Hardware Reference
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Δ
a
δ
a
F
a
T
s
C
s
r
a
next
(
r
a
)
f
a
d
a
R
a
Figure 5.6
Response time of an aperiodic job scheduled by a Polling Server with the
highest priority.
A sufficient and necessary schedulability test can be derived for the case in which the
PS has the highest priority among the periodic tasks; that is, the shortest period. In
this case, in fact, it always executes at the beginning of its periods; thus the finishing
time of the aperiodic request can be estimated precisely. As shown in Figure 5.6, by
defining
C
a
C
s
de
=
F
a
−
1
r
a
T
s
T
s
de
=
next
(
r
a
)
the initial delay of request
J
a
is given by Δ
a
=
next
a
(
r
a
)
−
r
a
. Then, since
F
a
C
s
is the total budget consumed by
J
a
in
F
a
server periods, the residual execution to be
done in the next server period is
δ
a
=
C
a
−
F
a
C
s
.
As a consequence, the response time
R
a
can be computed as
R
a
=Δ
a
+
F
a
T
s
+
δ
a
,
which can be also written as:
R
a
=Δ
a
+
C
a
+
F
a
(
T
s
−
C
s
)
.
(5.9)
Note that the term
F
a
(
T
s
−
C
s
) in Equation (5.9), represents the delay introduced by
the
F
a
inactive server intervals, each of size (
T
s
−
C
s
).
Then, the schedulability of the aperiodic job can be guaranteed if and only if
R
a
≤
D
a
.
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