Hardware Reference
In-Depth Information
The four assumptions are initially considered to derive some important results on pe-
riodic task scheduling, then such results are extended to deal with more realistic cases,
in which assumptions A3 and A4 are relaxed. In particular, the problem of scheduling
a set of tasks under resource constraints is considered in detail in Chapter 7.
In those cases in which the assumptions A1, A2, A3, and A4 hold, a periodic task
τ
i
can be completely characterized by the following three parameters: its phase Φ
i
, its
period
T
i
and its worst-case computation time
C
i
. Thus, a set of periodic tasks can be
denoted by
{
τ
i
(Φ
i
,T
i
,C
i
)
,i
=1
,...,n
}
.
Γ=
The release time
r
i,k
and the absolute deadline
d
i,k
of the generic
k
th instance can
then be computed as
1)
T
i
d
i,k
=
r
i,k
+
T
i
=Φ
i
+
kT
i
.
Other parameters that are typically defined on a periodic task are described below.
r
i,k
=Φ
i
+(
k
−
Hyperperiod
. It is the minimum interval of time after which the schedule repeats
itself. If
H
is the length of such an interval, then the schedule in [0
,H
] is the
same as that in [
kK,
(
k
+1)
K
] for any integer
k>
0. For a set of periodic
tasks synchronously activated at time
t
=0, the hyperperiod is given by the least
common multiple of the periods:
H
=
lcm
(
T
1
,...,T
n
)
.
Job response time
. It is the time (measured from the release time) at which the
job is terminated:
R
i,k
=
f
i,k
−
r
i,k
.
Task response time
. It is the maximum response time among all the jobs:
R
i
=max
k
R
i,k
.
Critical instant
of a task.
It is the arrival time that produces the largest task
response time.
Critical time zone
of a task. It is the interval between the critical instant and the
response time of the corresponding request of the task.
Relative Start Time Jitter
of a task. It is the maximum deviation of the start
time of two consecutive instances:
RRJ
i
=max
k
|
(
s
i,k
−
r
i,k
)
−
(
s
i,k−
1
−
r
i,k−
1
)
|
.
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