On the Existence of Solutions to the Dynamic User Equilibrium Problem

@article{Zhu2000OnTE,
  title={On the Existence of Solutions to the Dynamic User Equilibrium Problem},
  author={Daoli Zhu and Patrice Marcotte},
  journal={Transp. Sci.},
  year={2000},
  volume={34},
  pages={402-414}
}
This paper is concerned with the existence of solutions to a dynamic network equilibrium problem modeled as an infinite dimensional variational inequality. Our results are based on properties of operators that map path flow departure rates to consistent time-dependent path flows and other link performance functions. The existence result requires the introduction of a novel concept that strengthens the familiar concept of First-In-First-Out (FIFO). 
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References

SHOWING 1-10 OF 40 REFERENCES
A Variational Inequality Formulation of the Dynamic Network User Equilibrium Problem
TLDR
It is shown for the first time that there is a variational inequality formulation of dynamic user equilibrium with simultaneous route choice and departure time decisions which, when appropriate regularity conditions hold, preserves the first in, first out queue discipline.
A Discrete Time, Nested Cost Operator Approach to the Dynamic Network User Equilibrium Problem
TLDR
This paper shows how arc exit flow functions and nested cost operators can be used to calculate unit path costs given the departure time and route choices of network users, and demonstrates that a discrete time dynamic network user equilibrium is guaranteed to exist.
Dynamic Network Traffic Assignment Considered as a Continuous Time Optimal Control Problem
TLDR
It is established that a constraint qualification and convexity requirements for the Hamiltonian, which together ensure that the necessary conditions are also sufficient, are satisfied under commonly encountered regularity conditions.
Advances in the Continuous Dynamic Network Loading Problem
TLDR
The authors show, under a boundedness condition, that there exists a unique solution to the CDNLP problem and propose for its solution a finite-step algorithm.
A Model and an Algorithm for the Dynamic Traffic Assignment Problems
TLDR
A discrete time model is presented for dynamic traffice assignment with a single destination and can be solved for a global optimum using a one-pass simplex algorithm---branch-and-bound is not required.
Dynamic User Equilibrium Departure Time and Route Choice on Idealized Traffic Arterials
An extension of a recent framework for analyzing the time-dependent departure pattern arising in an idealized situation of a pool of commuters going from a single origin to a single destination along
...
...