An interface-free multi-scale multi-order model for traffic flow

Abstract

In this paper we present a new multi-scale method for reproducing traffic flow which couples a first-order macroscopic model with a second-order microscopic model, avoiding any interface or boundary conditions between them. The multi-scale model is characterized by the fact that microscopic and macroscopic descriptions are not spatially separated. On the contrary, the macro-scale is always active while the micro-scale is activated only if needed by the traffic conditions. The Euler-Godunov scheme associated to the model is conservative and it is able to reproduce typical traffic phenomena like stop & go waves.

Macroscopic and Multi-Scale Models for Multi-Class Vehicular Dynamics with Uneven Space Occupancy: A Case Study

“…Due to this difference, it is plain that the model ( 2) is not the many-particle limit of the model (1). We refer the interested reader to [3] for a review of various many-particle limits (i.e., micro-to-macro correspondences) and the existing multi-scale models.…”

Properties of the LWR model with time delay

“…Starting from empirical observations and the work done in [18,47], let us assume the velocity function as follow:…”

“…a slowdown, in the initial data, our aim is to find out if it is possible to recover a S&G wave. In this direction, let us consider the example presented in [18], in which the initial data is given by:…”

“…In [18], the density evolution is computed by coupling the LWR model with a second order microscopic model, specifically conceived to reproduce S&G waves. Instead of switching to multiscale models in which we have to manage the microscopic model too, let us see if we can recover the density evolution with the delayed model.…”

“…To do this, the equation that describes the variation of the velocity in time has to be added to the system, replacing the typical given law of the fist order models. Other ways are also possible to improve first order models, just considering phase transition models [6,14], non-local traffic models [5,15,23,25,29,43] or multi-scale approaches [16,18]. Instead of switching to second order models, we propose a first order macroscopic model with a time delay term in the flux function, for taking into account that the velocity can not change instantaneously.…”