Hardware Reference
In-Depth Information
Note that, being Q i
C i for all i 's, all tasks can execute non preemptively.
8.4
Under Rate Monotonic, using the Liu and Layland test, the blocking tolerance
of each task can be computed by Equation (8.20):
U lub ( i )
.
i
C h
T h
β i = T i
h =1
And, according to Theorem (8.2), Q i results to be:
Q i =min
{
Q i− 1 i− 1 +1
}
where Q 1 =
and β 1 = D 1
C 1 . Hence, we have
U lub ( i ) i h =1 U h
β i
Q i
τ 1
1.0
1/4
6
τ 2
0.828
9/20
3
7
τ 3
0.780
37/60
4
4
τ 4
0.757
42/60
3
4
τ 5
0.743
44/60
0
4
Hence, to make the task set schedulable under RM, one preemption point must
be inserted in τ 3 and τ 4 .
8.5
First of all, from the task structures, the following parameters can be derived:
q max
i
q last
i
C i
T i
U i
B i
τ 1
6
24
1/4
3
0
7
τ 2
10
40
1/4
4
4
7
τ 3
18
120
3/20
8
5
5
τ 4
15
150
1/10
6
6
0
We note that since the total utilization is U =0 . 75, the task set is schedulable
under Rate Monotonic in fully preemptive mode (in fact U lub (4) = 0 . 757).
Hence, the worst-case response time of each task can be computed considering
the first job under the critical instant, using Equations (8.32) and (8.33).
For task τ 1 we have
R 1
=
B 1 + C 1 =7+6=13 .
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