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C
0
C
0
C
s
C
s
c
s
(
t
)
c
s
(
t
)
r
a
next
(
r
a
)
r
a
next
(
r
a
)
(b)
(a)
Figure 5.12
Execution of
J
a
in the first server period.
F
a
T
s
δ
a
Δ
a
C
s
c
s
(
t
)
r
a
next
(
r
a
)
f
a
d
a
R
a
Figure 5.13
Response time of an aperiodic job scheduled by a Deferrable Server with the
highest priority.
Using the same notation introduced for Polling Server, we define:
⎧
⎨
Δ
a
=
next
(
r
a
)
−
r
a
=
C
a
−C
0
C
s
F
a
−
1
⎩
δ
a
=
C
a
−
C
0
−
F
a
C
s
.
Hence, as depicted in Figure 5.13, the response time
R
a
of job
J
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
−
C
0
+
F
a
(
T
s
−
C
s
)
.
(5.16)
Note that the term
F
a
(
T
s
−
C
s
) in Equation (5.16) 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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