Implicit Methods for Equation-Free Analysis: Convergence Results and Analysis of Emergent Waves in Microscopic Traffic Models

We introduce a general formulation for an implicit equation-free method in the setting of slow-fast systems. First, we give a rigorous convergence result for equation-free analysis showing that the implicitly defined coarse-level time stepper converges to the true dynamics on the slow manifold within an error that is exponentially small with respect to the small parameter measuring time scale separation. Second, we apply this result to the idealized traffic modeling problem of phantom jams generated by cars with uniform behavior on a circular road. The traffic jams are waves that travel slowly against the direction of traffic. Equation-free analysis enables us to investigate the behavior of the microscopic traffic model on a macroscopic level. The standard deviation of cars' headways is chosen as the macroscopic measure of the underlying dynamics such that traveling wave solutions correspond to equilibria on the macroscopic level in the equation-free setup. The collapse of the traffic jam to the free flow then corresponds to a saddle-node bifurcation of this macroscopic equilibrium. We continue this bifurcation in two parameters using equation-free analysis.Comment: 35 page

Developments in Estimation and Control for Cloud-Enabled Automotive Vehicles.

Cloud computing is revolutionizing access to distributed information and computing resources that can facilitate future data and computation intensive vehicular control functions and improve vehicle driving comfort and safety. This dissertation investigates several potential Vehicle-to-Cloud-to-Vehicle (V2C2V) applications that can enhance vehicle control and enable additional functionalities by integrating onboard and cloud resources. Firstly, this thesis demonstrates that onboard vehicle sensors can be used to sense road profiles and detect anomalies. This information can be shared with other vehicles and transportation authorities within a V2C2V framework. The response of hitting a pothole is characterized by a multi-phase dynamic model which is validated by comparing simulation results with a higher-fidelity commercial modeling package. A novel framework of simultaneous road profile estimation and anomaly detection is developed by combining a jump diffusion process (JDP)-based estimator and a multi-input observer. The performance of this scheme is evaluated in an experimental vehicle. In addition, a new clustering algorithm is developed to compress anomaly information by processing anomaly report streams. Secondly, a cloud-aided semi-active suspension control problem is studied demonstrating for the first time that road profile information and noise statistics from the cloud can be used to enhance suspension control. The problem of selecting an optimal damping mode from a finite set of damping modes is considered and the best mode is selected based on performance prediction on the cloud. Finally, a cloud-aided multi-metric route planner is investigated in which safety and comfort metrics augment traditional planning metrics such as time, distance, and fuel economy. The safety metric is developed by processing a comprehensive road and crash database while the comfort metric integrates road roughness and anomalies. These metrics and a planning algorithm can be implemented on the cloud to realize the multi-metric route planning. Real-world case studies are presented. The main contribution of this part of the dissertation is in demonstrating the feasibility and benefits of enhancing the existing route planning algorithms with safety and comfort metrics.PhDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/120710/1/zhaojli_1.pd

Statistical Physics of Vehicular Traffic and Some Related Systems

In the so-called "microscopic" models of vehicular traffic, attention is paid explicitly to each individual vehicle each of which is represented by a "particle"; the nature of the "interactions" among these particles is determined by the way the vehicles influence each others' movement. Therefore, vehicular traffic, modeled as a system of interacting "particles" driven far from equilibrium, offers the possibility to study various fundamental aspects of truly nonequilibrium systems which are of current interest in statistical physics. Analytical as well as numerical techniques of statistical physics are being used to study these models to understand rich variety of physical phenomena exhibited by vehicular traffic. Some of these phenomena, observed in vehicular traffic under different circumstances, include transitions from one dynamical phase to another, criticality and self-organized criticality, metastability and hysteresis, phase-segregation, etc. In this critical review, written from the perspective of statistical physics, we explain the guiding principles behind all the main theoretical approaches. But we present detailed discussions on the results obtained mainly from the so-called "particle-hopping" models, particularly emphasizing those which have been formulated in recent years using the language of cellular automata.Comment: 170 pages, Latex, figures include

A fully-discrete-state kinetic theory approach to modeling vehicular traffic

This paper presents a new mathematical model of vehicular traffic, based on the methods of the generalized kinetic theory, in which the space of microscopic states (position and velocity) of the vehicles is genuinely discrete. While in the recent literature discrete-velocity kinetic models of car traffic have already been successfully proposed, this is, to our knowledge, the first attempt to account for all aspects of the physical granularity of car flow within the formalism of the aforesaid mathematical theory. Thanks to a rich but handy structure, the resulting model allows one to easily implement and simulate various realistic scenarios giving rise to characteristic traffic phenomena of practical interest (e.g., queue formation due to roadworks or to a traffic light). Moreover, it is analytically tractable under quite general assumptions, whereby fundamental properties of the solutions can be rigorously proved.Comment: 22 pages, 3 figure

The Dynamics of Vehicular Networks in Urban Environments

Vehicular Ad hoc NETworks (VANETs) have emerged as a platform to support intelligent inter-vehicle communication and improve traffic safety and performance. The road-constrained, high mobility of vehicles, their unbounded power source, and the emergence of roadside wireless infrastructures make VANETs a challenging research topic. A key to the development of protocols for inter-vehicle communication and services lies in the knowledge of the topological characteristics of the VANET communication graph. This paper explores the dynamics of VANETs in urban environments and investigates the impact of these findings in the design of VANET routing protocols. Using both real and realistic mobility traces, we study the networking shape of VANETs under different transmission and market penetration ranges. Given that a number of RSUs have to be deployed for disseminating information to vehicles in an urban area, we also study their impact on vehicular connectivity. Through extensive simulations we investigate the performance of VANET routing protocols by exploiting the knowledge of VANET graphs analysis.Comment: Revised our testbed with even more realistic mobility traces. Used the location of real Wi-Fi hotspots to simulate RSUs in our study. Used a larger, real mobility trace set, from taxis in Shanghai. Examine the implications of our findings in the design of VANET routing protocols by implementing in ns-3 two routing protocols (GPCR & VADD). Updated the bibliography section with new research work