Kinetic Model for Vehicular Traffic with Continuum Velocity and Mean Field Interactions

This paper is concerned with the modeling and mathematical analysis of vehicular traffic phenomena. We adopt a kinetic theory point of view, under which the microscopic state of each vehicle is described by: (i) position, (ii) velocity and also (iii) activity, an additional varible that we use to describe the quality of the driver-vehicle micro-system. We use methods coming from game theory to describe interactions at the microscopic scale, thus constructing new models within the framework of the Kinetic Theory of Active Particles; the resulting models incorporate some of the symmetries that are commonly found in the mathematical models of the kinetic theory of gases. Short-range interactions and mean field interactions are introduced and modeled to depict velocity changes related to passing phenomena. Our main goal is twofold: (i) to use continuum-velocity variables and (ii) to introduce a non-local acceleration term modeling mean field interactions, related to, for example, the presence of tollgates or traffic highlights.J.C. and J.N. are partially supported by Junta de Andalucía Project P12-FQM-954 and MINECO Project RTI2018-098850-B-I00. J.C. is supported by Universidad de Granada (“Plan propio de investigación, programa 9”) through FEDER funds. M.Z. was supported by CNRST (Morocco), project “Modèles Mathématiques appliqués à l’environnement, à l’imagerie médicale et aux biosystèmes”

Some exact solutions to the Lighthill Whitham Richards Payne traffic flow equations II: moderate congestion

We find a further class of exact solutions to the Lighthill Whitham Richards Payne (LWRP) traffic flow equations. As before, using two consecutive Lagrangian transformations, a linearization is achieved. Next, depending on the initial density, we either obtain exact formulae for the dependence of the car density and velocity on x, t, or else, failing that, the same result in a parametric representation. The calculation always involves two possible factorizations of a consistency condition. Both must be considered. In physical terms, the lineup usually separates into two offshoots at different velocities. Each velocity soon becomes uniform. This outcome in many ways resembles not only Rowlands, Infeld and Skorupski J. Phys. A: Math. Theor. 46 (2013) 365202 (part I) but also the two soliton solution to the Korteweg-de Vries equation. This paper can be read independently of part I. This explains unavoidable repetitions. Possible uses of both papers in checking numerical codes are indicated at the end. Since LWRP, numerous more elaborate models, including multiple lanes, traffic jams, tollgates etc. abound in the literature. However, we present an exact solution. These are few and far between, other then found by inverse scattering. The literature for various models, including ours, is given. The methods used here and in part I may be useful in solving other problems, such as shallow water flow.Comment: 15 pages, 7 figure

Kinetic Theory and Swarming Tools to Modeling Complex Systems—Symmetry problems in the Science of Living Systems

This MPDI book comprises a number of selected contributions to a Special Issue devoted to the modeling and simulation of living systems based on developments in kinetic mathematical tools. The focus is on a fascinating research field which cannot be tackled by the approach of the so-called hard sciences—specifically mathematics—without the invention of new methods in view of a new mathematical theory. The contents proposed by eight contributions witness the growing interest of scientists this field. The first contribution is an editorial paper which presents the motivations for studying the mathematics and physics of living systems within the framework an interdisciplinary approach, where mathematics and physics interact with specific fields of the class of systems object of modeling and simulations. The different contributions refer to economy, collective learning, cell motion, vehicular traffic, crowd dynamics, and social swarms. The key problem towards modeling consists in capturing the complexity features of living systems. All articles refer to large systems of interaction living entities and follow, towards modeling, a common rationale which consists firstly in representing the system by a probability distribution over the microscopic state of the said entities, secondly, in deriving a general mathematical structure deemed to provide the conceptual basis for the derivation of models and, finally, in implementing the said structure by models of interactions at the microscopic scale. Therefore, the modeling approach transfers the dynamics at the low scale to collective behaviors. Interactions are modeled by theoretical tools of stochastic game theory. Overall, the interested reader will find, in the contents, a forward look comprising various research perspectives and issues, followed by hints on to tackle these

Heritage Patterns—Representative Models

The Heritage Patterns—Representative Models issue of Heritage welcomed twelve articles that discussed traditional and contemporary methodologies, as well as scholars from different backgrounds who intended to seek patterns of tangible heritage and its underlying principles to understand the diversity of heritage approaches. The Special Issue aims to research the patterns in heritage and the underlying rules that define tangible heritage as a universal value in spatial coexistence, economics, urban life, and design via case studies and theoretical proposals that could be implemented in the future. The pattern language and the heritage phenomenon could act as a base of observation to deduct logic and create generative algorithms (generative design); to understand the importance of spatial connection with tangible heritage and urban forms (space syntax, urban morphology, and urban morphometrics) and its visibility; as well as archaeological, architectural, and urban heritage. Based on the UNESCO-ICOMOS doctrines and the examination of morphological regions, urban morphological research and its different layers (urban forms, structural components, built environment, urban tissue, and their interaction) act as a background and foundation for general urban heritage conservation and protection proposals, and also as the base of specific interventions in the built environment caused by natural disasters

VII data use analysis and processing (DUAP): final project report (phase II)

This report covers several key subjects related to the generation of IntelliDriveSM probe vehicle data and use of this data in application of interest to state departments of transportation and local public transportation agencies. The evaluations conducted as part of this project are primarily based on the probe vehicle data collection system that was deployed by the U.S. Department of Transportation (USDOT) around Novi, Michigan, in 2008 for its Vehicle‐Infrastructure Integration (VII) Proof‐of‐Concept (POC) test program. This system was designed around the use of the 5.9‐GHz Dedicated Short Range Communication (DSRC) wireless protocol to enable vehicles to communicate with Roadside Equipment (RSE). The generation of snapshots further followed the protocols defined within the SAE J2735 DSRC Message Set standard. Following a general introduction in Chapter 1, Chapter 2 briefly reviews the protocols that were used to generate and retrieve probe vehicle snapshots, while Chapter 3 presents a general evaluation of the POC test data that were accumulated during the 2008 test program. This is followed by a presentation in Chapter 4 of the evaluation framework of the current project. This presentation includes an overview of the envisioned DUAP system and descriptions of project stakeholders, potential data sources, supporting technologies, applications of interests, and potential operational constraints. Chapter 5 then presents a general description of the Paramics IntelliDriveSM virtual simulator that is used to conduct some of the subsequent evaluations. While the initial POC test program aimed to evaluate data collection capabilities across a range of application, this program was significantly shortened due to various technical issues. This resulted in incomplete data collection and partial application designs that were insufficient to complete the initial project deliverables associated without rely on simulation. Chapter 6 then examines the effects of snapshot generation protocols and privacy policies on data latency, data quality, and the ability to track vehicles over short distances. Chapter 7 follows with a mapping of application data needs and general descriptions of processes required to convert raw probe data into useful information, while Chapter 8 evaluates how basic traffic flow performance measures (flow rates, flow density, travel times, speed profiles, queue parameters) can be estimated from probe data in systems featuring full and partial proportions of probe vehicles. Chapter 9 further develops a concept of operations for an enhanced traffic monitoring system incorporating probe vehicle and other data sources, while Chapter 10 investigates various issues that must be considered when developing application deployment plans. Chapters 11, 12 and 13 finally present a summary of primary findings, lessons learned and recommendations for future work.Michigan Department of Transportation, Lansing, MIhttp://deepblue.lib.umich.edu/bitstream/2027.42/78569/1/102726.pd