Integrated speed modeling and traffic management to precisely model the effect and dynamics of temporary speed restrictions to high-speed railway traffic

Abstract

This paper investigates the integrated optimization problem of train rescheduling and train control for high-speed railway lines, where perturbations occur and cause Temporary Speed Restriction (TSR) to trains. We consider microscopic details (i.e., block sections) for ensuring the feasibility of the solution from a train signaling point of view, and an even higher level of detail, to accurately represent the train speed profiles. Running time and headway time are variable, at the same time depending from, and affecting, traffic. We optimize train speed profiles by considering vehicle and infrastructure constraints (e.g., traction, slopes). The model naturally considers the transition along the normal, disturbed and the recovery operation periods. A mixed-integer nonlinear programming (MINLP) model is first developed to simultaneously optimize train orders, routes, and departure and arrival times, as well as train speed profiles, aiming at reducing total train deviation time. The MINLP model is difficult to solve; thus we further reformulate it into a mixed-integer linear programming (MILP) model by means of piecewise linear approximation. A two-step approach is designed to speed up the solving procedure of the MILP model: first estimate the upper/lower bounds of train speeds and then solve the MILP model based on the estimated bounds of train speeds. Three instances (i.e., a small-scale line, a medium-scale line, and a large-scale network) are used to highlight the performance of the approach, verify the benefit of the integration, and its dependence on the parameters used. According to the experimental results, our integrated optimization method leads to an average improvement of 3%-36% in solution quality, compared with the integrated approach without train rerouting measure. Moreover, the integrated optimization method outperforms the sequential approach, achieving 6%-9% improvement in solution quality.