Hardware Reference
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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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