  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.
