Interactions and Equilibrium Between Rescheduling Train Traffic and Routing Passengers in Microscopic Delay Management: A Game Theoretical Study

In the last decade, optimization models for railway traffic rescheduling mostly focused on incorporating an increasing detail of the infrastructure, with the goal of proving feasibility and quality from the point of view of the managers of the infrastructure (tracks and stations). Different approaches that manage only the passenger flows instead focus more explicitly on the quality of service perceived by the passengers. This paper investigates microscopic railway traffic optimization models and algorithms, merging these two streams of research. In particular, we analyze the characterization of an equilibrium point between the reordering choices of train dispatchers in railway traffic optimization and the route choice of passengers in the available services of the railway transport network. We describe how passenger choice at stations along the route intertwines deeply with the problem of rescheduling trains over tracks and station resources in a very complicated setting that might not exhibit equilibrium points in general. Delaying trains and /or dropping passenger connections and/or giving particular route advice to passengers might influence the behavior of traffic controllers and passengers, determining a trade-off between the delays of trains, weighted by the passenger load, and the travel time of passengers. We study this problem with a game theoretical approach, focusing on the solutions corresponding to Nash equilibria of a game involving passengers and infrastructure managers. The proposed game theoretical approach is able to easily consider information and interdependence of the actions of multiple stakeholders. Computational results based on a real-world Dutch railway network quantify the trade-off between the minimization of train delays and passenger travel times and the performance, stability, and convergence of the equilibrium point given different algorithms and information available. The final aim of this work is to study the impact of effective implementations of railway traffic management and dissemination of information to passengers and operators.