The Hyperbolic Schedulability Bound for Multiprocessor RM Scheduling

To verify the feasibility of real-time task sets on homogeneous multiprocessor systems, Lopez et al. derived the utilization bound based on Best Fit Decreasing allocation algorithm and Rate-Monotonic scheduling, which coincides with the maximum achievable multiprocessor utilization bound, using Liu & Lyland bound as the uniprocessor schedulability condition. In this paper, a novel feasibility test for the same target problem is developed based on the hyperbolic bound due to Bini et al., instead of the Liu & Layland bound. Analytical and experimental results show that the proposed utilization bound performs better than the existing bound under quite a lot of parameter settings, and combining these two bounds together can significantly increase the number of schedulable task sets with little extra overhead.