SMTP is used to send mail.
POP/IMAP is used to get mail.
Your problem description makes it sound like you have having problems with one or possibly both. First of all, if no one is browsing the pages of course you will not receive notices. There is no one writing updates.
If you are trying to say that, you setup OST to poll for POP or IMAP emails and create tickets and not only are they not being created and their new ticket notices aren't being sent, then right again.
Short answer:
setup cron (*nix) or taskscheduler (windows) to run cron.php every so often.
Long answer:
This is taken from the POP3/IMAP settings document regarding setting up polling located at: http://osticket.com/wiki/POP3/IMAP_Settings(http://osticket.com/wiki/POP3/IMAP_Settings)
Recurring tasks scheduler (Cron Job)
This is the most convenient method if your hosting provider allows scheduling recurring tasks via crontab on *nix or "Scheduled Tasks" on a Windows server. Please refer to your hosting manual or contact your hosting provider for instructions. The PHP CLI executable is called to run cron.php.
Add the following entry to cron file normally in /etc/crontab in *nix systems and adjust the time and paths accordingly.
*/5 * * * * nobody /path/to/php /path/to/api/cron.php
For windows users in "Scheduled Tasks" add "c:\php\bin\php.exe c:\website\osticket\api\cron.php"
I personally have a .bat file and use Task Scheduler to call it. Make sure that you set the optional Start In path. Here is the contents of my .bat
C:\Progra~1\PHP\php.exe -f c:\Inetpub\wwwroot\OSTICKET\api\cron.php > osticket.log
You should of course edit the code to reflect your own path to both PHP and cron.php.
TIP: to hide the DOS window while fetching mail, you can create a link with "minimize to tray" option and schedule the .lnk instead of the .bat.