Processor failures in distributed computing that are not crash or Byzantine There are two main types of processor failures in distributed computing models:

(1) Crash failures: a processor stops, and never starts again.
(2) Byzantine failures: processors behave adversarially, maliciously.

My question is:


  What are some other types of processor failures that have been studied, that do not reduce to crash or Byzantine failures?  


Also, a more specific question:


  Has a model been studied where, with some probability, a process is on at time step $t$, and otherwise off?  So each process is winking on and off, as it were.


I am most interested in how these failures relate to consensus and other distributed agreement problems.

Thank you.
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I have taken theory of distributed computing with Michel Raynal and he described a third model, where messages can be dropped randomly. In that model a message can fail silently to be delivered, but that doesn't necessarily mean that the node has failed. It is about link failures rather than node failures "fair lossy channel model", you can read more about it here : Quiescent Uniform Reliable Broadcast as an Introductory Survey to Failure Detector Oracles - Michel Raynal (ftp.irisa.fr/techreports/2000/PI-1356.ps.gz)