What tools help calibrate time-varying origin-destination matrices?

The DynusT research team developed a a two-stage model to calibrate the time-varying origin-destination (OD) matrices. The first-stage is to estimate O-D trip rates by minimizing link demand deviation with a one-norm formulation approach, aiming to efficiently match the traffic demand on calibration links with the link demand from the field data. Then, the second-stage is formulated as a time-dependent, user equilibrium traffic assignment model to adjust departure time profile iteratively, aiming to match the calibrated result with field observed dynamic traffic conditions, i.e. time dependent traffic speed profile.

The proposed sequential decomposition framework departs from previous related literature mainly in two aspects. First, compared with the commonly seen least-square type of bi-level model formulation, the one-norm formulation proposed is more computationally effective and solvable on large real-life networks due to its linear model structure. Second, the second-stage model adopts an innovative approach to utilize field data in the calibration process. Specifically, it starts from the concept of 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. In other words, by incorporating time dependent speed profiles along with link volume data, it derives an estimate of “arrival” or “demand” information for the congested bottleneck locations that need calibration. Then, based on the idea of using travel time propagation between origin and bottleneck locations, the real traffic demand at origin locations can be inferred through proper spatial-temporal mapping. Consequently, the O-D calibration results can properly depict the traffic demand pattern at the bottleneck location.

A Stage 1 example on the Denver I-70 model below show that after 19 calibration iterations the simulated link volumes match with the actual volumes very well.

Taking one of the sensor locations for further examination, we can find that the speed profile (lower left corner chart) does not match well. The actual speed profile (red) has a deeper speed drop compared to the simulation.

After applying the State 2 methodology, the simulated and actual speed profiles match very well.