Image Processing Reference
In-Depth Information
R
m
w
m
J
m
C
m
B
m
C
j
C
j
C
j
Msg.
k
Msg.
j
Msg.
i
Msg.
j
Msg.
l
Msg.
j
Message
m
t
start(
m
)
t
win(
j,
1)
t
win(
j,
2)
t
win(
j,
3)
t
win(
m
)
t
end(
m
)
t
req(
m
)
t
start(
j,
1)
t
start(
j,
2)
t
start(
j,
3)
t
start(
j,
4)
t
req(
j,
2)
t
req(
j,
3)
t
req(
j,
4)
t
req(
j,
1)
J
j
T
j
T
j
T
j
FIGURE .
Blocking time and interference.
interference, as the related transmission request takes place after the SOF bit of message
m
has been
successfully sent (and no other higher priority message is queued waiting for transmission at that
time). It is worth noting that the generation of interfering messages could be affected by jitters as
well,becauseoftheoverheadofnetworkcontrollers(e.g.,
J
j
in Figure .).
At the same time, however, the queuing delay
w
m
depends on both the blocking time
B
m
and the
interference caused by all higher priority messages, which in turn depends on
h
parameters and their
duration
C
w
m
=
B
m
+
j
m
(
h
m
,
j
⋅
C
j
)
<
This leads to the following recurrence relation, which provides the transmission delay at step
n
+
given the one at step
n
w
m
+
J
j
+
t
bit
w
n
+
=
B
m
+
j
m
⌈
⌉⋅
C
j
m
T
j
<
From a practical point of view, the evaluation of
w
m
proceeds as follow: the initial value
w
m
is
set to , then the recurrence relation is repeatedly evaluated until either the value of
w
m
settles
(i.e.,
w
n
m
equals
w
m
)orthedeadline
D
m
is exceeded. Convergence of this iterative approach is
ensured, provided that network utilization
U
MS
is below one.
The above technique enables the evaluation of the transmission delay (and, consequently, of
the worst-case transmission time) for every single message. Then, by checking it against message
deadlines, the schedulability of the whole message set
MS
canbeassessed.
In , Davis et al. [DAV] found that, in some cases, the above analysis is optimistic. Despite it
was able to correct the flaws in the original method, the newer version of the schedulability test they
introduced was more complex, hence it lost a bit in usability. If approximate results are acceptable,
an easy way to compute (correctly) the recurrence relation is the following
+
w
m
+
J
j
+
t
bit
w
n
+
=
B
MAX
+
j
m
⌈
⌉⋅
C
j
m
T
j
<
