From Microscopic to Macroscopic Traffic Flow: A Queuing Theoretic Approach

无人驾驶汽车和车辆间通信方面的新兴能力正在超过传统的基于模拟的建模工具的分析和设计能力。该项目将侧重于将车辆规模特征与系统级性能指标联系起来的方法。例如，自动跟车和换道等功能将与高峰通行能力和平均出行时间等宏观交通属性相关。城市交通系统的系统分析和设计可以挽救生命，防止伤害，缓解交通拥堵，改善环境。更广泛地说，该项目将创建一种严格的统计力学理论，适用于其他多粒子/代理系统，如人群运动和移动机器人的队形。这项研究将通过PI开发的研究生和本科生课程的软件项目与教育部分紧密结合。将利用南加州大学的现有方案，将包容性教学做法纳入教育活动，以解决留住妇女、任职人数不足和少数族裔学生的问题。该项目旨在克服现有基于分析和模拟的交通模型的缺点。现有的分析技术要么只适用于封闭系统，即固定数量的车辆，其运动可能由领头人协调，要么假设流动动力学是准静态的。基于模拟的方法不适合开发基本的洞察力。这个项目将通过两个新的研究推动力来解决这些缺点。第一个推力是在各种跟车和变道模型下建立严格的水平交通排队理论。这一理论的显著特点是能够捕捉微观拥塞影响，而不是使用点排队模型的方法固有的有限分辨率。该分析首先针对基础道路基础设施的特定参数、车辆之间的通信网络以及单个车辆的机械约束，确定与交通流量相关联的吞吐量和平均行程时间之间的基本关系。第二个研究重点是使用流体极限来推导给定的微观相互作用规则集的宏观交通流模型。这里的一个关键工具是取自处理器共享队列文献的测量值状态描述符的概念，它为在公共状态空间中分析具有时变维度的交通系统提供了统一的设置。

Emerging capabilities in driverless cars and inter-vehicle communication are outpacing the analysis and design capabilities of traditional simulation-based modeling tools. This project will focus on methods linking vehicle-scale characteristics to system-level performance metrics. For example, features such as autonomous car-following and lane-changing will be related to macroscopic traffic properties such as peak capacity and average travel times. Systematic analysis and design of urban traffic systems may save lives, prevent injuries, ease traffic congestion, and improve the environment. More generally, the project will create a rigorous statistical mechanics theory applicable to other multi-particle/agent systems, such as crowd motion and formations of mobile robots. The research will be tightly integrated with the education component through software projects in the graduate and undergraduate courses developed by the PI. Existing programs at the University of Southern California will be utilized to integrate inclusive teaching practices into educational activities in order to address retention of women, underrepresented and minority students. This project seeks to overcome the shortcomings of existing analytical and simulation-based traffic models. Available analytical techniques either apply only to closed systems, i.e., to a fixed number of vehicles whose motion is possibly coordinated by a leader, or they assume that the flow dynamics are quasi-static. Simulation-based methodologies are not suitable for developing fundamental insights. This project will address these shortcomings through two novel research thrusts. The first thrust is formulation of a rigorous horizontal traffic queuing theory under various car following and lane-changing models. The distinguishing feature of this theory is the ability to capture microscopic congestion effects, in contrast to the limited resolution inherent in approaches that use point queue models. The analysis begins by identifying fundamental relationships between throughput and average travel times associated with traffic flow for specified parameters of the underlying road infrastructure, communication network between the vehicles, and mechanical constraints of individual vehicles. The second research thrust is use of the fluid limit to derive macroscopic traffic flow models for a given set of microscopic interaction rules. A key tool here is the notion of measure-valued state descriptors, taken from the processor sharing queue literature, which provides a unified setting for the analysis of traffic systems with time-varying dimension in a common state space.