Towards a theory of optimal roads

The purpose is to find an allocation of a given total amount of road capital in two-dimensional space such that total transportation costs for a region are minimized. A continuous model in analogy to hydrodynamics is used. Transports are supposed to be generated by the gravity hypothesis. It is discussed how transportation paths are optimally adjusted to a given distribution of road capital, and how road capital should be distributed at a given traffic distribution. It is also discussed how the latter problem should be solved when it is taken into account that the distribution of roads affects the choice of paths.