Hardware Reference
In-Depth Information
1
0.95
PS bound
RM bound
0.9
0.85
0.8
0.75
0.7
0.65
0.6
0
0.2
0.4
0.6
0.8
1
Server Utilization factor Us
Figure 5.5
Schedulability bound for periodic tasks and PS as a function of the server
utilization factor
U
s
.
Finally, the response time of a periodic task
τ
i
in the presence of a Polling Server at the
highest priority can be found as the smallest integer satisfying the following recurrent
relation:
R
i
=
C
i
+
R
i
T
s
C
s
+
R
i
T
j
C
j
.
i−
1
(5.6)
j
=1
5.3.2
DIMENSIONING A POLLING SERVER
Given a set of periodic tasks, how can we compute the server parameters (
C
s
and
T
s
)
that can guarantee a feasible schedule? First of all, we need to compute the maxi-
mum server utilization
U
ma
s
that guarantees the feasibility of the task set. Since the
response time is not easy to manipulate, due to the ceiling functions, we can derive
U
ma
s
from the hyperbolic test of Equation (5.5), which is tighter than the utilization
test of Equation (5.4). If we define
n
de
=
P
(
U
i
+1)
,
(5.7)
i
=1
for the schedulability of the task set, from Equation (5.5), it must be
2
U
s
+1
;
P
≤
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