Travel time prediction with viscoelastic traffic model

Travel time through a ring road with a total length of 80 km has been predicted by a viscoelastic traffic model(VEM), which is developed in analogous to the non-Newtonian fluid flow. The VEM expresses a traffic pressure for the unfree flow case by space headway, ensuring that the pressure can be determined by the assumption that the relevant second critical sound speed is exactly equal to the disturbance propagation speed determined by the free flow speed and the braking distance measured by the average vehicular length. The VEM assumes that the sound speed for the free flow case depends on the traffic density in some specific aspects, which ensures that it is exactly identical to the free flow speed on an empty road. To make a comparison, the open Navier-Stokes type model developed by Zhang(ZHANG, H. M. Driver memory, traffic viscosity and a viscous vehicular traffic flow model. Transp. Res. Part B, 37, 27–41(2003)) is adopted to predict the travel time through the ring road for providing the counterpart results.When the traffic free flow speed is 80 km/h, the braking distance is supposed to be 45 m,with the jam density uniquely determined by the average length of vehicles l ≈ 5.8 m. To avoid possible singular points in travel time prediction, a distinguishing period for time averaging is pre-assigned to be 7.5 minutes. It is found that the travel time increases monotonically with the initial traffic density on the ring road. Without ramp effects, for the ring road with the initial density less than the second critical density, the travel time can be simply predicted by using the equilibrium speed. However, this simpler approach is unavailable for scenarios over the second critical.     

KINEMATIC WAVE PROPERTIES OF ANISOTROPIC DYNAMICS MODEL FOR TRAFFIC FLOW

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Generalized macroscopic traffic model with time delay

The effect of delay or reaction time on traffic flow dynamics has been investigated widely in the literature using microscopic traffic models. Recent studies using second-order Payne-type models have shown analytically that, on a macroscopic scale, time delay does not contribute to whether traffic instabilities occur. This paper will attempt to show that it all depends on the (macroscopic) model used for the analysis that delay does have effect on traffic instabilities or not. To this end, we will formulate a generalized (linear) stability condition for a second-order macroscopic model with delay and investigate analytically the effect of such delay on traffic instabilities in some specific macroscopic models. It is found that the choice of the equilibrium speed function in a (second order) macroscopic model will determine how delay affects such (linear) stability condition     

Investigation of the adaptive features of a real-time nonlinear freeway traffic state estimator

This paper reports on real-data testing results for a real-time nonlinear freeway traffic state estimator with particular focus on its adaptive features. The pursued general approach to the real-time adaptive estimation of the complete traffic state in freeway stretches is based on stochastic nonlinear macroscopic traffic flow modeling and extended Kalman filtering that are outlined in the paper. One major innovative aspect of the estimator is the on-line estimation of important model parameters (free speed, critical density, and capacity) simultaneously with the estimation of traffic flow variables (flows, mean speeds, and densities), which leads to three significant advantages of the traffic state estimator: (1) avoidance of off-line model calibration; (2) automatic adaptation to changing external conditions (e.g. weather and light conditions); (3) enabling of incident alarms. The purpose of the reported real-data testing is, first, to demonstrate advantage (1) by investigating some basic properties of the estimator and, second, to explore some adaptive capabilities of the estimator that enable the other two advantages. The achieved testing results are quite satisfactory and promising for subsequent work.     

TWO-DIMENSIONAL CELLULAR AUTOMATON TRAFFIC MODELWITH RANDOMLY SWITCHING TRAFFIC LIGHTS

I.IntroductionWiththedevelopmentofsocietyandeconomyinmetropolises,thecontradictionbet\"eentheincreaseoftrat'ficflowandtheexistingconditionoftrafticftlcilitiesbecolllesmorealldmore'serious,resultinginaprincipalI'actorofconstrainingthedevelopmentofmetropolititneconomy.Therefore,inrecentdecadesthetrat'l'ictlowproblemhasdrawntheattelltiollofInanyspecialistsinvariousfieldsincludingphysics,mechanicsalldmathelllatics.Alargenumberoftraftic1llodelshavebeenpropes.Inthispaper,thecellularautomaton(CA)tr…     

Multi-mode solitons in a long-short range traffic lattice model with time delay

We consider a new form of solutions of a special lattice model for traffic system. By analyzing nearest sites’ interactions, time delay, and bumpy effects, we deduce the bifurcation lines and surfaces for stable and unstable regions and show how they vary as parameters vary. It shows that keeping other conditions unchanged, as the incoming flow increases, the traffic flow becomes unstable, opposite to when outgoing flow increases, it becomes stable. Besides, considering delayed optimal flow, multiple sites effect or artificial parameters can also help stabilize the traffic road condition. Moreover, by putting it into the framework of mKdV equations, we obtain the kink–antikink solitons involving all parameters, which show the feature of the traffic congestion. The result is original, and our model in differential or difference form can be reduced into the previous ones by choosing appropriate parameters. Since the optimal velocity function we considered involves finitely or infinitely many sites, the density waves can be in multi-mode and high dimension forms and can also be quasi-periodic, we show a new feature of the traffic lattice system.

     

Determination of correlation functions of turbulent velocity and sound speed fluctuations by means of ultrasonic technique

An experimental study of the propagation of high-frequency acoustic waves through grid-generated turbulence by means of an ultrasound technique is discussed. Experimental data were obtained for ultrasonic wave propagation downstream of heated and non-heated grids in a wind tunnel. A semi-analytical acoustic propagation model that allows the determination of the spatial correlation functions of the flow field is developed based on the classical flowmeter equation and the statistics of the travel time of acoustic waves traveling through the kinematic and thermal turbulence. The basic flowmeter equation is reconsidered in order to take into account sound speed fluctuations and turbulent velocity fluctuations. It allows deriving an integral equation that relates the correlation functions of travel time, sound speed fluctuations and turbulent velocity fluctuations. Experimentally measured travel time statistics of data with and without grid heating are approximated by an exponential function and used to analytically solve the integral equation. The reconstructed correlation functions of the turbulent velocity and sound speed fluctuations are presented. The power spectral density of the turbulent velocity and sound speed fluctuations are calculated.     

基于场力的驾驶员影响因素交通流动力学模型

为研究驾驶员行为对道路交通的定量影响, 针对驾驶员行为特点, 综合考虑了驾驶员受到的直接物理影响和间接心理影响、相对速度以及车辆自身特性等因素, 结合场力、图论等方法, 提出了一种用于模拟考虑驾驶员影响因素的元胞自动机交通流动力学模型(简称IDCA模型). 通过计算机数值模拟, 研究了考虑驾驶员影响因素下车流演化机理及不同驾驶员类型对道路交通流的影响. 结果表明: 与NaSch模型相比, 本文建立的IDCA模型能够模拟得到丰富的交通行为, 再现了同步流等交通现象, 从速度波动和车头间距波动分析得出IDCA模型下道路交通流具有更强的稳定性, 堵塞消融效率更高. 此外得到了由不同驾驶员类型按不同比例组成的混合交通流的密度-速度图和密度-流量图, 发现在道路相同中高密度下, 激进型驾驶员所占的比例越大, 车辆速度与交通流量越大, 交通流量随着保守型驾驶员比例的增加而降低. 最后模拟实现了车辆高速跟驰现象, 得到小间距高速跟驰率超过7%的结果与实测结果相符合.      

Numerical simulation of pedestrian flow past a circular obstruction

In this paper, a revisiting Hughes' dynamic continuum model is used to investigate and predict the essential macroscopic characteristics of pedestrian flow, such as flow, density and average speed, in a two dimensional continuous walking facility scattered with a circular obstruction. It is assumed that pedestrians prefer to walk a path with the lowest instantaneous travel cost from origin to destination, under the consideration of the current traffic conditions and the tendency to avoid a high-density region and an obstruction. An algorithm for the pedestrian flow model is based on a cellcentered finite volume method for a scalar conservation law equation, a fast sweeping method for an Eikonal-type equation and a second-order TVD Runge-Kutta method for the time integration on unstructured meshes. Numerical results demonstrate the effectiveness of the algorithm. It is verified that density distribution of pedestrian flow is influenced by the position of the obstruction and the path-choice behavior of pedestrians.     

Empirical test of a microscopic three-phase traffic theory

A review of dynamic nonlinear features of spatiotemporal congested patterns in freeway traffic is presented. The basis of the review is a comparison of theoretical features of the congested patterns that are shown by a microscopic traffic flow model in the context of the Kerner's three-phase traffic theory and empirical microscopic and macroscopic pattern characteristics measured on different freeways over various days and years. In this test of the microscopic three-phase traffic flow theory, a model of an "open" road is applied: Empirical time-dependence of traffic demand and drivers' destinations are used at the upstream model boundaries. At downstream model boundary conditions for vehicle freely leaving a modeling freeway section(s) are given. Spatiotemporal congested patterns emerge, develop, and dissolve in this open freeway model with the same types of bottlenecks as those in empirical observations. It is found that microscopic three-phase traffic models can explain all known macroscopic and microscopic empirical congested pattern features (e.g., probabilistic breakdown phenomenon as a first-order phase transition from free flow to synchronized flow, moving jam emergence in synchronized flow rather than in free flow, spatiotemporal features of synchronized flow and general congested patterns at freeway bottlenecks, intensification of downstream congestion due to upstream congestion at adjacent bottlenecks). It turns out that microscopic optimal velocity (OV) functions and time headway distributions are not necessarily qualitatively different, even if local congested traffic behavior is qualitatively different. Model performance with respect to spatiotemporal pattern emergence and evolution cannot be tested using these traffic characteristics. The reason for this is that important spatiotemporal features of congested traffic patterns are lost in these and many other macroscopic and microscopic traffic characteristics, which are widely used as the empirical basis for a test of traffic flow models. PACS: 89.40. + k, 47.54. + r, 64.60.Cn, 64.60.Lx     

Lattice hydrodynamic model for traffic flow on curved road with passing

In order to investigate the effect of passing upon traffic flow on curved road, in this paper, an extended one-dimensional lattice hydrodynamic model for traffic flow on curved road with passing is proposed. The stability condition is obtained by the use of linear stability analysis. The result of stability analysis shows that passing behavior plays an important role in influencing the stability of traffic flow as well as radian of curved road. The nonlinear wave equations including Burgers, Korteweg-de Vries and modified Korteweg-de Vries equations are derived to describe the nonlinear traffic behavior in different regions, respectively. The analytical results show that reducing the coefficient of passing may enhance the stability of traffic flow. Jamming transition occurs between uniform flow and kink jam when the coefficient of passing is less than the critical value. When the coefficient of passing is larger than the critical value, jamming transition occurs from uniform flow to irregular wave through chaotic phase with decreasing sensitivity parameter. In addition, compared with other segments of curved road, traffic flow with passing easily becomes unstable and complicated at the entrance and exit of curved road, especially at the entrance of curved road. The numerical simulations are given to illustrate and clarify the analytical results.     

Phase transitions in the two-lane density difference lattice hydrodynamic model of traffic flow

In this paper, we derive the KdV equation from the two-lane lattice hydrodynamic traffic model considering density difference effect. The soliton solution is obtained from the KdV equation. Under periodical boundary, the KdV soliton of traffic flow is demonstrated by numerical simulation. The numerical simulation result is consistent with the nonlinear analytical result. Under open system, the density fluctuation of the downstream last one lattice is designed to explore the empirical congested traffic states. A phase diagram is presented which includes free traffic, moving localized cluster, triggered stop-and-go traffic, oscillating congested traffic, and homogeneous congested traffic. Finally, the spatiotemporal evolution of all the traffic states described in phase diagram are reproduced. Results suggest that the two-lane density difference hydrodynamic traffic model is suitable to describe the actual traffic.     

A traffic flow model considering influence of car-following and its echo characteristics

Taking into account the driving characteristics of vehicles following the vehicle in front on the imported lane of urban signalized intersections, we introduce the acceleration parameters of the vehicle and consider the queue length and volatility of the acceleration that have been affected by the time of fixed signal cycles in the mixed traffic flow. Thereby, we obtain a mixed traffic flow cellular automaton model with the effect of acceleration on the imported lane. Through analyzing the results of numerical simulation, it is found that the maximum queue length and the volatility of acceleration have a great influence on the intersection lane mixed traffic flow with the different time of fixed signal cycles and considerably on traffic arriving strength within a certain range. When the intensity is in specific range, the longer the fixed signal cycle, the shorter the maximum queue length, and the greater the volatility of acceleration, which has smaller queue jam affecting the intersection lane mixed traffic flow. Meanwhile, the improved model can reproduce the evolution and propagation characteristics of gathering–dissipating of the traffic wave in the intersection lane mixed traffic flow.     

Solitary wave solutions to higher-order traffic flow model with large diffusion

This paper uses the Taylor expansion to seek an approximate Korteweg- de Vries equation （KdV） solution to a higher-order traffic flow model with sufficiently large diffusion. It demonstrates the validity of the approximate KdV solution considering all the related parameters to ensure the physical boundedness and the stability of the solution. Moreover, when the viscosity coefficient depends on the density and velocity of the flow, the wave speed of the KdV solution is naturally related to either the first or the second characteristic field. The finite element method is extended to solve the model and examine the stability and accuracy of the approximate KdV solution.     

关于交通流中扰动传播和发展的数值模拟

针对不同拥挤程度交通流中扰动的传播和发展，进行了系统的数值模拟研究. 讨论了PW模型、一维管流模型、单侧传播模型等几种典型交通流模型的不同特征；指出了 不同差分格式对数值结果的影响；也分析了数学模型中不同形式的平衡函数的作用. 结果发 现在适当的数学模型、平衡函数和离散格式下，能够对交通流中扰动的传播和发展，特别是 扰动波的传播速度，取得与实际测量数据相当接近的模拟效果. 建议了分别适用于不同密度 交通流的计算格式.     

Analysis of the structural properties of the solutions to speed gradient traffic flow model

In this paper, we carry out an analysis of the structural properties of the solutions to the speed gradient (SG) traffic flow model. Under the condition that the relaxation effect can be neglected, it is shown that a 1-shock or a 1-rarefaction is associated with the first characteristic, but on the other hand, a contact discontinuity rather than a 2-shock or a 2-rarefaction is associated with the second characteristic. Since the existence of a 2-shock or 2-rarefaction violates the physical mechanism of the traffic flow, the SG model is more reasonable. If the relaxation effect cannot be neglected, it is somewhat difficult to carry out the analytical analysis and the numerical simulation results should be obtained. The project supported by the National Natural Science Foundation of China (10272101)     

A new lattice model of the traffic flow with the consideration of the driver anticipation effect in a two-lane system

In this paper, a new lattice model of the traffic flow is proposed with the consideration of the driver anticipation effect for a two-lane system. The linear stability condition is derived by employing linear stability analysis. The analytical result shows that the driver anticipation effect can improve the stability of the traffic flow in a two-lane system. The mKdV equation near the critical point is obtained to describe the propagating behavior of a traffic density wave with the perturbation method. The simulation results are also in good agreement with the analytical results, which show that the traffic jam can be suppressed efficiently when the driver anticipation effect is considered in a two-lane system.     

Modeling non-equilibrium traffic dynamics in a Lagrangian framework

In this paper, we propose a formulation for modeling macroscopic traffic flow using a modified speed–density relationship. The flow model consists of a nonlinear hyperbolic system of conservation laws. The proposed modification distinguishes between acceleration and deceleration by assuming a different equilibrium velocity for a given traffic density based on whether a platoon of vehicles is accelerating or decelerating. We examine the appropriateness of this modification to two prominent traffic flow models in a Lagrangian reference frame, which we solve computationally. We show that a Lagrangian coordinate system is ideal for the incorporation of the proposed modification due to its ability to track the behavior of moving vehicles. We see that the modification is particularly well suited to “second order” models.