What happens when you try to starve out the AI?

[RickooClan]

it would make more sense to sally on the first or second turn of the siege before half the defenders have died of starvation and pestilence, but that's how they work.

I somehow disagree since as long as you resisting the siege you still have the chance somebody can help you out or the sieging army may retreat for whatever reason.

If you do know you get little chance to win in sallying out (which will directly hand over the city), it is more logical to hold the city as long as possible. (at least you still have a few turns of income! )