How do you know if nginx can't keep up with the number of requests?

Question

Nginx

nginx + php-fpm is getting more and more requests. Sometimes people complain that the page of the service “does not open” for them. I suspect:

1. SSL certificate from StartSSL and outdated versions of Chrome for these visitors;
   
2. nginx and its number of simultaneous connections, etc. settings.

How to catch the moment where nginx simply did not respond to the request, because overloaded?
"Doesn't open", for example, with their browser reporting "The web page at ... may be temporarily unavailable or permanently moved to a new address." Requests from complaining users are not displayed in the nginx access-log. In previous days they could enter normally.

Answer 1

If the request did not reach nginx, then there will be no errors in the logs either. An indicator that nginx is not doing well will be an increase in response time and 503 errors.
It is better to diagnose dissatisfied users, at least by understanding what kind of OS / browser they have.

Answer 2

1. The assumption makes sense. I myself have this.
2. So in the nginx logs, timeouts and in general, include errors and warnings in the log. And analyze it with any available tool.