Macro Model For Traffic Flow Research Articles

The difference of drivers' anticipation behaviors in a new macro model of traffic flow and numerical simulation

A valuable consideration is inserted into car-following theory to investigate the difference of drivers' anticipation. Furthermore, a fresh macro traffic model involving the difference of the drivers' anticipation is deduced from the car-following model by applying transformation relationship from micro to macro variables. And this effect resulted from the difference of the drivers' anticipation is observed via numerical simulation. The results show that the difference of drivers' anticipation has a negligible impact on traffic flow.

The nonlinear analysis for a new continuum model considering anticipation and traffic jerk effect

Considering the anticipation and traffic jerk simultaneously, a new macro model of traffic flow is put forwarded in this paper. By means of linear stability theory, the new model's linear stability with the effect of traffic jerk and anticipation term is obtained.Through nonlinear analysis, the KdV–Burgers equation is derived to describe the propagating behavior of traffic density wave near the neutral stability line. Numerical simulation is carried out to study the influence about the traffic jerk and anticipation effect. The evolution of traffic jam and corresponding energy consumption are then explored and compared each other. The outputs of these findings demonstrate the extended model can suppress traffic jam and reduce energy consumption in real traffic condition.

An extended macro traffic flow model accounting for multiple optimal velocity functions with different probabilities

Due to the maximum velocity and safe headway distance of the different vehicles are not exactly the same, an extended macro model of traffic flow with the consideration of multiple optimal velocity functions with probabilities is proposed in this paper. By means of linear stability theory, the new model's linear stability condition considering multiple probabilities optimal velocity is obtained. The KdV–Burgers equation is derived to describe the propagating behavior of traffic density wave near the neutral stability line through nonlinear analysis. The numerical simulations of influences of multiple maximum velocities and multiple safety distances on model's stability and traffic capacity are carried out. The cases of two different kinds of maximum speeds with same safe headway distance, two different types of safe headway distances with same maximum speed and two different max velocities and two different time-gaps are all explored by numerical simulations. First cases demonstrate that when the proportion of vehicles with a larger vmax increase, the traffic tends to unstable, which also means that jerk and brakes is not conducive to traffic stability and easier to result in stop and go phenomenon. Second cases show that when the proportion of vehicles with greater safety spacing increases, the traffic tends to be unstable, which also means that too cautious assumptions or weak driving skill is not conducive to traffic stability. Last cases indicate that increase of maximum speed is not conducive to traffic stability, while reduction of the safe headway distance is conducive to traffic stability. Numerical simulation manifests that the mixed driving and traffic diversion does not have effect on the traffic capacity when traffic density is low or heavy. Numerical results also show that mixed driving should be chosen to increase the traffic capacity when the traffic density is lower, while the traffic diversion should be chosen to increase the traffic capacity when the traffic density is heavier.

A new macro model of traffic flow by incorporating both timid and aggressive driving behaviors

In this paper, a novel macro model is derived from car-following model by applying the relationship between the micro and macro variables by incorporating the timid and aggressive effects of optimal velocity on a single lane. Numerical simulation shows that the timid and aggressive macro model of traffic flow can correctly reproduce common evolution of shock, rarefaction waves and local cluster effects under small perturbation. Also, the results uncover that the aggressive effect can smoothen the front of the shock wave and the timid effect results in local press peak, which means that the timid effect hastens the process of congregation in the shock wave. The more timid traffic behaviors are, the smaller is the stable range. Furthermore, the research shows that the advantage of the aggressive effect over the timid one lies in the fact that the aggressive traffic behaviors can improve the stability of traffic flow with the consideration of incorporating timid and aggressive driving behaviors at the same time.

A macro-model for traffic flow with consideration of driver’s reaction time and distance

Reaction delays from drivers are indispensable factors in modeling vehicle movements. In this paper, we present an extended car-following model considering the drivers reaction time and distance. A new macroscopic model based on the driver’s reaction time and distance is developed using the relationship between the microscopic and macroscopic variables. Analytical results show that the increase in reaction time and distance can potentially lead to more stable traffic flow. Furthermore, numerical results show that the proposed model can reproduce the evolution of shock, rarefaction wave, and small perturbation.

A New Macro Model Considering the Average Speed of Preceding Vehicles Group in CPS Environment

A new car following model considering the effect of average speed information of preceding vehicles group in real traffic is presented. Based on the new car following model, a new macro model for traffic flow is proposed employing the relationship between the micro and macro variables. The linear stability condition of the macro model is obtained by using the linear stability theory. The numerical tests show that the new model can not only simulate the dynamic process of shock, rarefaction wave, and small perturbation, but also can further stabilize the traffic flow.

An Improved Macro Model of Traffic Flow with the Consideration of Ramps and Numerical Tests

We present an improved macro model for traffic flow based on the existing models. The equilibrium point equation of the model is obtained. The stop-and-go traffic phenomenon is described in phase plane and the relationship between traffic jams and system instability is clearly shown in the phase plane diagrams. Using the improved model, some traffic phenomena on a highway with ramps are found in this paper. The numerical simulation is carried out to investigate various nonlinear traffic phenomena with a single ramp generated by different initial densities and vehicle generation rates. According to the actual road sections of Xi’an-Baoji highways, the situations of morning peak with several ramps are also analyzed. All these results are consistent with real traffic, which shows that the improved model is reasonable.

A novel macro model of traffic flow with the consideration of anticipation optimal velocity

In this paper, a novel macro model which can investigate wide moving jams is derived from car-following model by applying the relationship between the micro and macro variables with the consideration of anticipation optimal velocity on single lane. The theoretic analysis and numerical simulation show that the new macro model of traffic flow can correctly reproduce common evolution of shock, rarefaction wave and local cluster effect under small perturbation, which shows that the congested traffic patterns about wide moving jam propagation are in accordance with empirical results. Furthermore, the results uncover that the anticipation effect can smooth the front of the shock wave and the rarefaction wave, which means that anticipation effect hasten the diffusion process of congregate in the shock wave and dissolution in rarefaction wave. The key improvement of this new macro model over the previous ones lies in the fact that the anticipation traffic behaviors can improve the stability of traffic flow with the consideration of the proper anticipation effect.

An extended macro model for traffic flow with consideration of multi static bottlenecks

In this paper, we propose a macro model with consideration of multi static bottlenecks to study the impacts of multi static bottlenecks on traffic flow. The numerical results show that the influences are related to the number of static bottlenecks, the distance between two adjacent static bottlenecks and the initial density.

A Macro Model for Traffic Flow with Consideration of Static Bottleneck

In this paper, we develop a macro model for traffic flow with consideration of static bottleneck to explore the impacts of static bottleneck on traffic flow. The analytical and numerical results show that the proposed model can qualitatively describe the equilibrium flux, uniform flow and small perturbation under the action of a static bottleneck.

A macro model for traffic flow on road networks with varying road conditions

SUMMARYIn this paper, we develop a macro traffic flow model with consideration of varying road conditions. Our analytical and numerical results illustrate that good road condition can enhance the speed and flow of uniform traffic flow whereas bad road condition will reduce the speed and flow. The numerical results also show that good road condition can smooth shock wave and improve the stability of traffic flow whereas bad road condition will lead to steeper shock wave and reduce the stability of traffic flow. Our results are also qualitatively accordant with empirical results, which implies that the proposed model can qualitatively describe the effects of road conditions on traffic flow. These results can guide traffic engineers to improve the road quality in traffic engineering. Copyright © 2012 John Wiley & Sons, Ltd.

A New Macro Model for Traffic Flow on a Highway with Bus Stop

Based on the difference between the online bus stop and the offline bus stop, two macro models are developed to describe the two types of bus stops. The numerical results show that the two models can qualitatively reproduce some complex phenomena resulted by the two types of bus stops and that the offline bus stop is more effective than the online bus stop when the initial density is relatively low.

A new macro model for traffic flow with the consideration of the driver's forecast effect

In this Letter, we present a new car-following model based on the driver's forecast effect (DFE). Applying the relationship between the micro and macro variables, we obtain a new macro model for traffic flow with the consideration of DFE. The analytical results show that our model can improve the stability of traffic flow if properly considering DFE and will reduce the stable region of traffic flow if over considering DFE. The numerical results show that our model can not only reproduce the evolution of shock, rarefaction wave and small perturbation, but also improve the stability of traffic flow.

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.