A Sequential Decomposition Framework and Method for Calibrating Dynamic Origin-Destination Demand in a Congested Network

This paper presents a two-stage model to calibrate the time-dependent, dynamic origin-destination (O-D) demand under congested traffic conditions. The first-stage model estimates O-D trip rates by minimizing link demand deviation with a one-norm formulation approach, so that over the calibration time period, the traffic demand on calibration links matches with the link demand from the field data. Due to its linear model structure, the first-stage model is more computationally effective and solvable on large real-life networks compared with the commonly seen least-square formulation. Then, a time-dependent user equilibrium traffic assignment model is formulated at the second stage to adjust the departure time profile iteratively, aiming to match the calibrated result with the field observed dynamic traffic condition, i.e., time-dependent speed profile. The second-stage model starts from the concept of a demand-capacity-volume relationship at a congested road segment, where demand exceeds supply, and utilizes shockwave theory to capture the differences between true demand and volume output, together with the idea of using travel time propagation between origin and bottleneck locations to infer real demand at the origin location. The two-stage model was implemented and tested in a case study in Tucson, AZ, USA, as an experimental proof of concept, which demonstrated the effectiveness of the proposed calibration framework and method under circumstances, in which the departure time profile was systematically distorted and initial demand solutions deviated from the true O-D matrices.