Hardware Reference
In-Depth Information
normal execution
critical section
τ
1
blocked
τ
2
τ
3
p
3
P
1
P
2
P
3
Figure 7.7
Example of schedule under HLP, where
p
3
is raised at the level
C
(
R
)=
P
2
as soon as
τ
3
starts using resource
R
.
Note that the schedule produced under HLP for the example generating priority inver-
sion is the same as the one shown in Figure 7.5, since the ceiling of the shared resource
is
P
1
(the highest priority). Figure 7.7 shows another example in which the ceiling of
the shared resource is
P
2
; hence
τ
1
can preempt
τ
3
inside the critical section, whereas
τ
2
is blocked until
τ
3
exits its critical section. The figure also shows how the active
priority of
τ
3
is varied by the protocol during execution.
7.5.1
BLOCKING TIME COMPUTATION
Under HLP, a task
τ
i
can only be blocked by critical sections belonging to lower
priority tasks with a resource ceiling higher than or equal to
P
i
. Hence,
γ
i
=
{
Z
j,k
|
(
P
j
<P
i
) and
C
(
R
k
)
≥
P
i
}
.
Moreover, a task can be blocked at most once, as formally stated in the following
theorem.
Theorem 7.1
Under HLP, a task
τ
i
can be blocked, at most, for the duration of a
single critical section belonging to the set
γ
i
.
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