The siege of Troy was most likely fictional. The Greeks did not differentiate much between fact and fiction so we have to take their writings with a pinch of salt. For the more realistic campaigns it often takes ten years to gather supplies and then a huge logistics branch which dwarfs the army. For example the battle of Marathon was an attack on the Persian supply lines which consisted of the largest fleet ever seen up until that day. Without their supplies the Army, who went over land, were forced back and had to spend ten years until they could attack again. This time the logistics also went by land and resulted in the battle of Thermopoly.
The way a lot of these campaigns worked was that they gathered most of their supplies as they marched. This meant that soldiers had to detach from the main army to attack cities and farms along the way to gather food for the army. Even going so far as picking up farm tools to harvest the crops and animals that was still in the fields. There were usually only a few professional soldiers at this time and most of the army were composed of farmers so they were skilled at this. It is possible that in a prolonged siege the soldiers would maintain the local farms after driving the local farmers away so they would get enough food for themselves.
But there were also big supply chains following the army. If the army were unable to find enough food or when they were stationary for some time they needed supplies from the stores back home. So a big part of the army were concerned with transporting these supplies. The entire society were part of a campaign. Farmers would preserve and store any excess food they had, smiths would make armour and weapons whenever they had some time over from making farm equipment. Whenever the order to gather the army went out it was not only the farmers son who had to leave for the army, he was accompanied by wagonloads of food and weapons needed for the campaign. The farmer would send anything he could part with and start rebuilding for the next campaign.
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