This started happening with the last update. It is not related to the hardware as the machine is generally idle when the lag occurs, so I don't think it is related to the second server running on the same machine. If it was they would both have issues. Plus this specific issue started occurring after the last update, and the two servers have been running side by side for a bit. It is most likely a bug in one of our mods. Seems to cause chunk load times to take forever, and then everything get's backup up.
I would like to be able to determine what is triggering it to occur though. I know around the time we first noticed this there were a lot of chunks generated in the nether, and chunk generation could be a likely cause, but it does not appear to have always happened before lag has started. If you are online at the time when it starts, please check to see what everyone was doing at that time and post it (i.e. jumping into world x, crafting item y, sitting idle, etc).