A Constant-Approximate Feasibility Test for Multiprocessor Real-Time Scheduling

We devise an approximate feasibility test for multiprocessor real-time scheduling in the sporadic task model. We give an algorithm that, given a task system and $\epsilon>0$, correctly decides either that the task system can be scheduled using the Earliest Deadline First algorithm on m speed-$(2-1/m+\epsilon)$ machines, or that the system is not schedulable by any algorithm on m unit speed machines. This speedup bound is known to be the best possible for EDF. The running time of the algorithm is polynomial in the size of the task system and $1/\epsilon$. We also provide a generalized tight bound that trades off speed with additional machines.