As the title says. After testing around for a bit, I found that using --max-connections=500 --wait-timeout=600 or any of them to start the MySQL server for LuckPerms(bukkit & bungee) will make LuckPerms complain, for example:

17:09:49 [SEVERE] [LuckPerms Pool Thread #724] WARN com.zaxxer.hikari.pool.PoolBase - luckperms - Failed to validate connection com.mysql.jdbc.JDBC4Connection@6e9b20d9 (Communications link failure

The last packet successfully received from the server was 359,978 milliseconds ago.  The last packet sent successfully to the server was 1 milliseconds ago.)

Using no flag to launch the MySQL server seems to be fine. So, I wonder what would be the best value for them?

I've been watching this problem for several months now. The source is not yet understood but I do know that this is a third-party plugin. If you remove ScoreboardStats, then this problem is not observed. But on the other server with ScoreboardStats this error is absent. The problem is very serious, although I'm a little lazy to fix it.

I'm not too sure to be honest.

Here are the settings used by the LuckPerms pool:
https://github.com/lucko/LuckPerms/blob/master/common/src/main/java/me/lucko/luckperms/common/storage/backing/sqlprovider/MySQLProvider.java#L74-L101

You might find some more info to help here as well:
https://github.com/brettwooldridge/HikariCP/wiki

I'm still testing. I was using MySQL server, I switched to MariaDB server and the problem seems still exists. Maybe you want to keep the issue open so I can post further more information here, so if anyone else have the same problem we can discuss here?

Okay, I found something interesting.

According to my research on Google, people say that the

The last packet successfully received from the server was 359,978 milliseconds ago.

exception can be caused by a MySQL db connection which has been marked as timed-out by the MySQL server, thus the DB driver won't be able to use the same connection again.

Adjusting wait-timeout of the MySQL server should solve the problem. I'm still testing.

@simon44556 Left it like what?

The mysql configuration I have it set like this I think it is the default config:
max_connections = 300
connect_timeout = 5
wait_timeout = 600

I get the same error sometimes. I believe it just creates a new connection when the old one goes inactive so you shouldn't have any problem with this. I tried before to increase the timeout but then I get much worse performance with luckperms so I just left it like this.

I saw this from the LiteBans config:

  # LiteBans utilizes connection pooling for extra performance and reliability.
  # min_connections: Minimum amount of pooled connections.
  # max_connections: Maximum amount of pooled connections. See: https://github.com/brettwooldridge/HikariCP/wiki/About-Pool-Sizing
  # timeout: Connection timeout.
  # idle_timeout: Maximum amount of time a pooled connection can remain idle before it is closed for inactivity.
  pool:
    min_connections: 1
    max_connections: 10
    timeout: 30 seconds
    idle_timeout: 1 minute

LiteBans uses the same MySQL driver, so LuckPerms could implement the same thing too?

I linked you the LP settings above. It already uses similar options, and the pool size is configurable.

Idle timeout is whatever the default for Hikari is.