nginx as remote proxy - limit number of concurrent connections?

[John Moore]

I'm using nginx as a remote proxy server in front of a bunch of Tomcat 
instances, and occasionally I'm running into a situation where all 
available threads are used up in the Tomcat instances, which causes 
various problems. Rather than trying to deal with these problems in that 
layer, I was wondering about preventing the situation from arising by 
limiting the number of concurrent connections to the upstream servers in 
nginx. I'm not entirely sure how to do this, but I have no doubt it's 
doable. Suggestions, please!