Hardware Reference
In-Depth Information
τ
i
t
t
2
1
Figure 4.18
The instances in dark gray are those contributing to the processor demand in
[
t
1
,t
2
]
.
For the whole task set, the processor demand in [
t
1
,t
2
] is given by
n
g
(
t
1
,t
2
)=
g
i
(
t
1
,t
2
)
.
i
=1
Then, the feasibility of a task set is guaranteed if and only if
in any interval of time
the
processor demand does not exceed the available time; that is, if and only if
∀
t
1
,t
2
g
(
t
1
,t
2
)
≤
(
t
2
−
t
1
)
.
Referring to Figure 4.18, the number of instances of task
τ
i
that contribute to the
demand in [
t
1
,t
2
] can be expressed as
η
i
(
t
1
,t
2
)=
max
0
,
t
2
+
T
i
−
t
1
−
D
i
−
Φ
i
Φ
i
−
T
i
T
i
and the processor demand in [
t
1
,t
2
] can be computed as
n
g
(
t
1
,t
2
)=
η
i
(
t
1
,t
2
)
C
i
.
(4.24)
i
=1
If relatives deadlines are no larger than periods and periodic tasks are simultaneously
activated at time
t
=0(i.e., Φ
i
=0for all the tasks), then the number of instances
contributing to the demand in an interval [0
,L
] can be expressed as:
η
i
(0
,L
)=
L
+
T
i
−
.
D
i
T
i
Thus, the processor demand in [0
,L
] can be computed as
L
+
T
i
−
C
i
.
n
D
i
g
(0
,L
)=
T
i
i
=1
Function
g
(0
,L
) is also referred to as Demand Bound Function:
t
+
T
i
−
C
i
.
n
D
i
de
=
dbf
(
t
)
(4.25)
T
i
i
=1
Search WWH ::
Custom Search