Alberto Amaduzzi, Unibo Physics department 

When: November 9th, 2026 at 5pm

Where: Seminario 1 (Dip. Mat. UNIBO)

Abstract: Standard models of adaptive vehicle dynamics on a single long road admit steady-flow solutions that become unstable over certain density ranges. Small density fluctuations then evolve, at first order, according to a Korteweg–de Vries perturbation, known to admit soliton solutions in density. When studying congestion in a road network, however, intersections introduce bifurcations that prevent a purely PDE-based description of congestion. Several coarser models have therefore been proposed, exploiting the relation between speed and density established by macroscopic traffic theories, and using road capacity (maximum flow) as a proxy quantity of interest. Using a GPS dataset, we construct a Markov process that describes a steady-state solution for the number of travelers across the road network. We develop a method to estimate the associated transition matrix, moving toward a description of the system in terms of a Fokker–Planck equation.