As traditionally the Conclave follows the death of the previous Pope, and this requires the traditional 9-days mourning period (Novemdiales) after the funeral (which happens a few days, 6 days in the case of Blessed Pope John Paul II) before the Conclave can begin, this is why it takes about 15 days or so for the Conclave can begin. This period of time is also for Cardinals from all over the world to have the time to come to Rome to elect the new Pope and for preparation of the Conclave.
However, as the announcement of the date of retirement came early, more than two weeks before the actual date, the Cardinals have plenty of time to come to Rome, and without the Novemdiales, in fact, the Conclave can begin as early as 1 March 2013, and we’ll have a new Pope perhaps even by 3 March 2013 or so.