How to make nginx establish persistent connections with squid?

[selphon]

hi, 
I use nginx as load balance and forward request to squid use http/1.1, the
topology is below:

chrome ---> nginx(:80) ---> squid(:8080) ---> origin server(nginx :80)

the nginx configuration:
upstream backend {
    server 192.168.13.210:80;
    keepalive 10;
}


server {
    listen      80 default;
    server_name  _;

    proxy_set_header  Host  $host;

    proxy_http_version 1.1;
    proxy_set_header Connection "";

    location / {
        proxy_pass http://backend;
    }
}

the squid configuration of persistent connections  is supported on both
client side and server side:
##########timeout##########
client_persistent_connections on
server_persistent_connections on

request_timeout 240 seconds  #to client/wait client's request
client_lifetime 240 seconds  #to client/all request time
persistent_request_timeout 30 seconds  #to client/keepalive
pconn_timeout 30 seconds     #to origin server or peer/keepalive
connect_timeout 240 seconds  #to origin server/only connect
read_timeout 240 seconds     #to origin server or peer/wait recv data

Then, I made 5 requests such as 'http://test.cache.com/p3.jpg?tt=2013032206'
and could not find any persistent connection between nginx and squid.

the squid log show:
127.0.0.1 - - [22/Mar/2013:16:12:06 +0800] "GET
http://test.cache.com/p3.jpg?tt=2013032205 HTTP/1.1" 304 364
"http://test.cache.com/p3.jpg?tt=2013032205" "Mozilla/5.0 (Windows NT 6.1)
AppleWebKit/537.22 (KHTML, like Gecko) Chrome/25.0.1364.172 Safari/537.22"
TCP_REFRESH_HIT:DIRECT/192.168.13.210      0 

"Host: test.cache.com  #request header
Cache-Control: max-age=0
Accept: text/html,application/xhtml+xml,application/xml;q=0.9,*/*;q=0.8
User-Agent: Mozilla/5.0 (Windows NT 6.1) AppleWebKit/537.22 (KHTML, like
Gecko) Chrome/25.0.1364.172 Safari/537.22
Referer: http://test.cache.com/p3.jpg?tt=2013032205
Accept-Encoding: gzip,deflate,sdch
Accept-Language: zh-CN,zh;q=0.8
Accept-Charset: GBK,utf-8;q=0.7,*;q=0.3
If-Modified-Since: Tue, 23 Oct 2012 04:07:19 GMT" 

"HTTP/1.0 304 Not Modified  #response header
Server: nginx/1.2.6
Date: Fri, 22 Mar 2013 08:12:06 GMT
Last-Modified: Tue, 23 Oct 2012 04:07:19 GMT
Expires: Fri, 22 Mar 2013 10:12:06 GMT
Cache-Control: max-age=7200
X-Cache: MISS from vm-linux1.test.com
X-Cache-Lookup: HIT from vm-linux1.test.com:8080
Via: 1.1 vm-linux1.test.com:8080 (squid/2.7.STABLE9)
Connection: close"

as we see(last line), squid announced the Connection should be close after
the request. I think this is why nginx couldn't make a persistent connection
with squid.

then I try to set: proxy_set_header Connection "keep-alive"; forcing that
the request must be keep-alive.
the request and response is:

127.0.0.1 - - [22/Mar/2013:15:59:09 +0800] "GET
http://test.cache.com/p3.jpg?tt=2013032203 HTTP/1.1" 304 369
"http://test.cache.com/p3.jpg?tt=2013032203" "Mozilla/5.0 (Windows NT 6.1)
AppleWebKit/537.22 (KHTML, like Gecko) Chrome/25.0.1364.172 Safari/537.22"
TCP_REFRESH_HIT:DIRECT/192.168.13.210      0 

"Host: test.cache.com
Connection: keep-alive
Cache-Control: max-age=0
Accept: text/html,application/xhtml+xml,application/xml;q=0.9,*/*;q=0.8
User-Agent: Mozilla/5.0 (Windows NT 6.1) AppleWebKit/537.22 (KHTML, like
Gecko) Chrome/25.0.1364.172 Safari/537.22
Referer: http://test.cache.com/p3.jpg?tt=2013032203
Accept-Encoding: gzip,deflate,sdch
Accept-Language: zh-CN,zh;q=0.8
Accept-Charset: GBK,utf-8;q=0.7,*;q=0.3
If-Modified-Since: Tue, 23 Oct 2012 04:07:19 GMT" 

"HTTP/1.0 304 Not Modified
Server: nginx/1.2.6
Date: Fri, 22 Mar 2013 07:59:09 GMT
Last-Modified: Tue, 23 Oct 2012 04:07:19 GMT
Expires: Fri, 22 Mar 2013 09:59:09 GMT
Cache-Control: max-age=7200
X-Cache: MISS from vm-linux1.test.com
X-Cache-Lookup: HIT from vm-linux1.test.com:8080
Via: 1.1 vm-linux1.test.com:8080 (squid/2.7.STABLE9)
Connection: keep-alive"

though the Connection of response is keep-alive, nginx still didn't make any
persistent connection with squid.

Is there any way to configure nginx use a persistent connection where
forward requests to squid ? help help

nginx_version: 1.2.6
squid_version: 2.7.STABLE9

Posted at Nginx Forum: http://forum.nginx.org/read.php?2,237666,237666#msg-237666