While ethernet will support all of the functions that CAN, LIN and Flexray currently perform, I would dare say the costs at this stage would be prohibative for most major OEMs.
The old adage of "if it aint broke dont fix it" fits quite well, CAN and LIN a suitable for for their respective functions in an automotive application (such as door locking, window control etc), especially vs cost per unit, so why change .
Where ethernet will thrive is in the ADAS, infotainment and active safety, where the cost will be outweighed by the bandwidth and speed that ether can deliver. not to mention utilising POE (power over ethernet) to streamline harnessing to support small current devices such as cameras.
It was bound to happen. I've been involved in digital control system networks for the vast majority of my career. And I've seen any number of special purpose schemes giving way to IP/Ethernet, as Ethernet speeds have increased.
You can even see this in the commercial sector. For example, way back in the 1980s and early 1990s, starting with the telcos of Scandinavian countries, interest was mounting in migrating digital telephony from the strict circuit-oriented architectures, such as those in ISDN, the old DSn standards, SONET, and ATM, to packet-switched IP over Ethernet.
The automotive CAN bus is probably following this same trend.
Original objections are always about "predictability." However what invariably happens is, if the network speed is much higher than that of these criticial signals, then predicability can statistically be "guaranteed" anyway. And by the way, math works. The idea has merit.
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