Hardware Reference
In-Depth Information
C
i
T
i
D
i
τ
1
1
4
3
τ
2
1
5
4
τ
3
2
6
5
τ
4
1
11
10
Table 4.3
A set of periodic tasks with deadlines less than periods.
to be examined for feasibility. In fact, the interference on
τ
i
only increases when there
is a release of a higher-priority task.
To simplify the notation, let
R
(
k
)
i
and let
I
(
k
)
i
be the
k
-th estimate of
R
i
be the inter-
in the interval [0
,R
(
k
)
i
ference on task
τ
i
]:
R
(
k
)
i
T
j
i−
1
I
(
k
)
i
C
j
.
=
(4.18)
j
=1
Then the calculation of
R
i
is performed as follows:
=
j
=1
C
j
, which is the first point in time that
τ
i
could
1. Iteration starts with
R
(0)
i
possibly complete.
in the interval [0
,R
(
k
)
i
2. The actual interference
I
i
] is computed by equation (4.18).
3. If
I
(
k
)
i
+
C
i
=
R
(
k
)
, then
R
(
k
)
i
is the actual worst-case response time of task
τ
i
;
i
that is,
R
i
=
R
(
k
)
. Otherwise, the next estimate is given by
i
R
(
k
+1)
i
=
I
(
k
)
i
+
C
i
,
and the iteration continues from step 2.
Once
R
i
is calculated, the feasibility of task
τ
i
is guaranteed if and only if
R
i
≤
D
i
.
To clarify the schedulability test, consider the set of periodic tasks shown in Table 4.3,
simultaneously activated at time
t
=0. In order to guarantee
τ
4
, we have to calcu-
late
R
4
D
4
. The schedule produced by DM is illustrated in
Figure 4.16, and the iteration steps are shown below.
and verify that
R
4
≤
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