There is not really a rule of thumb other than Jamf's operating assumption that the database processes consecutive connections faster than concurrent ones ironically. They do have a formula for determining a baseline though that I have been taught by a few Jamf's (but this is not universal).
So assuming a max pool size in Tomcat of 45:
you would take 45 times the number of Tomcat web apps you have connecting to the database and add a single connection for you to get into MySQL in a crisis situation.
On a single standalone JSS that would give you a max connection value of 46. If you have a single server plus a DMZ Tomcat instance that would be (45 x 2) + 1 = 91
Now Max packet size is the only other value to consider on the MySQL side...I don't have any magic guidance to give, BUT I can tell you we set ours to 512M
The formula above can be attributed to various documentation found in Jamf training courses. The max packet size is literally what Jamf support said might be right for our environment.
