  The sporadic task model is often used to analyze recurrent execution of
identical tasks in real-time systems. A sporadic task defines an infinite
sequence of task instances, also called jobs, that arrive under the minimum
inter-arrival time constraint. To ensure the system safety, timeliness has to
be guaranteed in addition to functional correctness, i.e., all jobs of all
tasks have to be finished before the job deadlines. We focus on analyzing
arbitrary-deadline task sets on a homogeneous (identical) multiprocessor system
under any given global fixed-priority scheduling approach and provide a series
of schedulability tests with different tradeoffs between their time complexity
and their accuracy. Under the arbitrary-deadline setting, the relative deadline
of a task can be longer than the minimum inter-arrival time of the jobs of the
task. We show that global deadline-monotonic (DM) scheduling has a speedup
bound of $3-1/M$ against any optimal scheduling algorithms, where $M$ is the
number of identical processors, and prove that this bound is asymptotically
tight.
