Since Plesk uses qmail, it's actually an ALRM that is usually sent to the qmail-send process. A HUP may work as well, never tried it myself. One way to force a queue run would be via the command "qmailctl flush". You can also run /var/qmail/bin/qmail-tcpto to see the recent timeouts and number of retries.
If you're interested in getting some more detailed information about your qmail logs, check out qmailanalog. An exmaple of using qmailanalog would look like this:
cat /var/log/qmail/current | /usr/local/bin/tai64n2tai | /usr/local/qmailanalog/bin/matchup 5>/dev/null | /usr/local/qmailanalog/bin/zoverall | less
You can also do /var/log/qmail/\@* as well as /var/log/qmail/current
That will give you some information about the success/failure/deferral rates. You might also be interested in checking out the other z* commands in /usr/local/qmailanalog/bin/z*, such as zdeferrals, zfailures, zrecipients, and so on.