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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]

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]

To understand how the jamming on real communication networks depends on node capacity, we study the traffic model with heterogeneous node capacity. In this model, each movable packet takes a biased random walk and the capacity of a node with degree k is given as C( k) ∼ k with a tunable parameter x. Each packet disappears when it arrives at the preassigned target node. We analytically and numerically show that the transition from the free-flow phase to the jammed phase occurs when the balance between the packet generations and removals is broken. The balance breaking condition for the jamming is analytically determined by the competition between C( k) and the average number of packets on a node of degree k, m( k), in the free-flow phase. Based on the analytic arguments, we find that there exist three different jamming patterns depending on C( k). The analytic conjectures for jamming patterns are verified by numerical simulations. [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]

The efficiency of traffic flows in urban areas is known to crucially depend on signal operation. Here, elements of signal control are discussed, based on the minimization of overall travel times or vehicle queues. Interestingly, we find different operation regimes, some of which involve a “slower-is-faster effect”, where a delayed switching reduces the average travel times. These operation regimes characterize different ways of organizing traffic flows in urban road networks. Besides the optimize-one-phase approach, we discuss the procedure and advantages of optimizing multiple phases as well. To improve the service of vehicle platoons and support the self-organization of “green waves”, it is proposed to consider the price of stopping newly arriving vehicles. [ABSTRACT FROM AUTHOR]

Driven many-particle systems with nonlinear interactions are known to often display multi-stability, i.e. depending on the respective initial condition, there may be different outcomes. Here, we study this phenomenon for traffic models, some of which show stable and linearly unstable density regimes, but areas of metastability in between. In these areas, perturbations larger than a certain critical amplitude will cause a lasting breakdown of traffic, while smaller ones will fade away. While there are common methods to study linear instability, non-linear instability had to be studied numerically in the past. Here, we present an analytical study for the optimal velocity model with a stepwise specification of the optimal velocity function and a simple kind of perturbation. Despite various approximations, the analytical results are shown to reproduce numerical results very well. [ABSTRACT FROM AUTHOR]

Daganzo’s criticisms of second-order fluid approximations of traffic flow [C. Daganzo, Transpn. Res. B. 29, 277 (1995)] and Aw and Rascle’s proposal how to overcome them [A. Aw, M. Rascle, SIAM J. Appl. Math. 60, 916 (2000)] have stimulated an intensive scientific activity in the field of traffic modeling. Here, we will revisit their arguments and the interpretations behind them. We will start by analyzing the linear stability of traffic models, which is a widely established approach to study the ability of traffic models to describe emergent traffic jams. Besides deriving a collection of useful formulas for stability analyses, the main attention is put on the characteristic speeds, which are related to the group velocities of the linearized model equations. Most macroscopic traffic models with a dynamic velocity equation appear to predict two characteristic speeds, one of which is faster than the average velocity. This has been claimed to constitute a theoretical inconsistency. We will carefully discuss arguments for and against this view. In particular, we will shed some new light on the problem by comparing Payne’s macroscopic traffic model with the Aw-Rascle model and macroscopic with microscopic traffic models. [ABSTRACT FROM AUTHOR]

This contribution compares several different approaches allowing one to derive macroscopic traffic equation directly from microscopic car-following models. While it is shown that some conventional approaches lead to theoretical problems, it is proposed to use an approach reminding of smoothed particle hydrodynamics to avoid gradient expansions. The derivation circumvents approximations and, therefore, demonstrates the large range of validity of macroscopic traffic equations, without the need of averaging over many vehicles. It also gives an expression for the “traffic pressure”, which generalizes previously used formulas. Furthermore, the method avoids theoretical inconsistencies of macroscopic traffic models, which have been criticized in the past by Daganzo and others. [ABSTRACT FROM AUTHOR]

There has been a debate in the transportation research community over the validity of a class of traffic flow models. These models have the peculiar property that one of its characteristic speeds is faster than that of vehicular traffic. This note attempts to provide an overview of the diverging views on how to interpret this property, and specific comments on the interpretation of Helbing and Johansson [ On the controversy around Daganzo’s requiem for and Aw-Rascle’s resurrection of second-order traffic flow models, Eur. Phys. J. B (2009), DOI: 10.1140/epjb/e2009-00182-7]. We showed that having faster-than-traffic characteristics does produce counterintuitive predictions, and they cannot be explained away by a linear stability analysis. As such, the existence of such characteristics must be justified by the physics of traffic, and verified through empirical observations. [ABSTRACT FROM AUTHOR]

Starting from the instability diagram of a traffic flow model, we derive conditions for the occurrence of congested traffic states, their appearance, their spreading in space and time, and the related increase in travel times. We discuss the terminology of traffic phases and give empirical evidence for the existence of a phase diagram of traffic states. In contrast to previously presented phase diagrams, it is shown that “widening synchronized patterns” are possible, if the maximum flow is located inside of a metastable density regime. Moreover, for various kinds of traffic models with different instability diagrams it is discussed, how the related phase diagrams are expected to approximately look like. Apart from this, it is pointed out that combinations of on- and off-ramps create different patterns than a single, isolated on-ramp. [ABSTRACT FROM AUTHOR]

By comparing microscopic traffic flow models with a different number of phases in the context of a simple scenario, the similarities as well as the differences of the various traffic flow models can be discussed. It turns out that there is a certain range of traffic flow conditions, where it is difficult to discern the space-time patterns produced by the different models. However, there are some other regions in the parameter space, where clear differences can be detected. Although the results obtained here cannot directly transformed into a real test with real-world data, they may help to finally define realistic scenarios which would result in a clear decision about which model describes reality best. [ABSTRACT FROM AUTHOR]

Traffic is highly influenced by network structure and human behaviour. Small changes in the human behaviour can lead to huge changes in the load of a traffic network. Current transportation models do not, and most of them cannot, research such random behaviour but always calculate a steady state. In our multi-agent transport simulation, we frequently observe seemingly random “network breakdowns”, huge traffic jams that spread over a big part of the network, making a normal traffic flow impossible. This paper describes the investigations that were performed on the results of our large-scale multi-agent transport simulations in an attempt to contribute to the better understanding of the dynamic processes in such simulations and, hopefully, better understanding and modelling of the real-world. [ABSTRACT FROM AUTHOR]

Using computer simulations, we show that metastable states still occur in two-lane traffic models with slow to start rules. However, these metastable states no longer exist in systems where aggressive drivers ( which do not look back before changing lanes) are present. Indeed, the presence of only one aggressive driver in the circuit, triggers the breakdown of the high flow states. In these systems, the steady state is unique and its relaxation dynamics should depend on the lane changing probability pch and the number of aggressive drivers present in the circuit. It is found also that the relaxation time τ diverges as the form of a power-law: τ∝pch -β, β=1. 89.40.+k [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]

This paper studies a new model, which considers the effects of drivers reaction delay in the Nagel-Schreckenberg model. We studied the traffic flow properties in the new model under both periodic and open boundary conditions. The fundamental diagram, spatio-temporal patterns, density-density correlation functions, relaxation time, and distance headway distribution are investigated. Several interesting results are reported, for example, (i) the jam becomes less condensed when the delay effect is considered; (ii) the distance headway of the new model exhibits a multi-peak distribution when randomization p is small; (iii) for large p, the distribution of distance headway follows a power law in the new model; (iv) under open boundary conditions, the existence of a stationary jam near the left boundary will lower the flow rate. [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 suggest a disordered traffic flow model that captures many features of traffic flow. It is an extension of the Nagel-Schreckenberg (NaSch) stochastic cellular automata for single line vehicular traffic model. It incorporates random acceleration and deceleration terms that may be greater than one unit. Our model leads under its intrinsic dynamics, for high values of braking probability pr, to a constant flow at intermediate densities without introducing any spatial inhomogeneities. For a system of fast drivers pr→0, the model exhibits a density wave behavior that was observed in car following models with optimal velocity. The gap of the disordered model we present exhibits, for high values of pr and random deceleration, at a critical density, a power law distribution which is a hall mark of a self organized criticality phenomena. [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]

Examines the effects of open boundaries on the dynamical behavior of optimal velocity traffic flow model with a delay time allowing the car to reach its optimal velocity using numerical simulations. Mathematical description of the traffic flow model; Analysis of the critical value of traffic flows; Examination of the space-time evolution for various values of extracting rate probability.

: Anticipation in traffic means that drivers estimate their leaders' velocities for future timesteps. In the article a specific stochastic car-following model with non-unique flow-density relation is investigated with respect to anticipatory driving. It is realized by next-nearest-neighbour interaction which leads to large flows and short temporal headways. The underlying mechanism that causes these effects is explained by the headways of the cars which organize in an alternating structure with a short headway following a long one, thereby producing a strong anti-correlation in the gaps or in the headways of subsequent cars. For the investigated model the corresponding time headway distributions display the short headways observed in reality. Even though these effects are discussed for a specific model, the mechanism described is in general present in any traffic flow models that work with anticipation. [ABSTRACT FROM AUTHOR]

This contribution replies to Zhang’s comment on the manuscript “On the controversy around Daganzo’s requiem for and Aw-Rascle’s resurrection of second-order traffic flow models” published in Eur. Phys. J. B. The author clarifies several points and agrees that suitable experiments can be a way of deciding the controversy on the existence of propagation speeds faster than the speed of vehicles. Moreover, he proposes to aim at an integrated theory, which is both, theoretically consistent and practically relevant. [ABSTRACT FROM AUTHOR]