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Recent Hardness Results for Periodic Uni-processor Scheduling
Consider a set of periodic tasks where is described
by an execution time , a (relative) deadline and a period .
We assume that jobs are released synchronously (i.e. at each multiple of ) and consider pre-emptive, uni-processor schedules.
We show that computing the response time of a task in a Rate-monotonic schedule
i.e. computing
[
minleft{ r geq mid c_n + sum_{i=1}^{n-1} leftlceil frac{r}{p_i}
ight
ceil c_i leq r
ight}
]
is (weakly) -hard (where has the lowest priority and the deadlines
are implicit, i.e. ).
Furthermore we obtain that verifying EDF-schedulability, i.e.
[
forall Q geq 0: sum_{i=1}^n left( leftlfloor frac{Q-d_i}{p_i}
ight
floor +1
ight)cdot c_i leq Q
]
for constrained-deadline tasks () is weakly -hard