HTTP keep-alive: when client should stop reusing connection? - apache

Question

I understand that the client should stop reusing http keepalive socket after timeout or the max usage. However two popular server implementations seem to keep socket open for the longer duration than the timeout and hence this question to learn what strategies a client should adapt to optimally reuse the connection.
We were testing our implementation with various servers, and while apache seems to be adhering to timeout, lighttpd and nginx seem to keep connection open for longer duration than the timeout. As you can see from the logs below, despite of client-server agreed on 15 second timeout, the socket was kept open for more than 60 seconds and second request succeeded even after 60 seconds.
1) First request and response with timestamp
GET /en/CHANGES HTTP/1.1
Host: nginx.org
Accept: */*
Accept-Encoding: identity
Content-Length: 0
Connection: Keep-Alive
Keep-Alive: timeout=15, max=1000
E(2410-130624-216): HTTP/1.1 200 OK
E(2410-130624-216): Server: nginx/1.13.3
E(2410-130624-216): Date: Tue, 24 Oct 2017 07:36:23 GMT
E(2410-130624-216): Content-Type: text/plain; charset=utf-8
E(2410-130624-216): Content-Length: 282456
E(2410-130624-216): Last-Modified: Tue, 10 Oct 2017 15:39:18 GMT
E(2410-130624-216): Connection: keep-alive
E(2410-130624-216): Keep-Alive: timeout=15
E(2410-130624-216): ETag: "59dce9a6-44f58"
E(2410-130624-216): Accept-Ranges: bytes
E(2410-130624-216):
2) Second request on the same socket, 60 seconds later
GET /en/CHANGES HTTP/1.1
Host: nginx.org
Accept: */*
Accept-Encoding: identity
Content-Length: 0
Connection: Keep-Alive
Keep-Alive: timeout=15, max=1000
E(2410-130726-881): HTTP/1.1 200 OK
E(2410-130726-881): Server: nginx/1.13.3
E(2410-130726-881): Date: Tue, 24 Oct 2017 07:37:26 GMT
E(2410-130726-881): Content-Type: text/plain; charset=utf-8
E(2410-130726-881): Content-Length: 282456
E(2410-130726-881): Last-Modified: Tue, 10 Oct 2017 15:39:18 GMT
E(2410-130726-881): Connection: keep-alive
E(2410-130726-881): Keep-Alive: timeout=15
E(2410-130726-881): ETag: "59dce9a6-44f58"
E(2410-130726-881): Accept-Ranges: bytes
E(2410-130726-881):
There comes the question, when should client stop reusing connection in the optimal manner. Should client keep reusing the connection till it gives error? or should we discard the connection after timeout? What strategies browsers are using?
Thanks