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The research of traffic congestion control has been developed rapidly in recent years. Researching the bifurcation characteristics of traffic flow and designing control schemes for unstable bifurcation points can provide some new methods for relieving the traffic congestion. In this paper, we study the bifurcation characteristics and nonlinear control of traffic flow based on the continuum model considering the new energy vehicles effect. First, a macroscopic traffic flow model considering the number of new energy vehicles and their range is proposed. Then, we transform it into a traffic flow stability model suitable for branching analysis using the traveling wave transformation. Therefore, we can transform the traffic flow problem into the stability analysis problem of systems and reflect unstable traffic characteristics such as congestion. Based on the stability model, the existence conditions of the Hopf bifurcation are proved and some bifurcation points of the traffic system are found. Second, we study the congestion and stability abrupt change behaviors near the equilibrium point and branching point to seek for the formation mechanism of traffic congestion. Finally, for the unstable bifurcation point, the control scheme is designed by Chebyshev polynomial approximation, stochastic feedback control, and other methods to delay or disappear the unstable bifurcation point and alleviate traffic congestion. It has important theoretical significance and application value. [ABSTRACT FROM AUTHOR]

Due to the continuous development of economy and society, the pace of life is also accelerated, so people pay more and more attention to the time cost, and the transportation time cost is also a very important part of it. The traffic system is an important carrier to realize the traffic operation. The increase of automobile ownership requires the traffic system to be higher and higher. Moreover, vehicles in congested traffic flow inevitably start and stop operations with high frequency, which undoubtedly increases vehicle exhaust emissions, environmental pollution, noise pollution and other problems. For today's traffic system, vehicle dynamics information is also an important factor which affects the traffic system. Therefore, adding throttle, vehicle dynamics information, to the macro-traffic flow modeling research in this paper is a supplement and improvement to the current traffic flow theory research. By analyzing the equilibrium point, this paper proves the conditions for the existence of Hopf branch and saddle junction branch. Finally, numerical simulation is carried out, and the space–time diagram of density and phase plane are obtained through simulation, which can be used to describe the actual traffic phenomenon. Through numerical simulation, it is found that this model can better describe the congestion phenomenon of the actual traffic system, and provide scientific theoretical support for macroscopic traffic flow state analysis. [ABSTRACT FROM AUTHOR]

Bifurcation of traffic flow involves complex dynamic characteristics of the system. In order to understand the complex traffic phenomenon, this work designed a macro traffic model considering the driver's memory which plays an important role in the traffic flow. Based on this model, we investigate the effects of the driver's memory and wave velocity on the stability of the traffic flow. By means of one and two parameter bifurcation analysis, we explore how these parameters affect the bifurcation structure of the system, and further investigate the dynamic mechanisms of traffic flow. We explain various traffic phenomena related to the different types of equilibrium points and limit cycles by phase plane analysis. We also study how the initial density and bifurcation structure affect the energy consumption in the system. The results show that the driver's memory and wave velocity play an important role in the stability of the traffic flow. By considering the change of bifurcation structure, we can better understand the source of traffic congestion, and further predict and control the possible traffic congestion. [ABSTRACT FROM AUTHOR]

Congestion in transport networks is a topic of theoretical interest and practical importance. In this paper we study the flow of vehicles in urban street networks. In particular, we use a cellular automata model on a complex network to simulate the motion of vehicles along streets, coupled with a congestion-aware routing at street crossings. Such routing makes use of the knowledge of agents about traffic in nearby roads and allows the vehicles to dynamically update the routes towards their destinations. By implementing the model in real urban street patterns of various cities, we show that it is possible to achieve a global traffic optimization based on local agent decisions. [ABSTRACT FROM AUTHOR]

Cascading failures often occur in congested complex networks. Cascading failures can be expressed as a three phase process: generation, diffusion and dissipation of congestion. Different from betweenness centrality, we propose a congestion function to represent the extent of congestion on a given node. By introducing the concept of “delay time”, we construct an intergradation between permanent removal and nonremoval. We also build a new evaluation function of network efficiency, based on congestion, which measures the damage caused by cascading failures. Finally, based on Statnet and Webgraph topologies we investigate the effects of network structure and size, delay time, processing ability and traffic generation speed on congestion propagation. Also we uncover cascading process composed of three phases and some factors affecting cascade propagation. [ABSTRACT FROM AUTHOR]

The effects of some disorders, on the traffic flow behavior, are studied numerically. Especially, the effect of mixture of vehicles of different velocities and/or lengths, the effects of different drivers reactions, the position and the extraction rate of off-ramp in the free way. Using a generalized optimal velocity model, for a mixture of fast and slow vehicles, we have investigated the effect of delay times τ f and τ s on the fundamental diagram. It is Found that the small delay times have almost no effect, while, for sufficiently large delay time τ s , the current profile displays qualitatively five different forms, depending on τ f , τ s and the fractions f f and f s of the fast and slow cars, respectively. The velocity (current) exhibits first-order transitions at low and/or high densities, from freely moving phase to the congested state, and from congested state to a jamming one, respectively. The minimal current appears in intermediate values of τ s . Furthermore there exist, a critical value of τ f above which the meta-stability and hysteresis appear. The effects of disorder due to drivers behaviors have been introduced through a random delay time τ allowing the car to reach its optimal velocity traffic flow models with open boundaries. In the absence of the variation of the delay time Δτ, it is found that the transition from unstable to meta-stable and from meta-stable to stable state occur under the effect of the injecting and the extracting rate probabilities α and β respectively. Moreover, the perturbation of the traffic flow behavior due to the off-ramp has been studied using numerical simulations in the one dimensional cellular automaton traffic flow model with open boundaries. When the off-ramp is located between two critical positions i c1 and i c2 the current remains constant (plateau) for β0 c1 < β0 < β0 c2, and the density undergoes two successive first order transitions: from high density to plateau current phase and from average density to the low one. In the case of two off-ramps, these transitions occur only when the distance between ramps, is smaller than a critical value. [ABSTRACT FROM AUTHOR]

The relevant dynamics of a queueing process can be anticipated by taking future arrivals into account. If the transport from one queue to another is associated with transportation delays, as it is typical for traffic or productions networks, future arrivals to a queue are known over some time horizon and, thus, can be used for an anticipative control of the corresponding flows. A queue is controlled by switching its outflow between “on” and “off” similar to green and red traffic lights, where switching to “on” requires a non-zero setup time. Due to the presence of both continuous and discrete state variables, the queueing process is described as a hybrid dynamical system. From this formulation, we derive one observable of fundamental importance: the green time required to clear the queue. This quantity allows to detect switching time points for serving platoons without delay, i.e., in a “green wave” manner. Moreover, we quantify the cost of delaying the start of a service period or its termination in terms of additional waiting time. Our findings may serve as a basis for strategic control decisions. [ABSTRACT FROM AUTHOR]

Based on the Nagel-Schreckenberg (NaSch) model of traffic flow, a modified cellular automaton (CA) traffic model with the density-dependent randomization (abbreviated as the DDR model) is proposed to simulate traffic flow. The fundamental diagram obtained by simulation shows the ability of this modified NaSch model to capture the essential features of traffic flow, e.g., synchronized flow, metastable state, hysteresis and phase separation at higher densities. Comparisons are made between this DDR model and the NaSch model, also between this DDR model and the VDR model. And the underlying mechanism is analyzed. All these results indicate that the presented model is reasonable and more realistic. [ABSTRACT FROM AUTHOR]

In this paper, we investigate cascade defense and control in scale free networks via navigation strategy. It is found that with an appropriate parameter a, which is tunable in controlling the effect of degree in the navigation strategy, one can reduce the risk of cascade break down. By checking the distribution of efficient betweenness centrality (EBC) and the average EBC of vertices with degree k, the validity can be guaranteed. Despite the advantage of cascade defense, the degree based navigation strategy may also lead to lower network efficiency. To avoid this disadvantage, we propose a new navigation strategy. Importantly and interestingly, the new strategy can defend cascade break down effectively even without reducing the network efficiency. Distribution of the EBC and EBC-degree correlation of the new strategy are also investigated to explain the effectiveness in cascade defense. [ABSTRACT FROM AUTHOR]

In complex scale-free networks, ranking the individual nodes based upon their importance has useful applications, such as the identification of hubs for epidemic control, or bottlenecks for controlling traffic congestion. However, in most real situations, only limited sub-structures of entire networks are available, and therefore the reliability of the order relationships in sampled networks requires investigation. With a set of randomly sampled nodes from the underlying original networks, we rank individual nodes by three centrality measures: degree, betweenness, and closeness. The higher-ranking nodes from the sampled networks provide a relatively better characterisation of their ranks in the original networks than the lower-ranking nodes. A closeness-based order relationship is more reliable than any other quantity, due to the global nature of the closeness measure. In addition, we show that if access to hubs is limited during the sampling process, an increase in the sampling fraction can in fact decrease the sampling accuracy. Finally, an estimation method for assessing sampling accuracy is suggested. [ABSTRACT FROM AUTHOR]

An extended car following model is proposed by incorporating intelligent transportation system and the backward looking effect under certain condition in traffic flow. The neutral stability condition of this model is obtained by using the linear stability theory. The results show that anticipating the behavior of vehicles preceding and following one vehicle could lead to appreciable stabilization of traffic system. From the simulation of space-time evolution of the vehicle headways, it is shown that the traffic jam could be suppressed efficiently via taking into account the information about the motion of two preceding vehicles and one following vehicle, and the analytical result is consistent with the simulation one. [ABSTRACT FROM AUTHOR]

By introducing relative velocities of arbitrary number of cars ahead into the full velocity difference models (FVDM), we present a forward looking relative velocity model (FLRVM) of cooperative driving control system. To our knowledge, the model is an improvement over the similar extension in the forward looking optimal velocity models (FLOVM), because it is more reasonable and realistic in implement of incorporating intelligent transportation system in traffic. Then the stability criterion is investigated by the linear stability analysis with finding that new consideration theoretically lead to the improvement of the stability of traffic flow, and the validity of our theoretical analysis is confirmed by direct simulations. In addition, nonlinear analysis of the model shows that the three waves: triangular shock wave, soliton wave and kink-antikink wave appear respectively in stable, metastable and unstable regions. These correspond to the solutions of the Burgers equation, Korteweg-de Vries (KdV) equation and modified Korteweg-de Vries (mKdV) equation. [ABSTRACT FROM AUTHOR]

We study network traffic dynamics in a two dimensional communication network with regular nodes and hubs. If the network experiences heavy message traffic, congestion occurs due to finite capacity of the nodes. We discuss strategies to manipulate hub capacity and hub connections to relieve congestion and define a coefficient of betweenness centrality (CBC), a direct measure of network traffic, which is useful for identifying hubs which are most likely to cause congestion. The addition of assortative connections to hubs of high CBC relieves congestion very efficiently. [ABSTRACT FROM AUTHOR]

We explore packet traffic dynamics in a data network model near phase transition point from free flow to congestion. The model of data network is an abstraction of the Network Layer of the OSI (Open Systems Interconnect) Reference Model of packet switching networks. The Network Layer is responsible for routing packets across the network from their sources to their destinations and for control of congestion in data networks. Using the model we investigate spatio-temporal packets traffic dynamics near the phase transition point for various network connection topologies, and static and adaptive routing algorithms. We present selected simulation results and analyze them. [ABSTRACT FROM AUTHOR]

The aim of this paper is to control the vehicle system to move orderly by a feedback signal in the optimal velocity (OV) model under open boundary. Following the description of the OV model and its stability analysis, some problems about the definition of traffic jams in [12] are presented and illustrated by an example. Based on our analysis, a feedback signal acting on the traffic system has been introduced into the OV model. The signal will act in the system only if the state is inhomogeneous, and it will vanish in the homogeneous traffic flow. Theoretically, it is proved that the disorder state in traffic system could be suppressed by using the control method. Two kinds of noises are tested in our computer simulations. The simulation results demonstrate that the traffic system can move into a homogeneous phase by the control. [ABSTRACT FROM AUTHOR]