2022 Volume 78 Issue 3 Pages 150-165
This study develops a methodology for estimating parameters of urban/transportation equilibrium models with multiple equilibria, from the observed location patterns, traffic volumes, and so on. It is known that a potential game on a continuous-time and continuous state framework, whose state dynamics is denoted by a Langevin diffusion, has a Boltzmann-type steady-state distribution. This enables us to define the likelihood of the parameters against the observation and formulate the maximum likelihood estimation problem. We develop a numerical solution method by using an accelerated proximal gradient method that has been widely used in the machine learning field. Finally, we apply the proposed method to a simple equilibrium model that has multiple equilibria and examine that it estimates the appropriate parameters from the observations.
