Asymptotic solution of a wide moving jam to a class of higher-order viscous traffic flow models

The boundary-layer method is used to study a wide moving jam to a class of higher-order viscous models. The equations for characteristic parameters are derived to determine the asymptotic solution. The sufficient and essential conditions for the wide moving jam formation are discussed in detail, respectively, and then used to prove or disprove the existence of the wide moving jam solutions to many well-known higher-order models. It is shown that the numerical results agree with the analytical results.

WT-FCTGN:A wavelet-enhanced fully connected time-gated neural network for complex noisy traffic flow modeling

Accurate forecasting of traffic flow provides a powerful traffic decision-making basis for an intelligent transportation system. However, the traffic data's complexity and fluctuation, as well as the noise produced during collecting information and summarizing original data of traffic flow, cause large errors in the traffic flow forecasting results. This article suggests a solution to the above mentioned issues and proposes a fully connected time-gated neural network based on wavelet reconstruction(WT-FCTGN). To eliminate the potential noise and strengthen the potential traffic trend in the data, we adopt the methods of wavelet reconstruction and periodic data introduction to preprocess the data. The model introduces fully connected time-series blocks to model all the information including time sequence information and fluctuation information in the flow of traffic, and establishes the time gate block to comprehend the periodic characteristics of the flow of traffic and predict its flow. The performance of the WT-FCTGN model is validated on the public Pe MS data set. The experimental results show that the WT-FCTGN model has higher accuracy, and its mean absolute error(MAE), mean absolute percentage error(MAPE) and root mean square error(RMSE) are obviously lower than those of the other algorithms. The robust experimental results prove that the WT-FCTGN model has good anti-noise ability.

Incident indicators for freeway traffic flow models

Developed in this paper is a traffic flow model parametrised to describe abnormal traffic behaviour.In large traffic networks,the immediate detection and categorisation of traffic incidents/accidents is of capital importance to avoid breakdowns,further accidents.First,this claims for traffic flow models capable to capture abnormal traffic condition like accidents.Second,by means of proper real-time estimation technique,observing accident related parameters,one may even categorize the severity of accidents.Hence,in this paper,we suggest to modify the nominal Aw-Rascle(AR)traffic model by a proper incident related parametrisation.The proposed Incident Traffic Flow(ITF)model is defined by introducing the incident parameters modifying the anticipation and the dynamic speed relaxation terms in the speed equation of the AR model.These modifications are proven to have physical meaning.Furthermore,the characteristic properties of the ITF model is discussed in the paper.A multi stage numerical scheme is suggested to discretise in space and time the resulting non-homogeneous system of PDEs.The resulting systems of ODE is then combined with receding horizon estimation methods to reconstruct the incident parameters.Finally,the viability of the suggested incident parametrisation is validated in a simulation environment.

Lagrangian generic second order traffic flow models for node

This study sheds light on higher order macroscopic traffic flow modeling on road networks, thanks to the generic second order models （GSOM family） which embeds a myriad of traffic models. It has been demonstrated that such higher order models are easily solved in Lagrangian coordinates which are compatible with both microscopic and macroscopic descriptions. The generalized GSOM model is reformulated in the Lagrangian coordinate system to develop a more efficient numerical method. The difficulty in applying this approach on networks basically resides in dealing with node dynamics. Traffic flow characteristics at node are different from that on homogeneous links. Different geometry features can lead to different critical research issues. For instance, discontinuity in traffic stream can be an important issue for traffic signal operations, while capacity drop may be crucial for lane-merges. The current paper aims to establish and analyze a new adapted node model for macroscopic traffic flow models by applying upstream and downstream boundary conditions on the Lagrangian coordinates in order to perform simulations on networks of roads, and accompanying numerical method. The internal node dynamics between upstream and downstream links are taken into account of the node model. Therefore, a numerical example is provided to underscore the efficiency of this approach. Simulations show that the discretized node model yields accurate results. Additional kinematic waves and contact discontinuities are induced by the variation of the driver attribute.

Numerical Simulation of Diffusion Type Traffic Flow Model Using Second-Order Lax-Wendroff Scheme Based on Exponential Velocity Density Function

In order to control traffic congestion, many mathematical models have been used for several decades. In this paper, we study diffusion-type traffic flow model based on exponential velocity density relation, which provides a non-linear second-order parabolic partial differential equation. The analytical solution of the diffusion-type traffic flow model is very complicated to approximate the initial density of the Cauchy problem as a function of x from given data and it may cause a huge error. For the complexity of the analytical solution, the numerical solution is performed by implementing an explicit upwind, explicitly centered, and second-order Lax-Wendroff scheme for the numerical solution. From the comparison of relative error among these three schemes, it is observed that Lax-Wendroff scheme gives less error than the explicit upwind and explicit centered difference scheme. The numerical, analytical analysis and comparative result discussion bring out the fact that the Lax-Wendroff scheme with exponential velocity-density relation of diffusion type traffic flow model is suitable for the congested area and shows a better fit in traffic-congested regions.

Cellular automata model for traffic flow with safe driving conditions

In this paper, a recently introduced cellular automata （CA） model is used for a statistical analysis of the inner micro-scopic structure of synchronized traffic flow. The analysis focuses on the formation and dissolution of clusters or platoons of vehicles, as the mechanism that causes the presence of this synchronized traffic state with a high flow. This platoon formation is one of the most interesting phenomena observed in traffic flows and plays an important role both in manual and automated highway systems （AHS）. Simulation results, obtained from a single-lane system under periodic boundary conditions indicate that in the density region where the synchronized state is observed, most vehicles travel together in pla- toons with approximately the same speed and small spatial distances. The examination of velocity variations and individual vehicle gaps shows that the flow corresponding to the synchronized state is stable, safe and highly correlated. Moreover, results indicate that the observed platoon formation in real traffic is reproduced in simulations by the relation between vehicle headway and velocity that is embedded in the dynamics definition of the CA model.

A New Macro Model for Traffic Flow on a Highway with Ramps and Numerical Tests

In this paper, we present a new macro model for traffic flow on a highway with ramps based on the existing models. We use the new model to study the effects of on-off-ramp on the main road traffic during the morning rush period and the evening rush period. Numerical tests show that, during the two rush periods, these effects are often different and related to the status of the main road traffic. If the main road traffic flow is uniform, then ramps always produce stop-and-go traffic when the main road density is between two critical values, and ramps have little effect on the main road traffic when the main road density is less than the smaller critical value or greater than the larger critical value. If a small perturbation appears on the main road, ramp may lead to stop-and-go traffic, or relieve or even eliminate the stop-and-go traffic, under different circumstances. These results are consistent with real traffic, which shows that the new model is reasonable.

Continuum modeling for two-lane traffic flow with consideration of the traffic interruption probability

Considering the effects that the probability of traffic interruption and the friction between two lanes have on the car-following behaviour, this paper establishes a new two-lane microscopic car-following model. Based on this microscopic model, a new macroscopic model was deduced by the relevance relation of microscopic and macroscopic scale parameters for the two-lane traffic flow. Terms related to lane change are added into the continuity equations and velocity dynamic equations to investigate the lane change rate. Numerical results verify that the proposed model can be efficiently used to reflect the effect of the probability of traffic interruption on the shock, rarefaction wave and lane change behaviour on two-lane freeways. The model has also been applied in reproducing some complex traffic phenomena caused by traffic accident interruption.

Modelling vehicular interactions for heterogeneous traffic flow using cellular automata with position preference

This paper proposes and validates a modified cellular automata model for determining interaction rate （i.e. number of car-following/overtaking instances） using traffic flow data measured in the field. The proposed model considers lateral position preference by each vehicle type and introduces a position preference parameter fl in the model which facilitates gradual drifting towards preferred position on road, even if the gap in front is sufficient. Additionally, the model also improves upon the conven- tional model by calculating safe front and back gap dynamically based on speed and deceleration properties of leader and follower vehicles. Sensitivity analysis was carried out to determine the effect of β on vehicular interac- tions and the model was calibrated and validated using interaction rates observed in the field. Paired tests were conducted to determine the determining interaction rates validity of the model in Results of the simulations show that there is a parabolic relationship between area occupancy and interaction rate of different vehicle types. The model performed satisfactorily as the simulated interaction rate between different vehicle types were found to be statistically similar to those observed in field. Also, as expected, the interaction rate between light motor vehicles （LMVs） and heavy motor vehicles （HMVs） were found to be higher than that between LMVs and three wheelers because LMVs and HMVs share the same lane. This could not be done using conventional CA models as lateral movement rules were dictated by only speeds and gaps. So, in conventional models, the vehicles would end up in positions which are not realistic. The position preference parameter introduced in this model motivates vehicles to stay in their preferred positions. This study demonstrates the use of interaction rate as a measure to validate micro- scopic traffic flow models.

Solitary wave solution to Aw-Rascle viscous model of traffic flow

A traveling wave solution to the Aw-Rascle traffic flow model that includes the relaxation and diffusion terms is investigated. The model can be approximated by the well-known Kortweg-de Vries （KdV） equation. A numerical simulation is conducted by the first-order accurate Lax-Friedrichs scheme, which is known for its ability to capture the entropy solution to hyperbolic conservation laws. Periodic boundary conditions are applied to simulate a lengthy propagation, where the profile of the derived KdV solution is taken as the initial condition to observe the change of the profile. The simulation shows good agreement between the approximated KdV solution and the numerical solution.

Cellular Automata Models of Traffic Behavior in Presence of Speed Breaking Structures

In this article, we study traffic flow in the presence of speed breaking structures. The speed breakers are typically used to reduce the local speed of vehicles near certain institutions such as schools and hospitals. Through a cellular automata model we study the impact of such structures on giobal traffic characteristics. The simulation results indicate that the presence of speed breakers could reduce the global flow under moderate global densities. However, under low and high global density traffic regime the presence of speed breakers does not have an impact on the global flow. Further the speed limit enforced by the speed breaker creates a phase distinction. For a given global density and slowdown probability, as the speed limit enforced by the speed breaker increases, the traffic moves from the reduced flow phase to maximum flow phase. This underlines the importance of proper design of these structures to avoid undesired flow restrictions.

A study on the effects of the transit parking time on traffic flow based on cellular automata theory

This paper mainly deals with the effects of transit stops on vehicle speeds and conversion lane numbers in a mixed traffic lane. Based on thorough research of traffic flow and cellular automata theory, it calibrates the cellular length and the running speed. Also, a cellular automata model for mixed traffic flow on a two-lane system under a periodic boundary condition is presented herewith, which also takes into consideration the harbour-shaped transit stop as well. By means of computer simulation, the article also studies the effects of bus parking time on the traffic volume, the transit speed and the fast lane speed at the same time. The results demonstrate that, with the increase of the bus parking time, the traffic volume of the transit stop and the transit speed decrease while the fast lane speed increases. This result could help calculate the transit delay correctly and make arrangements for transit routes reasonably and scientifically.

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.

A viscous continuum traffic flow model with consideration of the coupling effect for two-lane freeways

In this paper, the viscous continuum traffic flow model for a single lane is extended to the traffic flow for two-lane freeways. The proposed model is a higher-order continuum model considering the coupling and lane changing effects of the vehicles on two adjacent lanes. It results from integrating the Taylor series expansion of the viscous continuum traffic flow model proposed by Ge （2006 Physiea A 371 667） into the multi-lane model presented by Daganzo （1997 Transpn. Res. B 31 83）. Our proposed model may be used to describe non-anisotropic behaviour because of lane changing in multi-lane traffic. A linear stability analysis is given and the neutral stability condition is obtained. Also, issues related to lane changing, shock waves and rarefaction waves, local clustering and phase transition are investigated through a simulation experiment. The simulation results show that the proposed model is capable of explaining some particular traffic phenomena commonly observable in real world traffic flow.

Wave propagation of the traffic flow dynamic model based on wavefront expansion

This paper discusses propagation of perturbations along traffic flow modeled by a modified second-order macroscopic model through the wavefront expansion technique. The coefficients in this expansion satisfy a sequence of transport equations that can be solved analytically. One of these analytic solutions yields information about wavefront shock. Numerical simulations based on a Padé approximation of this expansion were done at the end of this paper and results showed that propagation of perturbations at traffic flow speed conforms to the theoretical analysis results.

A genetic resampling particle filter for freeway traffic-state estimation

On-line estimation of the state of traffic based on data sampled by electronic detectors is important for intelligent traffic management and control. Because a nonlinear feature exists in the traffic state, and because particle filters have good characteristics when it comes to solving the nonlinear problem, a genetic resampling particle filter is proposed to estimate the state of freeway traffic. In this paper, a freeway section of the northern third ring road in the city of Beijing in China is considered as the experimental object. By analysing the traffic-state characteristics of the freeway, the traffic is modeled based on the second-order validated macroscopic traffic flow model. In order to solve the particle degeneration issue in the performance of the particle filter, a genetic mechanism is introduced into the resampling process. The realization of a genetic particle filter for freeway traffic-state estimation is discussed in detail, and the filter estimation performance is validated and evaluated by the achieved experimental data.

A new traffic model on compulsive lane-changing caused by off-ramp

In the field of traffic flow studies, compulsive lane-changing refers to lane-changing （LC） behaviors due to traffic rules or bad road conditions, while free LC happens when drivers change lanes to drive on a faster or less crowded lane. LC studies based on differential equation models accurately reveal LC influence on traffic environment. This paper presents a second-order partial differential equation （PDE） model that simulates both compulsive LC behavior and free LC behavior, with lane-changing source terms in the continuity equation and a lane-changing viscosity term in the momentum equation. A specific form of this model focusing on a typical compulsive LC behavior, the ＇off-ramp problem＇, is derived. Numerical simulations are given in several cases, which are consistent with real traffic phenomenon.

A new traffic model with a lane-changing viscosity term

In this paper, a new continuum traffic flow model is proposed, with a lane-changing source term in the continuity equation and a lane-changing viscosity term in the acceleration equation. Based on previous literature, the source term addresses the impact of speed difference and density difference between adjacent lanes, which provides better precision for free lane-changing simulation; the viscosity term turns lane-changing behavior to a ＂force＂ that may influence speed distribution. Using a flux-splitting scheme for the model discretization, two cases are investigated numerically. The case under a homogeneous initial condition shows that the numerical results by our model agree well with the analytical ones; the case with a small initial disturbance shows that our model can simulate the evolution of perturbation, including propagation,dissipation, cluster effect and stop-and-go phenomenon.

Scheduling of high-speed rail traffic based on discrete-time movement model

In this paper, a new simulation approach for solving the mixed train scheduling problem on the high-speed double-track rail line is presented. Based on the discrete-time movement model, we propose control strategies for mixed train movement with different speeds on a high-speed double-track rail line, including braking strategy, priority rule, travelling strategy, and departing rule. A new detailed algorithm is also presented based on the proposed control strategies for mixed train movement. Moreover, we analyze the dynamic properties of rail traffic flow on a high-speed rail line. Using our proposed method, we can effectively simulate the mixed train schedule on a rail line. The numerical results demonstrate that an appropriate decrease of the departure interval can enhance the capacity, and a suitable increase of the distance between two adjacent stations can enhance the average speed. Meanwhile, the capacity and the average speed will be increased by appropriately enhancing the ratio of faster train number to slower train number from 1.

Modeling and Generating Realistic Background Traffic by Hybrid Approach

One of the key challenges in largescale network simulation is the huge computation demand in fine-grained traffic simulation.Apart from using high-performance computing facilities and parallelism techniques,an alternative is to replace the background traffic by simplified abstract models such as fluid flows.This paper suggests a hybrid modeling approach for background traffic,which combines ON/OFF model with TCP activities.The ON/OFF model is to characterize the application activities,and the ordinary differential equations(ODEs) based on fluid flows is to describe the TCP congestion avoidance functionality.The apparent merits of this approach are(1) to accurately capture the traffic self-similarity at source level,(2) properly reflect the network dynamics,and(3) efficiently decrease the computational complexity.The experimental results show that the approach perfectly makes a proper trade-off between accuracy and complexity in background traffic simulation.