Abstract 
Partitioned multiprocessor scheduling has been widely accepted in academia and industry to statically assign and partition realtime tasks onto identical multiprocessor systems. This paper studies fixedpriority partitioned multiprocessor scheduling for sporadic realtime systems, in which deadlinemonotonic scheduling is applied on each processor. Prior to this paper, the best known results are by Fisher, Baruah, and Baker with speedup factors $4\frac{2}{M}$ and $3\frac{1}{M}$ for arbitrarydeadline and constraineddeadline sporadic realtime task systems, respectively, where $M$ is the number of processors. We show that a greedy mapping strategy has a speedup factor $3\frac{1}{M}$ when considering task systems with arbitrary deadlines. Such a factor holds for polynomialtime schedulability tests and exponentialtime (exact) schedulability tests. Moreover, we also improve the speedup factor to $2.84306$ when considering constraineddeadline task systems. We also provide tight examples when the fitting strategy in themapping stage is arbitrary and $M$ is sufficiently large. For both constrained and arbitrarydeadline task systems, the analytical result surprisingly shows that using exact tests does not gain theoretical benefits (with respect to speedup factors) if the speedup factor analysis is oblivious of the particular fitting strategy used.
