Dynamic Traffic Assignment using the Macroscopic Fundamental Diagram: A Review of Vehicular and Pedestrian Flow Models

TL;DR

This review discusses the use of the Macroscopic Fundamental Diagram in dynamic traffic assignment, highlighting gaps in theory application, and proposing directions for improving models for urban vehicular and pedestrian flow.

Contribution

It identifies the disconnect between MFD theory and existing continuum-space pedestrian flow models, and suggests research avenues for integrating departure choices, numerical methods, and real-time applications.

Findings

Continuum-space pedestrian models largely unaware of MFD theory.

No existing verification of MFD assumptions in pedestrian flow models.

Research needed to incorporate departure time choice and improve numerical methods.

Abstract

Traditional DTA models of large cities suffer from prohibitive computation times and calibration/validation can become major challenges faced by practitioners. The empirical evidence in 2008 in support of the existence of a Macroscopic Fundamental Diagram (MFD) on urban networks led to the formulation of discrete-space models, where the city is divided into a collection of reservoirs. Prior to 2008, a large body of DTA models based on pedestrian flow models had been formulated in continuum space as 2-dimensional conservation laws where the speed-density relationship can now be interpreted as the MFD. Perhaps surprisingly, we found that this continuum-space literature has been mostly unaware of MFD theory, and no attempts exist to verify the assumptions of MFD theory. This has the potential to create significant inconsistencies, and research is needed to analyze their extent and ways to resolve them. We also find that further research is needed to (i) incorporate departure time choice, (ii) improve existing numerical methods, possibly extending recent advances on the one-dimensional kinematic wave (LWR) model, (iii) study the properties of system optimum solutions, (iv) examine the real-time applicability of current continuum-space models compared to traditional DTA methods, and (v) formulate anisotropic models for the interaction of intersecting flows.