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C
T
Server
i
i
τ
2
10
C
= 1
1
s
τ
12
20
T
s
= 5
2
aperiodic
requests
2
1
C
s
1
τ
1
1
2
1
τ
2
0
2
4
6
8
10
12
14
16
18
20
Figure 5.15
Example of aperiodic service under a PE server.
lowest-priority level and
τ
1
is still active,
J
1
is preempted by
τ
1
and is resumed at time
t
=13, when
τ
1
completes.
5.5.1
SCHEDULABILITY ANALYSIS
Considering that, in the worst case, a PE server behaves as a periodic task, the schedu-
lability bound for a set of periodic tasks running along with a Priority Exchange server
is the same as the one derived for the Polling Server. Hence, assuming that PE is the
highest-priority task in the system, we have
U
lub
=
U
s
+
n
K
1
/n
1
.
−
(5.17)
where
K
=
2
U
s
+1
.
Thus, given a set of
n
periodic tasks and a Priority Exchange server with utilization
factors
U
p
and
U
s
, respectively, the schedulability of the periodic task set is guaranteed
under RM if
n
2
U
s
+1
1
.
1
/n
U
p
≤
−
(5.18)
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