Players are bouncing off a full server
What it looks like in your log
lost connection: The server is full!
What causes it
Joins were refused because the server was already at max-players.
How to fix it
Raise max-players in server.properties and restart. Watch RAM as you do it: every extra player loads more chunks and entities, so a slot raise on a box that is already tight buys you lag instead of players. Ops can bypass the limit; ordinary players cannot.
Not sure this is your problem? Paste your log and Roastd will tell you which of these it actually matched, and what else it found.
Check your own log