UC Irvine

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, we present an extension of the model in the Lagrangian coordinates. In particular, we 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, we 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, we assume that vehicles follow the First-In-First-Out (FIFO) principle on a multi-lane road, and their orders are constant and equal the average of the entry and exit orders; in the second algorithm, we 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, we 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 13%. This verifies the advantage of incorporating FIFO violation in the new model.