Street\
    Philadelphia, PA 19122
author:
- Shimao Fan
- Michael Herty
- Benjamin Seibold
bibliography:
- 'references\_complete.bib'
title: 'Comparative Model Accuracy of a Data-Fitted Generalized Aw-Rascle-Zhang Model'
---

.9ex

Introduction
============

The mathematical modeling of vehicular traffic flow knows a variety of types of descriptions (see [@Helbing2001; @BellomoDogbe2011] for review papers): *microscopic* (e.g., [@Pipes1953; @Newell1961; @BandoHesebeNakayama1995; @Helbing1995]), which model the individual vehicles and their interactions by ODE; *cellular* (e.g., [@NagelSchreckenberg1992; @FukuiIshibashi1996; @Daganzo2006; @SakaiNishinariIIda2006; @AlperovichSopasakis2008]), which divide the road into cells and prescribe stochastic rules how vehicles advance through cells; and *continuum*. This latter class divides into *mesoscopic/gas-kinetic* (e.g., [@HermanPrigogine1971; @Phillips1979; @KlarWegener2000; @IllnerKlarMaterne2003; @HertyPareschi2010; @HertyIllner2010]) and *macroscopic* (e.g., [@LighthillWhitham1955; @Richards1956; @Underwood1961; @Payne1971; @Payne1979; @Lebacque1993; @KernerKonhauser1993; @KernerKonhauser1994; @Daganzo1995; @AwRascle2000; @Daganzo2006; @GaravelloPiccoli2006; @Goatin2006; @BerthelinDegondDelitalaRascle2008; @BayenClaudel2011]), i.e., fluid-dynamical, models. Among the (inviscid) macroscopic models one distinguishes between first-order models based on scalar hyperbolic equations and second-order models comprised of systems of hyperbolic equations. Specific examples for the latter are the Payne-Whitham model [@Payne1971; @Whitham1974], two-phase models [@ColomboGoatin2006], and the Aw-Rascle-Zhang model [@AwRascle2000; @Greenberg2001; @Zhang2002; @BerthelinDegondDelitalaRascle2008].

All of these types of traffic models are of practical importance, however—due to their different mathematical structure—for different purposes. For instance, microscopic models are well-suited for traffic simulation, i.e., 