Hardware Reference
In-Depth Information
Hence, the period
T
s
that minimizes the average response time
R
avg
can be computed
i
by simple functional analysis. Thus, we have
d
R
avg
i
d
T
s
(
T
s
U
s
−
)
2
C
avg
,
=1
−
U
s
−
(6.14)
which is equal to zero when
+
C
avg
1
.
1
U
s
T
s
=
(6.15)
−
U
s
6.10
SUMMARY
The experimental simulations have established that from a performance point of view,
IPE, EDL, and TB* show the best results for reducing aperiodic responsiveness. Al-
though optimal, however, EDL is far from being practical, due to the overall complex-
ity. On the other hand, IPE and TB* achieve a comparable performance with much
less computational overhead. Moreover, both EDL and IPE may require significant
memory space when task periods are not harmonically related.
The Total Bandwidth algorithm also shows a good performance, sometimes compara-
ble to that of the nearly optimal IPE. Observing that its implementation complexity is
among the simplest, the TBS algorithm could be a good candidate for practical sys-
tems. In addition, the TBS deadline assignment rule can be tuned to enhance aperiodic
responsiveness up to the optimal TB* behavior. Compared to IPE and EDL, TB* does
not require large memory space, and the optimal deadline can be computed in
O
(
Nn
)
complexity,
N
being the maximum number of steps that have to be done for each task
to shorten its initial deadline (assigned by the TBS rule). As for the EDL server, this
is a pseudo-polynomial complexity since in the worst case
N
can be large.
One major problem of the TBS and TB* algorithms is that they do not use a server
budget for controlling aperiodic execution, but rely on the knowledge of the worst-
case computation time specified by each job at its arrival. When such a knowledge is
not available, not reliable, or too pessimistic (due to highly variable execution times),
then hard tasks are not protected from transient overruns occurring in the soft tasks
and could miss their deadlines. The CBS algorithm can be efficiently used in these
situations, since it has a performance comparable to the one of the TBS and also
provides temporal isolation, by limiting the bandwidth requirements of the served
tasks to the value
U
s
specified at design time.
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