Most efficient way to test the resilience of a server (C# networking)

I'm developing an application running a client/server configuration with many clients interacting with one server. It's working well and fast so far but I'd like to test the resilience (mostly thread safety and coherence of operations) as well as the performance of the server and the code behind it.

I already made a unitary test creating 200 threads each having one client connecting a constantly pinging the server, but this inevitably leads to the server (well the tcp client) refusing connections because they are all made in such a short time span.

What is then an efficient and reliable way to test such a configuration ? Thanks.