Micro-structure in linear elasticity

Since the subject of traffic dynamics has captured the interest of physicists, many surprising effects have been revealed and explained. Some of the questions now understood are the following: Why are vehicles sometimes stopped by ``phantom traffic jams'' even though drivers all like to drive fast? What are the mechanisms behind stop-and-go traffic? Why are there several different kinds of congestion, and how are they related? Why do most traffic jams occur considerably before the road capacity is reached? Can a temporary reduction in the volume of traffic cause a lasting traffic jam? Under which conditions can speed limits speed up traffic? Why do pedestrians moving in opposite directions normally organize into lanes, while similar systems ``freeze by heating''? All of these questions have been answered by applying and extending methods from statistical physics and nonlinear dynamics to self-driven many-particle systems. This article considers the empirical data and then reviews the main approaches to modeling pedestrian and vehicle traffic. These include microscopic (particle-based), mesoscopic (gas-kinetic), and macroscopic (fluid-dynamic) models. Attention is also paid to the formulation of a micro-macro link, to aspects of universality, and to other unifying concepts, such as a general modeling framework for self-driven many-particle systems, including spin systems. While the primary focus is upon vehicle and pedestrian traffic, applications to biological or socio-economic systems such as bacterial colonies, flocks of birds, panics, and stock market dynamics are touched upon as well.

Traffic and related self-driven many-particle systems

The ability to predict the response of a vehicle in a stream of traffic to the behaviour of its predecessor is important in estimating what effect changes to the driving environment will have on traffic flow. Various proposed to explain this behaviour have different strengths and weaknesses. The paper constructs a new model for the response of the following vehicle based on the assumption that each driver sets limits to his desired braking and acceleration rates. The parameters in the model correspond directly to obvious characteristics of driver behaviour and the paper goes on to show that when realistic values are assigned to the parameters in a simulation, the model reproduces the characteristics of real traffic flow.

A behavioural car-following model for computer simulation

A variety of nonlinear follow-the-leader models of traffic flow are discussed in the light of available observational and experimental data. Emphasis is placed on steady-state flow equations. Some trends regarding the advantages of certain follow-the-leader functionals over others are established. However, it is found from extensive correlation studies that more data are needed before one can establish the unequivocal superiority of one particular model. A discussion is given of some ideas concerning the possible reasons for the existence of a bimodal flow versus concentration curve especially for multilane highways.

Nonlinear Follow-the-Leader Models of Traffic Flow

In recent years, the topic of car-following has become of increased importance in traffic engineering and safety research. Models of this phenomenon, which describe the interaction between (typically) adjacent vehicles in the same lane, now form the cornerstone for many important areas of research including (a) simulation modelling, where the car-following model (amongst others) controls the motion of the vehicles in the network, and (b) the functional definition of advanced vehicle control and safety systems (AVCSS), which are being introduced as a driver safety aid in an effort to mimic driver behaviour but remove human error. Despite the importance of this area however, no overview of the models availability and validity exists. It is the intent of this paper therefore to briefly assess the range of options available in the choice of car-following model, and assess just how far work has proceeded in our understanding of what, at times, would appear to be a simple process.

Car-following: a historical review

The steady-state flow is examined for a car-following model in which the acceleration at time t of a car attempting to follow a lead car is proportional to the relative velocity at a time t − Δ and in which the sensitivity λ is no longer taken constant as in previous work but is inversely proportional to the car spacing. The characteristics of the steady-state flow for this model are described and compared with experimental data.

Car-Following Theory of Steady-State Traffic Flow

A theoretical analysis and observations of the behavior of motorists confronted by an amber signal light are presented. A discussion is given of the following problem when confronted with an improperly timed amber light phase a motorist may find himself, at the moment the amber phase commences, in the predicament of being too close to the intersection to stop safely or comfortably and yet too far from it to pass completely through the intersection before the red signal commences. The influence on this problem of the speed of approach to the intersection is analyzed. Criteria are presented for the design of amber signal light phases through whose use such “dilemma zones” can be avoided, in the interest of over-all safety at intersections.

http://redlightrobber.com/red/links_pdf/The-Problem-of-the-Amber-Signal-Light-in-Traffic-Flow.pdf

The Problem of the Amber Signal Light in Traffic Flow

A theoretical investigation of surface elastic waves in cubic crystals has been carried out using a theory developed by Stoneley. The range of elastic constants for which Rayleigh type surface waves exist on a (100) free surface has been determined. For other allowed values of the elastic constants generalized Rayleigh waves exist which are characterized by complex attenuation constants. In either case waves may not be propagated in certain directions parallel to the surface depending on the values of the elastic constants. A lattice dynamical theory of surface waves has been developed for a monatomic simple cubic lattice with nearest and next nearest neighbor central forces and angle-bending forces involving successive nearest neighbors. The surface waves exhibit dispersion when the wavelength is comparable to the lattice spacing. In the case of Rayleigh waves a critical wavelength exists, in general, such that for shorter wavelengths the atomic displacements show a reversal in phase between successive layers parallel to the surface.

Surface Elastic Waves in Cubic Crystals

When a slow-moving vehicle occupies one of the lanes of a multilane highway, it often causes queueing behind it, not unlike one caused by an actual stoppage on that lane. This happens when the traffic flow rate upstream from the slow vehicle exceeds a certain critical value. We define this situation as the case of the Moving Bottleneck. There are other situations when people caught in a traffic jam slowly advance to the point of a suspected breakdown or other obstruction, only to find out that no such obstruction exists but suddenly the flow of traffic is free and rapid. We define this situation as that of the Phantom Bottleneck. We present a model describing these two situations on the basis of reasonable assumptions about the behavior of drivers whose movement is obstructed by the slow vehicle. Using a phenomenological relationship between flow and concentration, we derive formulas describing the behavior of the moving queue caused by the obstruction. Finally, we suggest procedures for validating the mo...

Denos C. Gazis

Papers

Nonlinear Follow-the-Leader Models of Traffic Flow

Car-Following Theory of Steady-State Traffic Flow

The Problem of the Amber Signal Light in Traffic Flow

Surface Elastic Waves in Cubic Crystals

The Moving and “Phantom” Bottlenecks