An article written by Barthélemy and Flammini uses a model of city formation to study the interplay between the local density of population and the structure of the road network. This basic city model describes the interplay between the co-evolution of the population density and the topology of the road network. Specifically the rent cost and the demand for accessibility transforms the population spatial density. If transportation costs are higher, a densely populated area emerges around which the density decays exponentially. The demand for accessibility increases when rent costs are high. A very important element, how individuals or companies choose a location, is very important for modeling the evolution of a city. It is affected by two main factors, transportation costs and rent price. If β is very large, then the location which maximizes the cost is chosen. When λ is small density plays the dominant role in determining the location of the new centers.
Barthélemy, Marc & Flammini, Alessandro. (2009). Co-evolution of Density and Topology in a
Simple Model of City Formation. Networks and Spatial Economics. 9, 401-425.