Traditional DTA models of large cities suffer from prohibitive computationtimes and calibration/validation can become major challenges faced bypractitioners. The empirical evidence in 2008 in support of the existence of aMacroscopic Fundamental Diagram (MFD) on urban networks led to the formulationof discrete-space models, where the city is divided into a collection ofreservoirs. Prior to 2008, a large body of DTA models based on pedestrian flowmodels had been formulated in continuum space as 2-dimensional conservationlaws where the speed-density relationship can now be interpreted as the MFD.Perhaps surprisingly, we found that this continuum-space literature has beenmostly unaware of MFD theory, and no attempts exist to verify the assumptionsof MFD theory. This has the potential to create significant inconsistencies,and research is needed to analyze their extent and ways to resolve them. Wealso find that further research is needed to (i) incorporate departure timechoice, (ii) improve existing numerical methods, possibly extending recentadvances on the one-dimensional kinematic wave (LWR) model, (iii) study theproperties of system optimum solutions, (iv) examine the real-timeapplicability of current continuum-space models compared to traditional DTAmethods, and (v) formulate anisotropic models for the interaction ofintersecting flows.
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