A modeling framework to integrate frequency - and schedule-based passenger assignment approaches for coordinated path choice and space-time trajectory estimation based on multi-source observations

In this study, we focus on one of the practically important research problems of coordinated passenger path and space-time trajectory estimation in an urban rail transit network based on multi-source observations. This task was accomplished by developing a modeling framework to integrate frequency- and schedule-based passenger assignment approaches. To utilize the heterogeneous information of multisource observations, we established two groups of mapping relations from observations to the decision variables of different models. Flow-based observations were mapped to the link flow variables in the frequency-based passenger assignment model, and individual-based observations were mapped to the passenger space-time trajectory variables in the schedule-based passenger assignment model. To estimate the consistent internal states of the system between path choice and space-time trajectory, we formulated the coupling path flow constraint, which serves as a bridge between flow-based and individual-based decision variables. A general least-squares estimation framework was developed to integrate the path choice estimation in a frequency-based passenger assignment model and the space-time trajectory estimation in schedule-based passenger assignment with coupling constraints. The integrated estimation problem was solved using a Lagrangian relaxation-based heuristic approach. We demonstrated the advantages and practicality of our proposed model based on a large-scale case of the Beijing Subway Network, which includes 26 lines, 450 stations, and more than 5 million passengers, and revealed the benefits of the proposed methodology and its potential for data-driven decision-making in urban transit management centers.