Let say when you are laying a long siege, because you cannot take out the defenders. You pillage all the roads around the city and cut off all the trade routes and the city starves, I think every 2 turns the city starve, the city defenders lose 10% hp. So after 8 turns the city had starved, the city defenders can only have a max hp of 60%. Once the city stop starving, but the siege still takes place, the defenders do not gain back those lost hp. Instead, they can only gain it back when it is connected to a trade route to another friendly city. This way, long siege is more strategic if you have a small but solid army.

For more realistic warfare, I think all military units need food in additional to coin as supply cost. Perhaps a city can build a supply cart that carries a maximum of 20 food. When city has a surplus of food (when your city is growing), you can either choose the food to funnel for new population growth or put food in your supply cart/wagon. Each military eats up 1 food per 5 turns (arbitary), and this discourages a huge standing army. When military units are not in friendly lands, the supply wagon must accompany on the tile or adjacent to the military units or else they will suffer attrition. Perhaps they lose 10% hp every turn after 2 turns they are not supplied with food. On native land, military units automatically eats up food that is supported by the food granary of their nearest city.

As a digression, you can deliver food from farm cities to production cities or commerce cities and you can also buy/sell food from other civ.