Day-to-Day Dynamic Model in Discrete–Continuum Transportation Networks

Abstract

In a discrete–continuum transportation network, the freeway network is modeled as an ordinary discrete link–node network; the dense minor streets are approximated as a two-dimensional continuum; and the two are connected at a limited number of points (freeway ramps). This representation of a discrete–continuum network highlights the backbone role played by the freeway network in modern urban transportation systems, and the continuum approximation approach suits large-scale dense minor streets. Previous studies on continuum network modeling all focused on the concept of network equilibrium. In this paper, the disequilibrium flow evolution process is studied after some network disruption or facility change has taken place. A day-to-day dynamic model suitable for the discrete–continuum representation of urban transportation networks is proposed. This model captures travelers' cost-minimization behavior in their path finding and also captures their inertia. The fixed point of the proposed dynamical system is the classic Wardrop user equilibrium. A numerical example is provided to demonstrate the effectiveness of the model.

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