Comment by jhanschoo

> On the other hand, in real life there aren't unlimited numbers of messages and you rarely want to accept infinitely stale messages either, so it's a bit moot.

My understanding is that these happen IRL all the time in the guise of healing a network split or rebooting crashed nodes or bring new uninitialized servers into the system. Of course, IRL you usually translate the result to needing a different strategy to bring these systems up to speed beyond a certain threshold. But these thresholds and strategies and changing the number of nodes in the system are application-dependent, so the fiction of unbounded messages/memory/time helps focus the formal analysis and result.

In the context of, say, a distributed KV store, it cautions you that unless you have said other strategy, you will end up with an inconsistent system or failure state if your message buffers are more space-constrained than required.