Synchrony/Asynchrony vs. Stationary/Mobile? The Latter is Superior...in Theory

Like Asynchrony, Mobility of faults precludes consensus. Yet, a model M in which Consensus is solvable, has an analogue relaxed model in which Consensus is not solvable and for which we can ask, whether Consensus is solvable if the system initially behaves like the relaxed analogue model, but eventually morphs into M. We consider two relaxed analogues of M. The first is the traditional Asynchronous model, and the second to be defined, the Mobile analogue. While for some M we show that Consensus is not solvable in the Asynchronous analogue, it is solvable in all the Mobile analogues. Hence, from this perspective Mobility is superior to Asynchrony. The pie in the sky relationship we envision is: Consensus is solvable in M, if and only if binary Commit-Adopt is solvable in the mobile analogue. The ``only if'' is easy. Here we show case by case that the ``if'' holds for all the common faults types.