Morning Commute with Competing Modes and Distributed Demand: User Equilibrium, System Optimum, and Pricing

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Congestion in the bathtub (2015, methodology): “The engineering literature considers a second macroscopic relationship called the network exit function (Gonzales and Daganzo, 2012), which relates the rate at which trips are completed to density.”
Generalized bathtub model of network trip flows (2019, background): “…distribution of trip distances, the only unknown variable is λ ( t ) , and the bathtub model is equivalent to the simpliﬁed version of (24): In this case, the out-ﬂux or the trip completion rate equals (Gonzales and Daganzo, 2012) which is proportional to the trafﬁc ﬂow rate Q ( ρ ( t )) .”
Multimodal pricing and optimal design of urban public transport: The interplay between traffic congestion and bus crowding (2014, background): “2 Excluding non-motorised alternatives, the properties of the bimodal car-bus competition for user equilibrium and/or system optimum solutions are analysed in a number of contributions, e.g., Ahn (2009), Li et al. (2012), and Gonzales and Daganzo (2012, 2013).”