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
,β
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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