Earthquake model describes traffic jams caused by imperfect driving styles

The wide modeling potential of the classical spring-block type system is illustrated by an interdisciplinary application. A simple one-dimensional spring-block chain with asymmetric spring forces is used to model idealized single-lane highway traffic and the emergence of phantom traffic jams. Based on the stop-time statistics of one car in the row, a proper order parameter is defined. By extensive computer simulations the parameter space of the model is explored, analyzed and interpreted. Existence of free and congested flow phases is confirmed and the transition between them is analyzed.     

THE DYNAMIC FRICTION TERM IN THE SPRING-BLOCK MODELS FOR EARTHQUAKES: A CONSTRAINT FROM SEISMIC MOMENT AND ENERGY CATALOGUE

In the spring-block models of earthquakes, one of the key factors is the dynamic friction term which determines the complexity of the faulting process. Generally, two kinds of friction, namely velocity-dependent friction and slip-dependent friction, are used in the modelling. But until now there has still been a lack of information on which kind of friction term is more suitable for modelling the phenomenology of earthquakes. Based on the numerical studies of Shaw (1998 Bull. Seismol. Soc. Am. 88 1457), we have examined the ratio of the broadband radiated energy and the scalar seismic moment of shallow earthquakes worldwide from 1987 to 1998. The result shows that for earthquakes with strike-slip mechanisms, velocity-dependent friction seems to be predominant, while for thrust and normal events, slip-dependent friction seems predominant. This suggests that in the spring-block models for earthquakes, the type of focal mechanism has to be accounted for, and different types of earthquakes require different dynamic friction terms in the corresponding spring-block model.     

Exact Solution of a Cellular Automaton for Traffic

We present an exact solution of a probabilistic cellular automaton for traffic with open boundary conditions, e.g., cars can enter and leave a part of a highway with certain probabilities. The model studied is the asymmetric exclusion process (ASEP) with simultaneous updating of all sites. It is equivalent to a special case (v _max=1) of the Nagel–Schreckenberg model for highway traffic, which has found many applications in real-time traffic simulations. The simultaneous updating induces additional strong short-range correlations compared to other updating schemes. The stationary state is written in terms of a matrix product solution. The corresponding algebra, which expresses a system-size recursion relation for the weights of the configurations, is quartic, in contrast to previous cases, in which the algebra is quadratic. We derive the phase diagram and compute various properties such as density profiles, two-point functions, and the fluctuations in the number of particles (cars) in the system. The current and the density profiles can be mapped onto the ASEP with other time-discrete updating procedures. Through use of this mapping, our results also give new results for these models.     

Sliding size distribution in a simple spring-block system with asperities

We use a simple spring-block system as a qualitative analogous of a seismic fault. The role of the asperities present in a real seismic fault is played by sandpapers of several grades. With this experimental array Gutenberg-Richter type-laws are obtained. We also observed that the maximum characteristic event in each experimental run depends on both the mass of the sliding blocks and the age of the sandpapers used at the interface between the blocks and the rough track.     

Controlling Disorder in Traffic Flow by Perturbation

We propose a new technique for controlling disorder in traffic system. A kind of control signal which can be considered as a perturbation has been designated at a given site (perturbation point) of the single-lane highway. When a vehicle passes the perturbation point at a time, the velocity of the vehicle will be changed at the next time by the perturbation. This technique is tested for the deterministic NaSch traffic model. The simulation results indicate that the traffic system can be transited from the disorder states to the order states, such as fixed-point, periodic motion, etc.     

Criticism of generally accepted fundamentals and methodologies of traffic and transportation theory: A brief review

It is explained why the set of the fundamental empirical features of traffic breakdown (a transition from free flow to congested traffic) should be the empirical basis for any traffic and transportation theory that can be reliably used for control and optimization in traffic networks. It is shown that the generally accepted fundamentals and methodologies of the traffic and transportation theory are not consistent with the set of the fundamental empirical features of traffic breakdown at a highway bottleneck. To these fundamentals and methodologies of the traffic and transportation theory belong (i) Lighthill–Whitham–Richards (LWR) theory, (ii) the General Motors (GM) model class (for example, Herman, Gazis et al. GM model, Gipps’s model, Payne’s model, Newell’s optimal velocity (OV) model, Wiedemann’s model, Bando et al. OV model, Treiber’s IDM, Krauß’s model), (iii) the understanding of highway capacity as a particular (fixed or stochastic) value, and (iv) principles for traffic and transportation network optimization and control (for example, Wardrop’s user equilibrium (UE) and system optimum (SO) principles). Alternatively to these generally accepted fundamentals and methodologies of the traffic and transportation theory, we discuss the three-phase traffic theory as the basis for traffic flow modeling as well as briefly consider the network breakdown minimization (BM) principle for the optimization of traffic and transportation networks with road bottlenecks.     

Multifractal chaotic attractors in a system of delay-differential equations modeling road traffic

We study a system of delay-differential equations modeling single-lane road traffic. The cars move in a closed circuit and the system's variables are each car's velocity and the distance to the car ahead. For low and high values of traffic density the system has a stable equilibrium solution, corresponding to the uniform flow. Gradually decreasing the density from high to intermediate values we observe a sequence of supercritical Hopf bifurcations forming multistable limit cycles, corresponding to flow regimes with periodically moving traffic jams. Using an asymptotic technique we find approximately small limit cycles born at Hopf bifurcations and numerically preform their global continuations with decreasing density. For sufficiently large delay the system passes to chaos following the Ruelle-Takens-Newhouse scenario (limit cycles-two-tori-three-tori-chaotic attractors). We find that chaotic and nonchaotic attractors coexist for the same parameter values and that chaotic attractors have a broad multifractal spectrum. (c) 2002 American Institute of Physics.     

Controlling Disorder in Traffic Flow by Perturbation

We propose a new technique for controlling disorder in traffic system. A kind of control signal which can be considered as a perturbation has been designated at a given site (perturbation point) of the single-lane highway. When a vehicle passes the perturbation point at a time, the velocity of the vehicle will be changed at the next time by the perturbation. This technique is tested for the deterministic NaSch traffic model. The simulation results indicate that the traffic system can be transited from the disorder states to the order states, such as fixed-point, periodic motion, etc.     

Traffic Congestion Mechanism in Two Ramp Systems

The aim of this paper is to study traffic properties in an on/off-ramp system with a bus stop close to the on/off ramp. The location of the bus stop in the on/off-ramp (thereafter downstream or upstream case) is discussed. The simulation results show that in the two ramp systems, the reasons for traffic congestions are different. In the on-ramp system, buses and cars coming from on-ramp interweave each other, while in the off-ramp system, busesinterweave with cars exiting to off-ramp. Thus, in the on-ramp (off-ramp) system, the upstream (downstream) bus stop is helpful to reduce the interweaving situation. Moreover, the negative effect will disappear when the distance between the bus stop and the on/off-ramp is more than 20 cells (i.e. 150 m). These qualitative findings may provide some suggestions on traffic management and optimization.     

Transition from static to kinetic friction: insights from a 2D model

We describe a 2D spring-block model for the transition from static to kinetic friction at an elastic-slider-rigid-substrate interface obeying a minimalistic friction law (Amontons-Coulomb). By using realistic boundary conditions, a number of previously unexplained experimental results on precursory microslip fronts are successfully reproduced. From the analysis of the interfacial stresses, we derive a prediction for the evolution of the precursor length as a function of the applied loads, as well as an approximate relationship between microscopic and macroscopic friction coefficients. We show that the stress buildup due to both elastic loading and microslip-related relaxations depends only weakly on the underlying shear crack propagation dynamics. Conversely, crack speed depends strongly on both the instantaneous stresses and the friction coefficients, through a nontrivial scaling parameter.     

A stochastic multi-cluster model of freeway traffic

A stochastic approach based on the Master equation is proposed to describe the process of formation and growth of car clusters in traffic flow in analogy to usual aggregation phenomena such as the formation of liquid droplets in supersaturated vapour. By this method a coexistence of many clusters on a one-lane circular road has been investigated. Analytical equations have been derived for calculation of the stationary cluster distribution and related physical quantities of an infinitely large system of interacting cars. If the probability per time (or p) to decelerate a car without an obvious reason tends to zero in an infinitely large system, our multi-cluster model behaves essentially in the same way as a one-cluster model studied before. In particular, there are three different regimes of traffic flow (free jet of cars, coexisting phase of jams and isolated cars, highly viscous heavy traffic) and two phase transitions between them. At finite values of p the behaviour is qualitatively different, i.e., there is no sharp phase transition between the free jet of cars and the coexisting phase. Nevertheless, a jump-like phase transition between the coexisting phase and the highly viscous heavy traffic takes place both at and at a finite p. Monte-Carlo simulations have been performed for finite roads showing a time evolution of the system into the stationary state. In distinction to the one-cluster model, a remarkable increasing of the average flux has been detected at certain densities of cars due to finite-size effects. Received 17 September 1999     

Modeling U-turn traffic flow

Median U-turns are sometimes installed to improve the traffic flow at busy intersections by eliminating left turns. Using a microscopic traffic model, we confirmed the presence of transitions from free flow to congested flow with increasing car inflow density. In addition, our proposed rules inside a U-turn curve, which accounted for safety issues and an asymmetric lane changing behavior (outer-to-inner vs. inner-to-outer lane transitions), predicted the speed distribution of cars after the U-turn curve. We found that U-turn curves installed for improving traffic flow at busy intersections produced their desired effects only when there is minimal interaction between cars.     

Coupled vehicle and information flows: Message transport on a dynamic vehicle network

A freeway with vehicles transmitting traffic-related messages via short-range broadcasting is a technological example of coupled material and information flows in complex networks: information on traffic flows is propagated via a dynamically changing ad hoc network based on local interactions. As vehicle and information propagation occur on similar time scales, the network dynamics strongly influences message propagation, which is done by the movement of nodes (cars) and by hops between nearby nodes: two cars within the limited broadcast range establish a dynamic link. Using the cars of the other driving direction as relay stations, the weak connectivity within one driving direction when the density of equipped cars is small can be overcome. By analytical calculation and by microscopic simulation of freeway traffic with a given percentage of vehicles equipped for inter-vehicle communication, we investigate how the equipment level influences the efficiency and velocity of information propagation. By simulating the formation of a typical traffic jam, we show how the non-local information about bottlenecks and jam fronts can travel upstream and reach potential users.     

Efficiency promotion for an on-ramp system based on intelligent transportation system information

<正>The effect of cars with intelligent transportation systems(ITSs) on traffic flow near an on-ramp is investigated by car-following simulations.By numerical simulations,the dependences of flux on the inflow rate are investigated for various proportions of cars with ITSs.The phase diagrams as well as the spatiotemporal diagrams are presented to show different traffic flow states on the main road and the on-ramp.The results show that the saturated flux on the main road increases and the free flow region is enlarged with the increase of the proportion of cars with ITS.Interestingly,the congested regions of the main road disappear completely when the proportion is larger than a critical value.Further investigation shows that the capacity of the on-ramp system can be promoted by 13%by using the ITS information, and the saturated flux on the on-ramp can be kept at an appropriate value by adjusting the proportion of cars with ITS.     

Stochastic Description of Traffic Flow

We propose a traffic model based on microscopic stochastic dynamics. We built a Markov chain equipped with an Arrhenius interaction law. The resulting stochastic process is comprised of both spin-flip and spin-exchange dynamics which models vehicles exiting, entering and interacting in a two-dimensional lattice environment corresponding to a multi-lane highway. The process is further equipped with a novel look-ahead type, anisotropic interaction potential which allows drivers/vehicles to ascertain local fluctuations and advance to new cells forward or sideways. The resulting vehicular traffic model is simulated via kinetic Monte Carlo and examined under both, typical and extreme traffic flow scenarios. The model is shown to correctly predict both qualitative as well as quantitative traffic observables for any highway geometry. Furthermore it also captures interesting multi-scale phenomena in traffic flows after a simulated accident which lead to oscillatory, dissipating, traffic waves with different periods per lane.     

Traffic states and jamming transitions induced by a bus in two-lane traffic flow

We study the traffic states and jamming transitions induced by a bus (slow car) in a two-lane traffic of cars. We use the dynamic model which is an extended one of the optimal velocity model to take into account the lane changing. The fundamental (flow-density) diagram is presented. The fundamental diagram changes highly by introducing a bus on a two-lane roadway. It is found that there are the six distinct states for the two-lane traffic flow including a bus. The spatio-temporal patterns are presented for the distinct traffic states. The dynamical state of traffic changes with density of cars. It is shown that the dynamical transitions among the distinct traffic states occur at some values of density. The phase diagram (region map) is shown for the two-lane traffic flow including a bus.     

Second-order phase transition in two-dimensional cellular automaton model of traffic flow containing road sections

Two-dimensional cellular automaton model has been broadly researched for traffic flow, as it reveals the main characteristics of the traffic networks in cities. Based on the BML models, a first-order phase transition occurs between the low-density moving phase in which all cars move at maximal speed and the high-density jammed phase in which all cars are stopped. However, it is not a physical result of a realistic system. We propose a new traffic rule in a two-dimensional traffic flow model containing road sections, which reflects that a car cannot enter into a road crossing if the road section in front of the crossing is occupied by another car. The simulation results reveal a second-order phase transition that separates the free flow phase from the jammed phase. In this way the system will not be entirely jammed (“don’t block the box” as in New York City).     

中小学门口道路上学期间的一个元胞自动机模型

在已有交通流道路瓶颈、交织区和混合交通流研究的基础上,建立一个中小学门口道路区段上学期间的元胞自动机模型,对上学期间的道路交通流特性进行了模拟,对驾私家车送学生上学比例、乘校车上学比例和交警现场指挥对道路交通流的影响进行实验分析.模拟结果表明减少驾车送学生上学比例、增加乘校车学生比例、辅助以交警现场指挥,可保证交通安全,从而达到抑制交通拥堵、减少车辆总通行时间提高道路实际通行能力的目的.     

Reduction of equivalent continuous A-weighted sound pressure levels by porous elastic road surfaces

A porous elastic road surface (PERS) is superior to drainage asphalt pavement for reducing highway traffic noise. In earlier research and development, for example using a test track, the difference in sound power level (Lw) of cars has been regarded as the noise reduction effect since it was not possible to measure the change in equivalent continuous A-weighted sound pressure level (Leq) for a series of vehicles on such a limited length of surface. As the result of a comparatively major test construction on a highway, have measured the noise reduction effect of PERS as the difference in Leq. First, we measured the motor vehicle Lw and Leq on each section. However, we found that the neighbouring paved sections also influenced Leq. Next, we calculated Leq according to a highway traffic noise model, using the values of Lw measured in the different paved sections. Since the calculated Leq corresponded approximately with the measured Leq, we could verify the validity of the measured Lw. We again calculated Leq, assuming that each pavement is infinitely long. We assumed the improvement of noise reduction effect of PERS was indicated through the calculated Leq. Consequently, we have found that the noise reduction effect of drainage asphalt pavement was 5-6 dB, whereas that of PERS was 7-9 dB.     

Cellular Automaton Models of Highway Traffic Flow Considering Lane-Control and Speed-Control

As two kinds of management modes of highway traffic control, lane-control, and speed-control produce different effect under different conditions. In this paper, traffic flow cellular automaton models for four-lane highway system with two opposing directions under the above two modes are established considering car and truck mixed running. Through computer numerical simulating, the fundamental diagrams with different parameters are obtained, and after the analysis of density-flux diagrams, the variation discipline of flux with traffic density under different control models is gained. The results indicate that, compared with lane-control, utilization ratio of road can be further improved with speed-control when the truck number increases. The research result is of great significance for reasonable providing theoretical guidance for highway traffic control.