[exim] Saslauthd permission denied

Dear All,

    I have configured exim auth conf to use saslauthd for smtp auth.
    When I try to use  "exim4 -bh 127.0.0.1" to test my configuration. 
    It shows "Unable to authenticate at present: cannot connect to saslauthd daemon at /var/run/saslauthd/mux: Permission denied"
    following is the brief message on my console

***********************************************
EHLO localhost
>>> host in pipelining_advertise_hosts? yes (matched "*")
>>> host in auth_advertise_hosts? yes (matched "*")
>>> host in tls_advertise_hosts? no (option unset)
250-xxx.xxx.xxx Hello xxx.xxx.xxx [127.0.0.1]
250-SIZE 52428800
250-PIPELINING
250-AUTH LOGIN
250 HELP
AUTH LOGIN AHRlc3QAcGFzc3dvcmQ=
>>> login_saslauthd_server authenticator:
>>> $1 =
>>> $2 = test
>>> $3 = password
>>> expansion failed: cannot connect to saslauthd daemon at /var/run/saslauthd/mux: Permission denied
435 Unable to authenticate at present
LOG: login_saslauthd_server authenticator failed for xxx.xxx.xxx (localhost) [127.0.0.1]: 435 Unable to authenticate at present: cannot connect to saslauthd daemon at /var/run/saslauthd/mux: Permission denied
***********************************************

         But I had already add Debian-exim into sasl group. And also changed the directory permission of /var/run/saslauthd to 710

***********************************************
myhost:/var/run/saslauthd# groups Debian-exim
Debian-exim : Debian-exim sasl

myhost:/var/run/saslauthd# ls -al
total 12
drwx--x---   2 root sasl 4096 Jun 17 12:46 .
drwxr-xr-x  21 root root 4096 Jun 17 14:37 ..
srwxrwxrwx   1 root root    0 Jun 17 12:46 mux
-rw-------   1 root root    0 Jun 17 12:46 mux.accept
-rw-------   1 root root    5 Jun 17 12:46 saslauthd.pid
***********************************************

        Can anyone give me suggestion where should I check?

        Thank you all.