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domain the set of positive real numbers (non-negative integers). We present the
following well-known concepts in the theory of aperiodic real-time scheduling
Layland and Liu (
1973
):
An aperiodic task
nite collection of jobs that have their
request times constrained by a Worst Case Execution Time (WCET) Ci
i
and a
relative deadline Di.
i
.
τ
i
(C
i
; D
i
)isanin
Deadline: The time when a task must be
finished executing.
Worst Case Execution Time (WCET): The longest possible execution time for a
task on a particular type of system.
Response time: The time it takes a task to
finish execution. Measured from
release time to execution completes, including preemptions.
Preemptive scheduling: an executing task may be interrupted at any instant in
time and have its execution resumed later.
Release/ready time: The time a task is ready to run and just waits for the
scheduler to activate it.
A busy period is idle
ned as a time interval [a, b) such that there is no idle time in
[a, b) (the processor is fully busy) and such that both a and b are idle times.
¼
P
i¼1
C
i
U
T
i
is the processor utilization factor. In the case of synchronous and
asynchronous,
¼
P
i¼1
C
i
independent and periodic tasks. U
min
ð
T
i
;
D
i
Þ
1isa
suf
cient condition but not necessary for the EDF-based scheduling of real-time
tasks.
A hard real-time task is never allowed to miss a deadline because that can lead
to complete failure of the system. A hard real-time task can be safety-critical and
this means that if a deadline is missed it can lead to catastrophically conse-
quences which can harm persons or the environment.
A soft real-time task is a task when a deadline is allowed to be missed, while
there is no complete failure of the system, it can lead to decreased performance.
Mapping is the process of assigning each task in an application to a processor,
such that the processor executes the task and satis
es the task deadline, as well
as other constraints (power, throughput, completion time), if any.
Polling Server is a periodic task whose purpose is to provide relatively high
priority service to aperiodic task requests with a period T
S
, a computation time
C
S
(capacity) and scheduled in the same way as periodic tasks. It is ready to run
at the start of its period and services pending arriving aperiodic tasks over the
interval from the beginning of its period until C
S
time units later. The polling
server task is subject to preemption by higher priority tasks, until either it
exhausts its execution time or there is no execution time of aperiodic tasks left to
be executed. Otherwise, the polling server loses any of the unused execution
time and is unavailable to service aperiodic tasks until the start of its next period.
The polling server task is scheduled as if it was a periodic task with period if
S
.
Aperiodic tasks that arrive or remain when the polling server is unavailable can
be serviced at background priority.
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