Hardware Reference
In-Depth Information
5.4.2
DIMENSIONING A DEFERRABLE SERVER
Following the same procedure described in Section 5.3.2, the maximum utilization
U
ma
s
for a Deferrable Server can easily be computed from Equation (5.14), which
can be written, defining
P
as in Equation (5.7), as:
U
s
+2
2
U
s
+1
;
P
≤
that is,
2
−
P
U
s
≤
1
.
2
P
−
Hence,
2
−
P
U
max
s
=
1
.
(5.15)
2
P
−
Then,
T
s
can be set equal to the smallest period
T
1
, so that DS is executed by RM with
the highest priority (assuming that priority ties are broken in favor of the server), and
finally
C
s
=
U
s
T
s
.
5.4.3
APERIODIC GUARANTEE
The online guarantee of a firm aperiodic job can be performed by estimating its worst-
case response time in the case of a DS with the highest priority. Since DS preserves its
execution time, let
c
s
(
t
) be the value of its capacity at time
t
, and let
J
a
an aperiodic
job with computation time
C
a
and relative deadline
D
a
, arriving at time
t
=
r
a
, when
no other aperiodic requests are pending. Then, if
next
(
r
a
)=
T
s
is the next
server activation after time
r
a
, the two cases illustrated in Figure 5.12 can occur:
r
a
/T
s
1. Case (a):
c
s
(
t
)
r
a
. In this case, the capacity is completely dis-
charged within the current period and a portion
C
0
=
c
s
(
t
) of
J
a
≤
next
(
r
a
)
−
is executed in
the current server period.
2. Case (b):
c
s
(
t
)
>next
(
r
a
)
r
a
. In this case, the period ends before the server
capacity is completely discharged; thus a portion
C
0
−
=
next
(
r
a
)
−
r
a
of
J
a
is
executed in the current server period.
In general, the portion
C
0
executed in the current server period is equal to
C
0
=min
{
c
s
(
t
)
,nex
(
r
a
)
−
r
a
}
.
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