  Urban rail transit (URT) system plays a dominating role in many megacities
like Beijing and Hong Kong. Due to its important role and complex nature, it is
always in great need for public agencies to better understand the performance
of the URT system. This paper focuses on an essential and hard problem to
estimate the network-wide link travel time and station waiting time using the
automatic fare collection (AFC) data in the URT system, which is beneficial to
better understand the system-wide real-time operation state. The emerging
data-driven techniques, such as computational graph (CG) models in the machine
learning field, provide a new solution for solving this problem. In this study,
we first formulate a data-driven estimation optimization framework to estimate
the link travel time and station waiting time. Then, we cast the estimation
optimization model into a CG framework to solve the optimization problem and
obtain the estimation results. The methodology is verified on a synthetic URT
network and applied to a real-world URT network using the synthetic and
real-world AFC data, respectively. Results show the robustness and
effectiveness of the CG-based framework. To the best of our knowledge, this is
the first time that the CG is applied to the URT. This study can provide
critical insights to better understand the operational state in URT.
