Sorry, I will attempt to make it a little more clear.
TicketId is unique because it is autoincrement. However there is an additional attribute TicketNumber which is what I need to make unique within a customer. That is, I need to allow same ticket number across customers (C1-T1 and C2-T1), but need to ensure uniqueness within a customer (C1-T1 is unique). In summary, the CustomerId+TicketNumber combination should be unique. (Currently this is enforced by the application code and I am wondering whether any of the RDBMS support defining this as a DB constraint).