BECS Collaborative Research: Modeling the Dynamics of Traffic User Equilibria Using Differential Variational Inequalities

BECS 协作研究：使用微分变分不等式对交通用户均衡动态进行建模

• 批准号: 1412544
• 负责人: Jong-Shi Pang
• 金额: $ 4.09万
• 依托单位: University of Southern California
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-08-16 至 2014-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1412544&HistoricalAwards=false
• 关键词: BECS; Collaborative; Research; Modeling; Dynamics

The goal of this project is to employ a novel mathematical paradigm, known as a differential variational inequality (DVI), to study two fundamental problems in transportation analysis, namely, the continue-time dynamic user equilibrium with flow propagation and delays, and the problem of traffic disequilibrium in the face of network disruption. Our aim is to develop a nonlinear dynamical system theory that combines classical ordinary differential equation (ODE) methods with contemporary mathematical programming advances to study the equilibrium of short-time (e.g. within-day dynamics) and the equilibration process of longer-time (e.g. transient dynamics) traffic flows, answering questions such as: how to compute dynamic user equilibria, how traffic evolves from a disequilibrium state, due to network disruptions, toward an equilibrium, and how close the current traffic state is to an equilibrium. Results from this study will lead to a new paradigm integrating traffic network analysis methods with recent advances in mathematical science, and bridge the gaps between current practice of traffic analysis and the needs to consider short-term and long-term traffic dynamics in a holistic manner. The research will be the first step to develop a mathematical framework for traffic dynamic analysis that, in a long term, has the potential to revolutionize the traditional way of conducting transportation analyses such as network signal optimization, dynamic congestion pricing, emergency management after disruptions, among others. Since equilibrium analysis and system dynamics are widely used in other science and engineering fields, the concepts and methodologies developed in this research can also provide new perspectives for equilibrium based analysis in these fields. The research team plans to integrate research findings to undergraduate and graduate courses, and involve undergraduate and graduate students with multidisciplinary backgrounds in this research. The team also plans to reach out to policy makers and practitioners at various transportation management agencies for whom findings from the proposed research will enable them to better manage transportation systems.

该项目的目的是采用一种新型的数学范式，称为差异性不平等（DVI），研究运输分析中的两个基本问题，即，持续时间动态用户均衡，流动传播和延迟以及面对网络破坏时交通不平衡问题。 Our aim is to develop a nonlinear dynamical system theory that combines classical ordinary differential equation (ODE) methods with contemporary mathematical programming advances to study the equilibrium of short-time (e.g. within-day dynamics) and the equilibration process of longer-time (e.g. transient dynamics) traffic flows, answering questions such as: how to compute dynamic user equilibria, how traffic evolves from a disequilibrium state, due to network干扰，朝平衡以及当前的交通状态与平衡的距离程度。这项研究的结果将导致一个新的范式，将交通网络分析方法与数学科学的最新进展相结合，并弥合当前交通分析实践与以整体方式考虑短期和长期交通动态的需求之间的差距。 这项研究将是开发数学框架进行交通动态分析的第一步，从长远来看，该框架有可能彻底改变进行运输分析的传统方式，例如网络信号优化，动态拥堵定价，中断后的紧急管理等。由于平衡分析和系统动力学在其他科学和工程领域广泛使用，因此在本研究中开发的概念和方法还可以为这些领域的基于平衡分析提供新的观点。研究小组计划将研究结果纳入本科和研究生课程，并参与本研究中具有多学科背景的本科生和研究生。该团队还计划与各种运输管理机构的政策制定者和从业人员接触，拟议研究的发现将使他们能够更好地管理运输系统。