What question did this study set out to answer?

To develop a mathematical model that captures urban evolution through the interactions between workers and firms.

April 13, 2026Journal of Optimization Theory and Applications0 citationsOpen Access

A Network Model for Urban Planning

FCFabio CamilliUniversity of Rome Tor Vergata AFAdriano FestaPolytechnic University of Turin LMLuciano MarzuferoFree University of Bozen-Bolzano

Key Points

To develop a mathematical model that captures urban evolution through the interactions between workers and firms.
Used a network model to represent residential areas and communication routes.
Applied a Mean-Field Game system to analyze the dynamics of two competing populations.
Coupled model with an Optimal Transport problem to study space competition.
Performed numerical simulations to visualize model behavior.
Proved the existence and uniqueness of solutions to the proposed model.
Demonstrated diverse scenarios of urban evolution based on population interactions through simulations.

Abstract

Abstract We study a mathematical model to describe the evolution of a city, which is determined by the interaction of two large populations of agents, workers and firms. The map of the city is described by a network with the edges representing at the same time residential areas and communication routes. The two populations compete for space while interacting through the labour market. The resulting model is described by a two population Mean-Field Game system coupled with an Optimal Transport problem. We prove existence and uniqueness of the solution and we provide several numerical simulations.

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