Via Tiburtina ran from Rome to Tibur, probably diverging to the left from the Via Praenestina a little outside the Porta Esquilina of the Servian Walls and running to Porta Tiburtina (Porta S. Lorenzo) in the Aurelian Walls. Some topographers have proposed that the Via Tiburtina left the Servian Walls by Porta Viminalis and ran to the small postern gate called Porta Chiusa ("closed gate", because it was later walled shut) in the Aurelian Walls, just southeast of the Castra Praetoria. There can be no doubt that by the time of the building of the Aurelian Walls the other route was in heavier use. The fact that the Porta Tiburtina is built around a monumental arch built by Augustus, which took three aqueducts (Marcia, Tepula, and Julia) over the road, argues that by his day this was also the more important road. The identity of the Porta Chiusa road remains uncertain: the name Via Tiburtina sometimes used for it has no ancient support.
The road ran east-northeast to Tibur, 20 miles away, crossing the Anio River close to Rome and then running roughly parallel to it, but some distance away from it. The Via Tiburtina follows an irregular course through gently undulating country until it reaches the sharp rise of the Monti Tiburtini just below Tivoli (Tibur). Beyond Tivoli it changed its name and becomes the Via Valeria as far as Cerfennia, northeast of the Lacus Fucinus in the country of the Marsi. Thereafter, it became the Via Claudia Valeria, so named because Claudius extended the road to the Adriatic at the mouth of the Atemus River, a noteworthy feat of engineering.
For the historian Strabo it was one of the best known and most important Roman roads, ranking with the Via Appia and Via Latina. A number of inscriptions commemorate the officials charged with maintaining the road. These are all later than Claudius and seem generally to have been responsible for the full length of the road, but sometimes only the Via Tiburtina or the Via Valeria is mentioned, indicating that there may have been different caretakers for different sections at some times.
Platner Topo Dictionary: http://www.ku.edu/history/index/europe/ancient_rome/E/Gazetteer/Places/Europe/Italy/Lazio/Roma/Rome/.Texts/PLATOP*/Via_Tiburtina.html