Typically, hardware specs are based on a range of nodes. For insance, I cant give you specific specs on 3198 nodes, but there are specs available for 1k - 5k nodes.
1k - 5k should be 2-4 cores @ 2.4GHz or better with 2-4 GB RAM. What usually plays into this also is the IOPS on the disk. For virtual, you are looking for somewhere in the neighborhood of 160 on the package drive. OS drive should be seeing about 180 IOPS.
Going even farther, Zac brought up a good point. How is your WAN handling this? Are you utilizing any type of throttling, maintenance windows, or deployment schedules to not saturate your links?
I know the initial feeling is to get everything out as quick as possible. But, sometimes, a phased and methodical approach will lead to a lot less headaches.
For example, instead of patching 3000 at once, can you stagger the patching schedule? Same goes for plugin pushes.