如何找到MySQL / PHP中“太多连接”错误的根本原因

I'm running a web service which runs algorithms that serve millions of calls daily and run some background processing as well. Every now and than I see "Too many connections" error in attempts to connect to the MySQL box" for a few seconds. However this is not necessarily attributed to high traffic times or anything I can put my finger on.I'm running a web service which runs algorithms