Dynamic traffic assignment using the macroscopic fundamental diagram: A Review of vehicular and pedestrian flow models

Link-level Dynamic Traffic Assignment (DTA) models of large cities may suffer from prohibitive computation times, and calibration/validation can become the major challenge faced in their real-time implementation. 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 DTA models, where the link-level representation of networks replaced by a zone-based representation. In parallel, a large body of DTA models based on Hughes’ pedestrian model have been formulated in continuum space as 2-dimensional conservation laws, where the speed-density relationship has been recently interpreted as a MFD. Unfortunately, today it is not clear whether the continuum-space and discrete-space approaches are consistent with each other, in the sense that a well-defined discrete-space model should correspond to the numerical solution of a continuum model. This paper aims to shed light on this matter by performing a review of the literature in both modeling approaches. We found that (i) the discrete-space DTA models are prone to stalling problem leading to unrealistic gridlocks, (ii) with the exception of Hänseler’s pedestrian models, existing discrete-space models are not guaranteed to be consistent with a continuum formulation, which presents the potential for significant biases between the two approaches although they are trying to answer the same question, (iii) the speed-density relationships used in the continuum-space literature are very simplistic and do not incorporate the effects of network, particularly the effects of intersections, which is the strong suit of the MFD, (iv) the models mostly have been applied to the cases with only one or a few destinations and do not seem to be capable of modeling large-scale networks. We also found 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.