If you have 10,000 front-end users, having a connection pool of 10,000 would be shear insanity. 1000 still horrible. Even 100 connections, overkill. You want a small pool of a few dozen connections at most, and you want the rest of the application threads blocked on the pool awaiting connections.
imagine three threads (Tn=3), each of which requires four connections to perform some task (Cm=4). The pool size required to ensure that deadlock is never possible is:
