max_user_connections

By running the query SHOW PROCESSLIST; or SELECT * FROM INFORMATION_SCHEMA.PROCESSLIST; you can see all of the running queries on your database as well as count the rows to determine how many connections are open on the database.  If you just want to get the number of connections and not the details on those connections you can run a query such as SELECT COUNT(*) FROM INFORMATION_SCHEMA.PROCESSLIST;

Reference :
https://community.rackspace.com/products/f/26/t/4091

https://community.rackspace.com/community_central/f/10/t/4471