Data-driven method to estimate the maximum likelihood space-time trajectory in an Urban Rail Transit system

The Urban Rail Transit (URT) passenger travel space-time trajectory reflects a passenger's path-choice and the components of URT network passenger flow. This paper proposes a model to estimate a passenger's maximum-likelihood space-time trajectory using Automatic Fare Collection (AFC) transaction data, which contain the passenger's entry and exit information. First, a method is presented to construct a space-time trajectory within a tap in/out constraint. Then, a maximum likelihood space-time trajectory estimation model is developed to achieve two goals: (1) to minimize the variance in a passenger's walk time, including the access walk time, egress walk time and transfer walk time when a transfer is included; and (2) to minimize the variance between a passenger's actual walk time and the expected value obtained by manual survey observation. Considering the computational efficiency and the characteristics of the model, we decompose the passenger's travel links and convert the maximum likelihood space-time trajectory estimation problem into a single-quadratic programming problem. Real-world AFC transaction data and train timetable data from the Beijing URT network are used to test the proposed model and algorithm. The estimation results are consistent with the clearing results obtained from the authorities, and this finding verifies the feasibility of our approach.