Simulación computacional del sistema de transporte masivo TransMilenio: un enfoque desde la física estadística

Abstract

This work develops a statistical-physical model of Bogotá’s TransMilenio mass transit system, aiming to characterize congestion from the perspective of statistical mechanics and to formulate well-founded optimization strategies. The model integrates two components: the estimation of travel demand through the maximum entropy principle —which yields a doubly-constrained gravity model, formally analogous to the Boltzmann distribution, in which the cost sensitivity parameter is interpreted as an inverse temperature—and the mesoscopic simulation of the resulting flow over the city’s real network, reconstructed from geographic and operational data, using the open-source simulator UXsim. By sweeping the demand factor, the transition between the free-flow and congested regimes is characterized as a phase transition, taking the proportion of completed trips as the order parameter and locating the critical demand that separates both regimes. The analysis of different scenarios reveals that only the weekday demand exceeds the critical threshold, and that the effect of rain conditions depends on the system’s proximity to that threshold. Finally, the quantitative evaluation of optimization proposals shows that, while individual interventions are insufficient, an integral strategy combining capacity reinforcement, signal prioritization, and demand management shifts the critical demand by around twenty-seven percent, although without eliminating an irreducible physical limit under extreme demand.