Hardware Reference
In-Depth Information
From the CBS analysis, we know that, if the task set is feasible, that is, if the total
processor utilization is less than 1, then the served job can never miss the current
server deadline. Hence, the maximum response time
R
i
occurs when the other tasks
in the system create the maximum interference on the server. If the computation time
C
i
of the served job is exactly a multiple of the server budget
Q
s
, then the job finishes
at the server deadline; that is,
C
i
Q
s
C
i
U
s
R
i
=
T
s
=
.
(6.6)
More generally, if the computation time
C
i
of the job is not multiple of the budget
Q
s
,
the last portion of the job will not finish at the server deadline, but it will finish at most
Δ
i
units before the deadline, as shown in Figure 6.19, where
Δ
i
=
C
i
Q
s
Q
s
−
C
i
.
(6.7)
Δ
i
J
i
t
d
i
d
i
Q
s
t
Figure 6.19
Worst-case finishing time of a job served by a CBS.
Hence, the response time of the job becomes
C
i
Q
s
T
s
−
R
i
=
Δ
i
C
i
Q
s
T
s
−
C
i
Q
s
Q
s
−
C
i
=
C
i
+
C
i
Q
s
(
T
s
−
=
Q
s
)
.
(6.8)
Figure 6.20 illustrates the worst-case response time of a CBS as a function of the
budget.
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