Journal ArticleDOI
Complementarity formulations for the cell transmission model based dynamic user equilibrium with departure time choice, elastic demand and user heterogeneity
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This paper formulate the dynamic user equilibrium problem with an embedded cell transmission model on a network with a single OD pair, multiple parallel paths, multiple user classes with elastic demand, based on ideas from complementarity theory.Abstract:
In this paper we formulate the dynamic user equilibrium problem with an embedded cell transmission model on a network with a single OD pair, multiple parallel paths, multiple user classes with elastic demand. The formulation is based on ideas from complementarity theory. The travel time is estimated based on two methods which have different transportation applications: (1) maximum travel time and (2) average travel time. These travel time functions result in linear and non-linear complementarity formulations respectively. Solution existence and the properties of the formulations are rigorously analyzed. Extensive computational experiments are conducted to demonstrate the benefits of the proposed formulations on various test networks.read more
Citations
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A linear programming formulation for autonomous intersection control within a dynamic traffic assignment and connected vehicle environment
Feng Zhu,Satish V. Ukkusuri +1 more
TL;DR: In this paper, a linear programming formulation for autonomous intersection control (LPAIC) is proposed to account for traffic dynamics within a connected vehicle environment, where a lane based bi-level optimization model is introduced to propagate traffic flows in the network, accounting for dynamic departure time, dynamic route choice, and autonomous intersections control in the context of system optimum network model.
Journal ArticleDOI
Dynamic user equilibrium with a path based cell transmission model for general traffic networks
TL;DR: In this paper, the authors developed a formulation for the network level dynamic traffic equilibrium model with departure time choice and route choice, where the embedded network loading procedure follows the cell transmission model without the holding-back issues by using detailed representations of flows at merges and diverges.
Journal ArticleDOI
Accounting for dynamic speed limit control in a stochastic traffic environment: a reinforcement learning approach
Feng Zhu,Satish V. Ukkusuri +1 more
TL;DR: A link based dynamic network loading model is developed to simulate the traffic flow propagation allowing the change of speed limits and the optimal speed limit scheme is obtained by applying the R-Markov Average Reward Technique (R-MART) based reinforcement learning algorithm.
Journal ArticleDOI
Existence of simultaneous route and departure choice dynamic user equilibrium
Ke Han,Terry L. Friesz,Tao Yao +2 more
TL;DR: In this article, the authors derived the existence of the simultaneous route-and-departure choice dynamic user equilibrium (SRDC-DUE) in continuous time, first formulated as an infinite-dimensional variational inequality in Friesz et al. (1993).
Journal ArticleDOI
Formulation, existence, and computation of boundedly rational dynamic user equilibrium with fixed or endogenous user tolerance
TL;DR: In this paper, a unified approach for modeling both BR-DUE and variable tolerance dynamic user equilibrium is presented, which makes significant contributions to the model formulation, analysis of existence, solution characterization, and numerical computation of such problems.
References
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Book
Differential Equations with Discontinuous Righthand Sides
TL;DR: The kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics, algebraic geometry interacts with physics, and such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes.
Book
Finite-Dimensional Variational Inequalities and Complementarity Problems
TL;DR: Newton Methods for Nonsmooth Equations as mentioned in this paper and global methods for nonsmooth equations were used to solve the Complementarity problem in the context of non-complementarity problems.
Book
The Linear Complementarity Problem
TL;DR: In this article, the authors present an overview of existing and multiplicity of degree theory and propose pivoting methods and iterative methods for degree analysis, including sensitivity and stability analysis.
Journal ArticleDOI
The cell transmission model: a dynamic representation of highway traffic consistent with the hydrodynamic theory
TL;DR: In this paper, a simple representation of traffic on a highway with a single entrance and exit is presented, which can be used to predict traffic's evolution over time and space, including transient phenomena such as the building, propagation, and dissipation of queues.
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Congestion Theory and Transport Investment
TL;DR: In this paper, the authors discuss the investment designed to relieve congestion and distinguish six types of congested situations, which are: simple interaction, multiple interaction, bottleneck, triggerneck, network and control, and general density.