Optimal time-varying flows on congested networks
Operations Research
A new class of instantaneous dynamic user-optimal traffic assignment models
Operations Research
A Whole-Link Travel-Time Model with Desirable Properties
Transportation Science
On the Existence of Solutions to the Dynamic User Equilibrium Problem
Transportation Science
An Analytical Model for Traffic Delays and the Dynamic User Equilibrium Problem
Operations Research
Convergence of a Discretised Travel-Time Model
Transportation Science
Congestion Pricing for Schedule-Based Transit Networks
Transportation Science
Discrete time dynamic traffic assignment models and solution algorithm for managed lanes
Journal of Global Optimization
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This paper proposes a system optimal dynamic traffic assignment model that does not require the network to be empty at the beginning or at the end of the planning horizon. The model assumes that link travel times depend on traffic densities and uses a discretized planning horizon. The resulting formulation is a nonlinear program with binary variables and a time-expanded network structure. Under a relatively mild condition, the nonlinear program has a feasible solution. When necessary, constraints can be added to ensure that the solution satisfies the First-In-First-Out condition. Also included are approximation schemes based on linear integer programs that can provide solutions arbitrarily close to that of the original nonlinear problem.