DESIGN OF A CUSTOM ASIC INCORPORATING CAN™ AND 1 ...

The analysis to bind the worst-case latency of a given hard real-time message is an
almost direct application of processor scheduling theory [68 – 70]. However, there are some
assumptions made by this analysis: first, the deadline of a given message m (denoted Dm) must
not be more than the period of the message (denoted Tm), and second, the bus controller must not
release the bus to lower priority messages if there are higher priority messages pending (i.e. the
controller cannot release the bus between sending one message and entering any pending
message into the arbitration phase).
The worst-case response time of a given message m is denoted by Rm, and is defined as
the longest time between the start of a node queuing m and the latest time that the message
arrives at the destination nodes. From this, the worst-case response time of a given hard real-
time message m can be bound by equation 4.1.
Rm Jm wm Cm
(4.1)
The term Jm is the queuing jitter of message m, and gives the latest queuing time of the message,
relative to the start of the transmitting node. The term wm represents the worst-case queuing
delay of message m (due to both higher priority messages pre-empting message m, and a lower
priority message that has already obtained the bus). The term Cm represents the longest time
taken to physically send message m on the bus. This time includes the time taken by the frame
overheads, the data contents, and extra stuff bits (the CAN protocol specifies that the message
contents and 34 bits of the overhead are subject to bit stuffing with a stuff width of 4 – worst
case of 1 stuff bit for every 4 message bits). The stuff bit counts as the first bit in a new stuffing
sequence. For an 11-bit identifier (slightly different formula below for 29-bit header), only 34 of
the overhead bits are subject to stuffing; others aren’t subject to stuffing. Equation 4.2 gives Cm:
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