Multiscale Traffic Flow Model Based on the Mesoscopic Lighthill–Whitham and Richards Models

Abstract

This article reviews the multiscale modeling concept as an adaptive strategy in traffic flow modeling. The central objective for the multi-scale model is to describe and to predict traffic phenomena (e.g., individual accelerations, queuing) that occur at different scales by switching between modeling paradigms. The emphasis in this paper is placed on resolving inconsistencies that arise in the process of integrating models, which are addressed with the mesoscopic Lighthill–Whitham and Richards models—together, widely known as the Lighthill–Whitham–Richards (LWR) model—as the coarse-scale model in the framework. The mesoscopic model is fully consistent at the macroscopic scale with the classic LWR model but does facilitate tracking of individual vehicles. Because of this characteristic, this model can be combined with microscopic models, because no disaggregation or aggregation process is needed. It is thus implied, for example, that travel information (e.g., destination) can be carried over this model without loss of information. Also, vehicle heterogeneity can be incorporated in the mesoscopic model and, as a result, is preserved in the process of switching between models. A brief overview of the mesoscopic LWR model and its solution by the variational theory is presented. General boundary conditions, including internal boundaries (e.g., moving bottlenecks) and interfaces between models, are analyzed and evaluated. The solution of some cases, in which the stationary and moving bottlenecks interact, is provided. The paper concludes with a case study that demonstrates the integration of microscopic and mesoscopic models in a multiscale model and investigates the influence of various boundary conditions on traffic features.