Open Source Trouble Ticket System

I am looking for a trouble/support ticket system to track my clients issues
with. I have found a few open source options, but I am also looking for one
where my clients can log in and create the ticket themselves which I can
then later assign to the appropriate person. My ultimate goal is to have it
so I can see all the trouble tickets grouped by company, the techs can see
the items assigned to them, and the client can log in and see the status of
all tickets relating to them. If I can find a package to do this, it will
save me a huge amount of time everyday.

Thanks,
John A.
john@aciaz.com