Comment by dolinsky

To clarify (and answer @sureshv), Varnish allocates one worker-thread per session (active connection), but those threads are pooled by the managed thread pool @sureshv referred to. It's recommended to leave the thread_pool value at 2 and scale the thread_pool_min and _max values to suit your traffic.

As for the handling of the websockets, setting the pipe_timeout variable in the vcl file would release any persistent, yet silent, connections.