Hardware Reference
In-Depth Information
aperiodic requests in the interval [10
,
14], prevents task
τ
2
from executing during this
interval, causing its deadline to be missed.
Such an invasive behavior of the Deferrable Server results in a lower schedulability
bound for the periodic task set. The calculation of the least upper bound of the proces-
sor utilization factor in the presence of Deferrable Server is shown in the next section.
U
LUB
FOR RM+DS
CALCULATION OF
The schedulability bound for a set of periodic tasks with a Deferrable Server is derived
under the same basic assumptions used in Chapter 4 to compute
U
lub
for RM. To
simplify the computation of the bound for
n
tasks, we first determine the worst-case
relations among the tasks, and then we derive the lower bound against the worst-case
model [LSS87].
Consider a set of
n
periodic tasks,
τ
1
,...,τ
n
, ordered by increasing periods, and a De-
ferrable Server with a higher priority. The worst-case condition for the periodic tasks,
as derived for the RM analysis, is such that
T
1
<T
n
<
2
T
1
. In the presence of a DS,
however, the derivation of the worst-case is more complex and requires the analysis of
three different cases, as discussed by Strosnider, Lehoczky, and Sha [SLS95]. For the
sake of clarity, here we analyze one case only, the most general, in which DS may ex-
ecute three times within the period of the highest-priority periodic task. This happens
when DS defers its service at the end of its period and also executes at the beginning of
the next period. In this situation, depicted in Figure 5.10, the full processor utilization
is achieved by the following tasks' parameters:
⎧
⎨
(
T
s
+
C
s
)=
T
1
−T
s
2
C
s
=
T
1
−
C
1
=
T
2
−
T
1
C
2
=
T
3
−
T
2
...
C
n−
1
=
T
n
−
⎩
T
n−
1
C
s
−
n−
1
3
T
s
+
T
1
−
2
T
n
2
C
n
=
T
s
−
C
i
=
.
i
=1
Hence, the resulting utilization is
C
s
T
s
+
C
1
T
1
+
...
+
C
n
T
n
U
=
=
U
s
+
T
2
−
T
1
+
...
+
T
n
−
T
n−
1
T
n−
1
+
3
T
s
+
T
1
−
2
T
n
=
=
T
1
2
T
n
+
3
T
s
2
T
1
T
1
T
n
−
U
s
+
T
2
T
1
T
n
T
n−
1
+
1
2
+
...
+
n.
=
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