly generated task sets show the semi-federated scheduling approach significantly outperforms not only federated scheduling, but also all existing approaches for scheduling parallel real-time tasks on multi-cores

The Fenchel-type inequality in the 3-dimensional Lorentz space and a Crofton formula

We generalize the Fenchel theorem to strong spacelike (which means that the tangent vector and the curvature vector span a spacelike 2-plane at each point) closed curves with index 1 in the 3-dimensional Lorentz space, showing that the total curvatures must be less than or equal to $2\pi$. A similar generalization of the Fary-Milnor theorem is also obtained. We establish the Crofton formula on the de Sitter 2-sphere which implies the above results.Comment: 9 pages, 4 figures. Comments are welcom