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C
i
T
i
Server
τ
4 0
C
= 1
1
s
τ
8 0
T
= 5
2
s
aperiodic
1
1
requests
C
s
1
τ
1
1
2
1
τ
2
0
2
4
6
8
10
12
14
16
18
20
Figure 5.14
Example of aperiodic service under a PE server.
of
τ
1
. At time
t
=4,
τ
1
completes and
τ
2
begins to execute. Again, since no aperiodic
tasks are pending, another exchange takes place between
τ
1
and
τ
2
. At time
t
=5, the
capacity is replenished at the server priority, and it is used to execute the first aperiodic
request. At time
t
=10,
C
s
is replenished at the highest priority, but it is degraded
to the priority level of
τ
1
for lack of aperiodic tasks. At time
t
=12, the capacity
accumulated at the priority level of
τ
1
is used to execute the second aperiodic request.
At time
t
=15, a new high-priority replenishment takes place, but the capacity is
exchanged with the execution time of
τ
2
. Finally, at time
t
=18, the remaining
capacity accumulated at the priority level of
τ
2
is gradually discarded because no tasks
are active.
Note that the capacity overlapped to the schedule of a periodic task indicates, at any
instant, the amount of time by which the execution of that task is advanced with respect
to the case where there is no exchange.
Another example of aperiodic scheduling under the PE algorithm is depicted in Fig-
ure 5.15. Here, at time
t
=5, the capacity of the server immediately degrades down
to the lowest-priority level of
τ
2
, since no aperiodic requests are pending and
τ
1
is
idle. At time
t
=11, when request
J
1
arrives, it is interesting to observe that the
first unit of computation time is immediately executed by using the capacity accumu-
lated at the priority level of
τ
1
. Then, since the remaining capacity is available at the
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