No abstract

An historical overview of the development of traffic flow models is proposed in the form of a model tree. The model tree shows the genealogy of four families: the fundamental relation, microscopic, mesoscopic and macroscopic models. We discuss the families, branches and models. By describing the historical developments of traffic flow modeling, we take one step further back than conventional literature reviews that focus on the current state-of-the-art. This allows us to identify the main trends in traffic flow modeling: (1) convergence of many branches to generalized models, (2) adaptations and extensions of the LWR model to deal with real phenomena, (3) multi-class versions of many models and, (4) the development of hybrid models combining the advantages of different types of models.

No abstract

No abstract

In real-time traffic management and intelligent transportation systems (ITS) applications, an accurate picture of the prevailing traffic state in terms of speeds and densities is critical, for which traffic state estimation methods are needed. The most popular and effective techniques used are so-called model-based traffic state estimators, which consist of a dynamic traffic flow model to predict the evolution of the state variables; a set of observation equations relating sensor observations to the system state; and data-assimilation techniques to combine the model predictions with the sensor observations. Commonly, both process and observation models are formulated in Eulerian (space-time) coordinates. However, recent studies show that ( first-order) macroscopic traffic flow models can be formulated and solved more efficiently and accurately in Lagrangian (vehicle number-time) coordinates (which move with traffic stream) than in Eulerian coordinates (which are fixed in space). In this article such a Lagrangian system model for state estimation is used. The approach uses the extended Kalman filtering technique, in which the discretized Lagrangian kinematic wave model with an extension (node models) for network discontinuities is used as the process equation and the average relation between vehicle spacing and speed (the fundamental diagram) is used as the observation equation. The Lagrangian state estimator is validated and compared with itsEulerian counterpart based on ground-truth data from a microscopic simulation environment. The results demonstrate that networkwide Lagrangian state estimation is possible and provide evidence that the Lagrangian estimator outperforms the Eulerian approach.