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The study of traffic flow bifurcation control analysis is of great significance for understanding the essential evolution law of traffic flow, controlling traffic flow with practical means and alleviating traffic congestion. This paper describes the influence of lateral distance compensation in the process of lane change, and adjusts the traffic flow from the perspective of bifurcation control, which can capture the characteristics of traffic flow better, so as to describe the practical significance of the actual traffic phenomenon better. For example, the green ratio of traffic lights in the road, the planning and design of traffic signs, and the guidance of traffic condition prediction in ITS. In addition, the traffic flow is introduced and applied to the traffic model from the perspective of random function, and the bifurcation control is carried out according to the bifurcation behavior in traffic. That is, the bifurcation characteristics of the system are modified by the designed feedback controller, and the appearance of the equilibrium point of the system is adjusted to make it move forward, backward or disappear, so as to prevent or alleviate traffic congestion. There are few researches on bifurcation control of traffic flow model with lateral distance compensation. This paper introduces stochastic function based on lateral compensation model to study Hopf bifurcation phenomenon and Hopf bifurcation control. Firstly, the existence condition of Hopf bifurcation at the equilibrium point in the model is proved theoretically. Then, a feedback controller is designed to control the amplitudes of the Hopf bifurcation and the limit cycles formed by the Hopf bifurcation. Finally, the theoretical results are verified by numerical simulation. The research shows that by adjusting the control parameters in the feedback controller, the influence of boundary conditions on the stability of the traffic system is fully described, the effect of unstable focus and saddle point on the system is inhibited, and the traffic flow is slowed down. In addition, the unstable bifurcation points can be eliminated, and the amplitude of the limit cycle formed by Hopf bifurcation can be adjusted, so as to achieve the stability of the control system. • A new continuum model is proposed taking into account the lateral offset compensation. • Introducing the traffic flow into the traffic model from the perspective of the random function. • The designed feedback controller corrects the bifurcation characteristics of the system and adjusts the appearance of the balance point of the system to make it forward, backward or disappear, so as to prevent or reduce traffic jams. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a numerical stability analysis of a multi-phase car-following model under mild to severe disturbances. The results show that local stability was always conformed. An asymptotically unstable region was found for traffic in congested states. One of the previously calibrated boundary conditions for close-following situations was found to be in conflict with the stable condition required by the car-following model, which had attributed to speed oscillations during transition of the traffic from a non-congested to a congested state. Suggestions were made to the choice of model parameter values to meet the stability conditions and ways to improve the model. [Copyright &y& Elsevier]

Abstract: In this paper, we use a two-lane CA model to investigate the effect of a bus stop between two neighbouring intersections on the capacity of the bus. Both the case of a bus stop with a special stopping lane and that of one without are considered. The capacity versus the distance () between the stop and the upstream (downstream) intersection is studied, with respect to the entering probability and the traffic light cycle . It is found that a bus stop near an intersection can act as a bottleneck and cause a drop in the capacity when the (or ) is below a critical point (or ). However, the situation when the stop is located near the downstream intersection is worse than that of the upstream one. Furthermore, the simulation results show that the negative effect varies with the increase of the cycle time and the capacity can be maximized by adjusting . Comparisons between the two cases suggest that the stopping lane can improve the capacity to some extent. These results mean that the capacity can be exploited by changing the position of the bus stop or the cycle time, and adding a stopping lane if necessary. These findings may be useful in offering scientific guidance for the management and design of traffic networks. [Copyright &y& Elsevier]

Abstract: We study the congestion on a homogeneous roadway with open boundaries. Three different phases are identified. Both numerical and analytical results are presented. For stationary boundaries, three different flow can be associated with a single density on the fundamental diagram. When the congestion is characterized by numerous jams, the system is homogeneous and the traffic flow is low. When the system is dominate by a single jam, the time trajectory traces out finite cycles and a higher traffic flow can be supported. If the cycles fill up a two-dimensional area, the traffic flow remains constant as the density changes; if the cycles collapse into a one-dimensional loop, a much higher traffic flow can be achieved. We also discuss the effects of dynamical boundaries. [Copyright &y& Elsevier]

Abstract: 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). [Copyright &y& Elsevier]

Abstract: A new public conveyance model applicable to buses and trains is proposed in this paper by using stochastic cellular automaton. We have found the optimal density of vehicles, at which the average velocity becomes maximum, significantly depends on the number of stops and passengers behavior of getting on a vehicle at stops. The efficiency of the hail-and-ride system is also discussed by comparing the different behavior of passengers. Moreover, we have found that a big cluster of vehicles is divided into small clusters, by incorporating information of the number of vehicles between successive stops. [Copyright &y& Elsevier]

Menezes and Barabasi have once developed a framework by mean–variance analysis to investigate the relationship between the average flux and fluctuations and found a scaling-law behavior in two distinct phase. By then most related researches dedicated to understanding the scaling laws through the internal/external forces of the system. However, as for subway system, the demand of transporting a large amount of passengers during peak hours is a necessity. Thus, alternating the phase or reducing the impact of external forces by cutting down the total passengers is completely unrealistic. The more operable approaches are specifically regulating the distribution of passenger flow in order to drive the system into a more stable phase. In this paper, we carried out the mean–variance analysis on subway traffic and dedicated to discover the effect of spatial–temporal distributions of passenger flow on the fluctuations in subway traffic. By analyzing the control properties of the transit networks constructed according to different passenger flow threshold , it is found that the control mode of transit networks might differ the phase change of fluctuations, which proposed a new perspective of controlling the fluctuations in subway traffic. • Transit network of metro system was constructed to character the spatial–temporal distribution of traffic. • Clear scaling-law can be observed between the mean and variance of passenger flow in the transit network. • The scale exponent vary within a day and are dominated by the traffic variation and the control mode of the transit networks. • Traffic restrictions should be given in priority to stations with large inbound and outbound traffic at morning (evening) peak hours. [ABSTRACT FROM AUTHOR]