William the Conqueror: 1061 to 1066
The city is easily able to stand a siege of any length: the English fleet, augmented by the Norse ships that fell to Harold, are able to constantly bring in reinforcements and provisions. Your army, on the other hand, is in hostile territory, has few ships (and even those are soon lost in a battle that seizes your camp at Hastings not long after the siege begins): food is harder to come by, and then winter arrives. Your men are cold, hungry and miserable: you have lost the war. Harold is generous in his terms: you must leave England, never come back, and release him from all of his oaths of fealty. History remembers you as William the (rash) Bastard.