Schedulability tests based on utilization
RM Scheduling
Schedulability tests for RM based on task utilization.
Valid with preemption, n independent tasks, D=T.
Liu&Layland’s (1973), Least Upper Bound (LUB).
Bini&Buttazzo&Buttazzo’s (2001), Hyperbolic Bound.
Interpretation of the Liu&Layland test
Some values
Example 1
Task properties.
Example 2
Task properties.
But the task set is schedulable (see Gantt chart).
Example 3
Task set properties.
And the task set indeed is not schedulable (see Gantt chart).
Harmonic Periods
Particular case: if the task periods are harmonic then the task set is schedulable iif U(n) ≤ 1.
E.g. Γ = {(1, 2); (2, 4)}
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