Calculus of Variations and Geometric Measure Theory

G. Buttazzo - A. Pratelli - E. Stepanov

Optimal pricing policies for public transportation networks

created on 29 Jun 2004
modified by stepanov on 06 Mar 2006


Published Paper

Inserted: 29 jun 2004
Last Updated: 6 mar 2006

Journal: SIAM J. Opt
Volume: 16
Number: 3
Pages: 826-853
Year: 2006


In this paper we study the problem of finding an optimal pricing policy for the use of the public transportation network in a given populated area. The transportation network, modeled by a Borel set $\Sigma\subset *R*^n$ of finite length, the densities of the population and of the services (or workplaces), modeled by the respective finite Borel measures $\varphi_0$ and $\varphi_1$, as well as the effective cost $A(t)$ for a citizen to cover a distance $t$ without the use of the transportation network, are assumed to be given. The pricing policy to be found is then a cost $B(t)$ to cover a distance $t$ with the use of the transportation network (i.e.\ the ``price of the ticket for a distance $t$''), and has to provide an equilibrium between the needs of the population (hence minimizing the total cost of transportation of the population to the servicesworkplaces) and that of the owner of the transportation network (hence maximizing the total income of the latter). We present a model for such a choice and discuss the existence as well as some qualitative properties of the resulting optimal pricing policies.

Keywords: optimal transportation, transportation network, optimal pricing, Nash equilibrium