I've been running for 3 and a half days and I notice that my work queue is now short and that it says that there are only 4,880 work units waiting on the server, so we'll be through them shortly.

Does this happen often? Have we finished all the jobs they had scheduled?

Jobs are scheduled throughout the week. The crunching power of the R@h volunteers has roughly gone up 500% in the past two weeks as shown in this post

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Rosetta Moderator: Mod.Sense

One thing I've done (but it's a bit wonky to set up) is to make World Community Grid my backup project by setting its resource share (which they call "project weight") to zero and then joining my Rosetta systems to WCG as well. That way, if no Rosetta units are forthcoming, it can seamlessly switch to WCG.

Some pointers: https://boinc.berkeley.edu/wiki/Preferences