George Spafford at http://www.itsmwatch.com has a good article on Incidents, Problems, Known Errors and Changes. It's at http://www.itsmwatch.com/itil/article.php/3584706.
I think some of the information presented can really help in implementing Tivoli at your site. Read on for more of my take on this.
I like the difference that Mr. Spafford makes between an Incident and an Incident Record, since they really do need to be treated as two different entities. I've seen too many customers who use a TEC event as a means to track the progress on the resolution of the incident. In my opinion, that's just wrong. I think that a TEC event should be used to OPEN an Incident Report (in your service desk software of choice), but once that occurs, the event should be ACK'd or CLOSEd, depending upon your other business requirements.
You've still got to be concerned about reporting on the outage, and that can be done by mining your service desk data.
These requirements (and others) have been around since before ITIL, but ITIL identifies these needs, and allows you to define tasks that must be completed to conform to the ITIL recommendations. ITIL itself doesn't provide any answers or solutions - it's the correct application and implementation of the concepts and processes modelled by ITIL that will actually make your life easier.