Hardware Reference
In-Depth Information
3
7
DPE
0
6
12
18
24
3
τ
1
0
8
16
24
3
τ
2
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Figure 6.1
Dynamic Priority Exchange server example.
C
1
S
2
is completely consumed. Note that at time
t
=6the server capacity
C
s
=
C
1
S
is
set at value 3 and is preserved until time
t
=8, when it becomes the highest-priority
entity in the system (ties among aperiodic capacities are assumed to be broken in a
FIFO order). At time
t
=8, two units of
C
1
S
are exchanged with
C
1
S
1
, while the third
unit of the server is consumed since the processor is idle.
At time
t
=14, an aperiodic request,
J
1
, of seven units of time enters the system.
Since
C
1
S
=2, the first two units of
J
1
are served with deadline 18, while the next
two units are served with deadline 24, using the capacity
C
2
S
2
. Finally, the last three
units are also served with deadline 24 because at time
t
=18the server capacity
C
2
S
is set to 3.
6.2.1
SCHEDULABILITY ANALYSIS
The schedulability condition for a set of periodic tasks scheduled together with a DPE
server is now analyzed. Intuitively, the server behaves like any other periodic task.
The difference is that it can trade its runtime with the runtime of lower-priority tasks.
When a certain amount of time is traded, one or more lower-priority tasks are run at a
higher-priority level, and their lower-priority time is preserved for possible aperiodic
requests. This run-time exchange, however, does not affect schedulability; thus, the
periodic task set can be guaranteed using the classical Liu and Layland condition:
U
p
+
U
s
≤
1
,
where
U
p
is the utilization factor of the periodic tasks and
U
s
is the utilization factor
of the DPE server.
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