The main factor is the quantity of goods which need to be inspected, and that tends to scale with the population which is buying the goods.
> your number of entry points should scale like your perimeter
Is that really true? An entry-point is generally something the people choose to create to satisfy the pre-existing need to transport goods, by building roads, rail, harbor-piers, etc.
Border-checkpoint facilities don't spontaneously generate in trackless wilderness or barren coastlines, like some fantasy-dungeon that the Adventurers' Guild must periodically raid in to avert a stampede of monsters.
> your number of entry points should scale like your perimeter
Is that really true? An entry-point is generally something the people choose to create to satisfy the pre-existing need to transport goods, by building roads, rail, harbor-piers, etc.
Border-checkpoint facilities don't spontaneously generate in trackless wilderness or barren coastlines, like some fantasy-dungeon that the Adventurers' Guild must periodically raid in to avert a stampede of monsters.