Which fact mostly clearly shows the difficulty in defending the roman empire against invasion

The size of the empire, at its prime it comprised of 60 million people and a territory of 2 million square miles -- for comparison, the contiguous area of the US, that is, without Alaska and Hawaii  is 3.1 million square miles. The Roman Empire was mostly formed by conquered peoples and terriotories, so civil wars and rebellions against a state that had became bureaucratic and demanded lots of taxes was quite common, also the size of the state permitted that the different tribes from the north, the so-called barbarians would attch from different points, so basically a gigantic state which had to deal with internal an external problems is the cause of this difficulty.