Hardware Reference
In-Depth Information
Z
(
t
)
3Q
2Q
α
Q
Δ
t
0
Q
2(
P − Q
)
Figure 9.20
A reservation implemented by a static partition of intervals.
Expressing
Q
k
and
T
k
as a function of
α
k
and Δ
k
we have
α
k
Δ
k
2(1
Q
k
=
−
α
k
)
Δ
k
P
k
=
α
k
)
.
2(1
−
Hence,
=
α
k
+
2
σ
(1
−
α
k
)
α
e
k
.
(9.18)
Δ
k
Within a reservation, the schedulability analysis of a task set under fixed priorities can
be performed by extending Theorem 4.4 as follows [BBL09]:
Theorem 9.3
A set of preemptive periodic tasks with relative deadlines less than or
equal to periods can be scheduled by a fixed priority algorithm, under a reservation
characterized by a supply function
Z
k
(
t
)
, if and only if
∀
i
=1
,...,n
∃
t
∈TS
i
:
W
i
(
t
)
≤
Z
k
(
t
)
.
(9.19)
where
W
i
(
t
)
is defined by Equation
(4.19)
and
TS
i
by Equation
(4.21)
.
Similarly, the schedulability analysis of a task set under EDF can be performed by
extending Theorem 4.6 as follows [BBL09]:
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