Hardware Reference
In-Depth Information
Definition 8.3
The blocking tolerance
β
i
of a task
τ
i
is the maximum amount of block-
ing
τ
i
can tolerate without missing any of its deadlines.
A simple way to compute the blocking tolerance is from the Liu and Layland test,
which according to Equation (7.19) becomes:
C
h
T
h
+
B
i
∀
i
=1
,...,n
T
i
≤
U
lub
(
i
)
h
:
P
h
≥P
i
where
U
lub
(
i
)=
i
(2
1
/i
1) under RM, and
U
lub
(
i
)=1under EDF. Isolating the
blocking factor, the test can also be rewritten as follows:
−
⎛
⎞
C
h
T
h
⎝
U
lub
(
i
)
⎠
.
B
i
≤
T
i
−
h
:
P
h
≥P
i
Hence, considering integer computations, we have:
⎣
T
i
⎛
⎞
⎦
.
C
h
T
h
⎝
U
lub
(
i
)
⎠
β
i
=
−
(8.20)
h
:
P
h
≥P
i
A more precise bound for
β
i
can be achieved by using the schedulability test expressed
by Equation (7.23), which leads to the following result:
∃
t
∈TS
i
:
B
i
≤{
t
−
W
i
(
t
)
}
.
B
i
≤
t∈T S
i
{
max
t
−
W
i
(
t
)
}
.
β
i
=max
t∈T S
i
{
t
−
W
i
(
t
)
}
.
(8.21)
where set
TS
i
has been defined by equation (4.21).
Given the blocking tolerance, the feasible test can also be expressed as follows:
∀
i
=1
,...,n
B
i
≤
β
i
and by Equation (8.19), we can write:
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