While Ostia was established as a riverine port near the mouth of the Tiber relatively early in Rome's history (4th c. BC), it was not suitable to handle the volume of maritime traffic that Rome eventually developed in the late Republic and early Empire. Ostia operated as one of a series of ports, including Centumcellae (Civitavecchia), Anzio, Terracina, and Puteoli, which furnished Rome.

This multi-harbour system was inconvenient, so Claudius first devised the plan to construct a new harbour with a deep-water basin capable of handling large vessels in great quantity (though new research at the port in Ostia has revealed that the basin there was capable of handling large tonnages, see Goiran et al. 2014 in Journal of Archaeological Science). This was an improvement, but not perfect - Tacitus tells us of a large storm in AD 62 which destroyed many ships at the site. Trajan substantially redeveloped the site to include a new basin with better protection, including the new hexagonal harbour which is still visible. The construction of this port and the improvement of the infrastructure which connected it to Rome, including several canals and the via Portuensis, helped link Rome directly to the wider Mediterranean. The level of state investment in building and improving Portus demonstrates how important it was for the city to have a direct connection to the wider Empire.

At this time, Rome was already on par with the largest cities in the Mediterranean, including Alexandria, Corinth, Ephesos, and Carthage. The improvement of harbour infrastructure enabled direct links between Rome and these other cities without the danger of the river port in Ostia or the lengthy over-land transit from Puteoli or elsewhere.

Currently, Portus is being excavated by Simon Keay from Southampton and the British School in Rome, and will operate as a field school (meaning it will train students) for the coming years. More information about this project can be found at http://www.portusproject.org/

With regards to your question about comparing Portus to Alexandria or Carthage, we know relatively little about the town around the Harbour. As already said, Rome surpassed these other cities a century before Trajan improved the harbour, so as an extension of the city of Rome, Portus did as well. Future excavations may help clarify the actual urban environment around the basin and monumental buildings.