Macroscopic Fundamental Diagrams for Freeway Networks: Theory and Observation

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Hysteresis Phenomena of a Macroscopic Fundamental Diagram in Freeway Networks (2011, background): “Recently, Cassidy et al. (2011), observed macro-relations in freeway networks if data come from periods where all lanes on all links of the studied network are either in the congested or the uncongested regime.”
Generalized bathtub model of network trip flows (2019, methodology): “For freeway networks, we can use the triangular fundamental diagram (Cassidy et al., 2011): V (ρ) = min{u,w(κ ρ −1)}, (15) where u is the free-flow speed, w the shock wave speed in congested traffic, and κ the per-lane jam density.”
Exploring Properties of Networkwide Flow–Density Relations in a Freeway Network (2012, background): “showed that when observations are limited to periods in which traffic is in the stable regime in all lanes and on all links, well-defined, low-scatter, and reproducible freeway MFDs can be obtained (11).”
Stochastic Approximations for the Macroscopic Fundamental Diagram of Urban Networks (2015, background): “…empirical (Geroliminis and Daganzo, 2007, 2008; Wu et al., 2011; Saberi and Mahmassani, 2012; Geroliminis and Sun, 2011; Geroliminis and Ji, 2011; Cassidy et al., 2011; Knoop, 2012; Gayah and Daganzo, 2011; Buisson and Ladier, 2009; Daganzo et al., 2011), (ii) analytical (Daganzo and…”