Image Processing Reference
In-Depth Information
All of the above parameters are defined in the design phase of the control system, and do not depend
specifically on the characteristics of the network used to interconnect devices. Starting from them
severalotherparameterscanbederived,thatwillbeuseddirectlytoassessthenetworkschedulability:
•
Transmission time
:TimetakentotransmitseriallyovertheCANbusallthebitsof
the frame that embeds message
m
(when the transmitting node wins the arbitration)
•
Worst-case response time
(
C
m
)
: Maximum end-to-end response time that message
m
may
experience under the given conditions (message set
MS
and bit rate
R
on the network)
•
Worst-case queuing delay
(
R
m
)
,alsoknownas
transmission delay
:Maximumdelaythe
transmitting node of message
m
may experience before it wins the arbitration (or, better,
before it starts the successful transmission of the frame)
•
Utilization
(
w
m
)
: Fraction of the available network bandwidth needed to exchange all
the messages included in the message set
(
U
MS
)
The frame transmission time
C
m
can be computed directly from the message size
S
m
by taking into
account the overhead due to the protocol control information added by CAN. Besides fixed size fields
(e.g., identifier, DLC, CRC, etc.), a variable number of stuff bits are inserted into the transmitted frame
bythebitstuingmechanismofCAN,whichdependsontheactualcontentoftheframe.Aswewant
schedulability to be always ensured, the worst case has to be considered (i.e., when the maximum
number of stuff bits are added).
Each CAN frame includes bits of protocol control information (i.e., SOF, arbitration, control,
CRC, ACK, and EOF fields, as well as intermission). he bit stuffing mechanism affects of those
bits (from the SOF bit up to the CRC field), and the data field (payload) too. Up to one stuff bit could
be added every bits of the original frame (an exception is at the very beginning of the frame, where
the stuff bit can be added only after bits), and this means that the (worst-case) transmission time
C
m
is simply given by
+
⋅
S
m
−
C
m
=(
+
⋅
S
m
+⌊
⌋+
)⋅
T
bit
=(
+
⋅
S
m
)⋅
T
bit
where
R
is the transmission speed
T
bit
=
/
R
is the bit time in the network
Amessagesetissaidtobeschedulableiftheresponsetimeofeverymessageinthesetisalways
(i.e., in the worst case, too) lower than or equal to its deadline. his means, that the condition
R
m
≤
D
m
must hold for every message
m
in
MS
.
Schedulability in a CAN network is tightly related to the network utilization
U
MS
.hisparameter
canbeeasilycomputedfromthetransmissiontimeandperiodofthemessagesinthemessagesetas
C
m
T
m
U
MS
=
m
∈
MS
Obviously, utilization must be strictly less than in order to ensure feasibility of the schedule (this
means,theoferedloadisnotallowedtoexceedtheavailablebandwidth).Itisworthnoting,however,
that despite necessary this condition is not sufficient to ensure schedulability.
Let
t
req
be the time the transmission request for message
m
is issued in the originating node,
(
m
)
t
start
thetimethetransmissiononthebusoftherelatedframecanbeirststarted(irrespective
of whether or not the transmitting node will win the contention),
t
win
(
m
)
the time the successful
(
m
)
