Caesar's army mainly foraged, he says in the de bello Gallico that while he was preparing the blockade of the city his forces were somewhat reduced in number since they were out on the plain foraging for grain and cutting timber. Alesia sits in the middle of a fertile plain watered by two rivers, which fed the city in peacetime and which would have fed Caesar's troops readily enough. Consider also that the Romans could, albeit with some difficulty, cart supplies up from the coast, since the main Gallic force was shut up inside Alesia.

As for starving out the besiegers, such an action would necessarily have involved sacrificing Alesia and the main army. Caesar mentions that Vercingetorix's force was out of provisions by the time Commius' force was even raised, and only barely did the Gauls there decide not to surrender. They did, for lack of food, send out their women and children, whom Caesar refused to allow to pass through his lines. Commius' immediate attack on reaching the city was not a tactical judgement on his part, it was a necessity. The Gauls within Alesia were in such bad shape that when Commius' force fell apart they surrendered immediately, even though Caesar had not tried their walls yet.