Abstract
Newell’s simplified kinematic wave model has been widely used in studying traffic dynamics in a road network. However, it cannot account for First-In-First-Out violation among vehicles on multi-lane roads. In this study, the authors present an extension of the model in the Lagrangian coordinates. In particular, the authors define a new variable of a vehicle’s order as its corresponding cumulative flows at different times and locations. The new kinematic wave model is consistent at the aggregate level with Newell’s simplified kinematic wave model, but allows for FIFO violation among individual vehicles.Based on the new model, the authors then present two algorithms to estimate vehicles’ trajectories from Eulerian data (cumulative flows provided by loop detectors) and Lagrangian data (the vehicle’s entry and exit times provided by reidentification technologies) at two boundaries of a road segment. In the first algorithm, the authors assume that vehicles follow the First-In-First-Out (FIFO) principle on a multi-lane road, and their orders are constant; in the second algorithm, the authors introduce a linear order-changing model to interpolate a vehicle’s orders at different times according to its entry and exit times. With Next Generation Simulation (NGSIM) datasets, the authors demonstrate that both algorithms are effective, but the second one, with an estimation error of around 10%, greatly outperforms the first one, with an estimation error of around 17%. This verifies the advantage of incorporating FIFO violation in the new model.