Traffic Flow Instability Research Articles

Determination of Route Delivery in the Logistic Service Provider (LSP) by Reviewing the Performance of Street in The City of Malang

Malang as the National Activity Centre (PKN) led to increased economic growth and increased the demand for goods both primary and tertiary goods. Demand of goods which is increasing and also diversing will certainly have an impact on the process of transportation of goods involving a freight forwarder. Shipping of goods is part of the supply chain, which handles the flow of goods, distribution and delivery service or commonly called the courier. Fulfilling the request of goods would require Logistics Service Provider (LSP) that distribute goods from point of origin to destination. Delays in the distribution of goods will slow(DOWN) economic growth in Malang, therefore focused studies on the movement of goods which includes the election of the delivery route is needed. The purpose of this study is to get the delivery route for LSP by identifying its patterns of freight transport movement and to analyze the network performance of the road that is passed by freight transportation. Data collection techniques in this research are interviews, questionnaires and observations of moving-car and traffic counting to get the volume of traffic. The study used road’s performance analysis to get the level of service (LOS) of roads which are used by the freight transportation of LSP and Dijkstra’s algorithm analysis to determine the delivery routes. The results showed that the Level of Service of the roads (LOS) is at the level of D to F which indicates that the chosen roads experience instability of traffic flow even reach a critical condition. Therefore by considering delivery routes selection both of existing condition and analysis result as well as the condition of the road network in Malang, then given alternative is by deliverying goods on the chosen routes but not at peak hour.

Stability analysis and fundamental diagram of heterogeneous traffic flow mixed with cooperative adaptive cruise control vehicles

This paper is aimed at building a framework for string stability analysis of traffic flow mixed with different cooperative adaptive cruise control (CACC) market penetration rates. In addition to the string stability, the fundamental diagram of the mixed flow is also taken into consideration for evaluating the effect of CACC vehicles on capacity. In order to describe the car-following dynamics of real CACC vehicles, the CACC model proposed by PATH is employed, which is validated by real experimental data. The intelligent driver model (IDM) is used as a surrogate car-following model for traditional manual driven vehicles. Based on the guidelines proposed by Ward[Ward J A 2009 Ph. D. Dissertation (Bristol:University of Bristol)], a framework is developed for the analytical investigation of heterogeneous traffic flow string stability. The framework presented considers the instability condition of traffic flow as a linear function of CACC market penetration rate. Following the framework, the string stabilities of the mixed traffic flow under different CACC market penetration rates and equilibrium velocities are analyzed. For fundamental diagram of the heterogeneous traffic flow, the equilibrium velocity-spacing functions of manual vehicles and CACC vehicles are obtained respectively based on car-following model. Then, the fundamental diagram of the density-velocity relationship of the heterogeneous traffic flow is derived based on the definition of traffic flow density. In addition, the theoretical fundamental diagram is plotted to show the property of traffic throughput. The numerical simulations are also carried out in order to investigate the effect of CACC vehicle on the characteristics of fundamental diagram. Besides, sensitivity analyses on CACC desired time gap are conducted for both string stability and fundamental diagram. Analytical studies and simulation results are as follows. 1) The heterogeneous traffic flow is stable for different equilibrium velocities and CACC market penetration rates, if manual driven vehicles are stable. Otherwise, the instability of traditional traffic flow is improved gradually with the increase of the CACC market penetration rate. Additionally, the stability will become better when equilibrium velocity is away from the velocity range of 9.6-18.6 m/s. 2) Because CACC vehicles can travel at free-flow speed in a relatively small headway, CACC vehicles can improve the capacity of heterogeneous traffic flow. 3) The results of sensitivity analysis indicate that with the increase of the CACC desired time gap, the stable region of heterogeneous traffic flow increases. However, the capacity of the fundamental diagram drops. Therefore, the value of the desired time gap should be determined with considering the effects of the two aspects on the heterogeneous traffic flow. It is noted that the CACC model used in this paper is based on the current state-of-the-art real CACC vehicle experiments. In the future, more experimental observations will yield new CACC models. However, the framework presented in this paper can still be used for the analytical investigation of string stability of the heterogeneous traffic flow at that time.

Experimental and Empirical Investigations of Traffic Flow Instability

Experimental and Empirical Investigations of Traffic Flow Instability

The Intelligent Driver Model with Stochasticity -New Insights Into Traffic Flow Oscillations

Traffic flow oscillations, including traffic waves, are a common yet incompletely understood feature of congested traffic. Possible mechanisms include traffic flow instabilities, indifference regions or finite human perception thresholds (action points), and external acceleration noise. However, the relative importance of these factors in a given situation remains unclear. We bring light into this question by adding external noise and action points to the Intelligent Driver Model and other car-following models thereby obtaining a minimal model containing all three oscillation mechanisms. We show analytically that even in the subcritical regime of linearly stable flow (order parameter ϵ < 0), external white noise leads to spatiotemporal speed correlations “anticipating” the waves of the linearly unstable regime. Sufficiently far away from the threshold, the amplitude scales with (−ϵ)−0.5. By means of simulations and comparisons with experimental car platoons and bicycle traffic, we show that external noise and indifference regions with action points have essentially equivalent effects. Furthermore, flow instabilities dominate the oscillations on freeways while external noise or action points prevail at low desired speeds such as vehicular city or bicycle traffic. For bicycle traffic, noise can lead to fully developed waves even for single-file traffic in the subcritical regime.

New full velocity difference model considering the driver’s heterogeneity of the disturbance risk preference for car-following theory

This paper proposes a new full velocity difference model considering the driver’s heterogeneity of the disturbance risk preference for car-following theory to investigate the effects of the driver’s heterogeneity of the disturbance risk preference on traffic flow instability when the driver reacts to the relative velocity. We obtain traffic flow instability condition and the calculation method of the unstable region headway range and the probability of traffic congestion caused by a small disturbance. The analysis shows that has important effects the driver’s heterogeneity of the disturbance risk preference on traffic flow instability: (1) traffic flow instability is independent of the absolute size of the driver’s disturbance risk preference coefficient and depends on the ratio of the preceding vehicle driver’s disturbance risk preference coefficient to the following vehicle driver’s disturbance risk preference coefficient; (2) the smaller the ratio of the preceding vehicle driver’s disturbance risk preference coefficient to the following vehicle driver’s disturbance risk preference coefficient, the smaller traffic flow instability and vice versa. It provides some viable ideas to suppress traffic congestion.

Microscopic theory of traffic-flow instability governing traffic breakdown at highway bottlenecks: Growing wave of increase in speed in synchronized flow.

We have revealed a growing local speed wave of increase in speed that can randomly occur in synchronized flow (S) at a highway bottleneck. The development of such a traffic flow instability leads to free flow (F) at the bottleneck; therefore, we call this instability an S→F instability. Whereas the S→F instability leads to a local increase in speed (growing acceleration wave), in contrast, the classical traffic flow instability introduced in the 1950s-1960s and incorporated later in a huge number of traffic flow models leads to a growing wave of a local decrease in speed (growing deceleration wave). We have found that the S→F instability can occur only if there is a finite time delay in driver overacceleration. The initial speed disturbance of increase in speed (called "speed peak") that initiates the S→F instability occurs usually at the downstream front of synchronized flow at the bottleneck. There can be many speed peaks with random amplitudes that occur randomly over time. It has been found that the S→F instability exhibits a nucleation nature: Only when a speed peak amplitude is large enough can the S→F instability occur; in contrast, speed peaks of smaller amplitudes cause dissolving speed waves of a local increase in speed (dissolving acceleration waves) in synchronized flow. We have found that the S→F instability governs traffic breakdown-a phase transition from free flow to synchronized flow (F→S transition) at the bottleneck: The nucleation nature of the S→F instability explains the metastability of free flow with respect to an F→S transition at the bottleneck.

Analysis on Molecular Kinetics for Traffic Flow Stability

AbstractTo prevent effectively the occurrence of traffic congestion and to reduce the traffic accident rate, traffic flow stability is analyzed by molecular kinetics based on the Lyapunov stability criterion, and a model is developed regarding the traffic flow in a state of uniform synchronous flow as the object, considering the integrated effect of people, vehicles, roads, environment, etc. With a trajectory graph of vehicles and state diagrams of traffic flow, the evolution process of traffic flow stability influenced by various factors of traffic disturbance is analyzed. The mechanism inducing the phenomenon of traffic flow instability is revealed. Traffic flow stability can be improved by considering traffic scenes such as people, vehicles, roads, and the environment.

Jam-absorption driving with a car-following model

Jam-absorption driving (JAD) refers to the action performed by a single car to dynamically change its headway to remove a traffic jam. Because of its irregular motion, a car performing JAD perturbs other cars following it, and these perturbations may grow to become the so-called secondary traffic jams. A basic theory for JAD (Nishi et al. 2013) does not consider accelerations of cars or the stability of traffic flow. In this paper, by introducing car-following behaviors, we implement these elements in JAD. Numerous previous studies on the instability of traffic flow showed that even in a region whose density is below a critical density, perturbation may grow if its initial magnitude is large. According to these previous studies, we expect that the perturbations caused by JAD, if they are sufficiently small, do not grow to become secondary traffic jams. Using a microscopic car-following model, we numerically confirmed that the stability of a flow obeying the model depends on the magnitude of JAD perturbations. On the basis of this knowledge, numerical results indicate that parameter regions exist where JAD allows traffic jams to be removed without causing secondary traffic jams. Moreover, JAD is robust against a parameter of acceleration in the model, as well as the choice of car-following models.

Effects of the lattice point drivers’ heterogeneity of the disturbance risk preference on traffic flow instability

This paper defines the lattice point drivers’ heterogeneity of the disturbance risk preference and proposes a new one-dimensional traffic flow lattice model to research the effects of the lattice point drivers’ heterogeneity of the disturbance risk preference on traffic flow instability. By the analytical analysis, we obtain the traffic flow instability condition and the modified Korteweg–de Vries (mKdV) equation and the calculation formula of the unstable area density range, and the calculation method of the probability of traffic congestion caused by a small disturbance. Both the analytical and the simulation analysis show that there are important effects of the lattice point drivers’ heterogeneity of the disturbance risk preference on traffic flow instability, namely the smaller the ratio of the preceding lattice point drivers’ coefficient of the disturbance risk preference to the following lattice point drivers’ coefficient of the disturbance risk preference is, the smaller the traffic flow instability is and vice versa. It provides a viable idea to ease traffic congestion.

Effect of the car-following combinations on the instability of heterogeneous traffic flow

Heterogeneous traffic flow contains the mixed operation of the different vehicle classes such as cars, trucks and buses. Previous study has indicated that the overall stability of the heterogeneous traffic flow is governed by a weighted mean of stability parameters corresponding to each vehicle class and is not affected by the order in which a vehicle class is put into the system, for example either car or truck. However, it has been recently reported that the effect of mixed composition on traffic flow dynamics is also determined by the car-following vehicle type, that is either car following a car or car following a truck. This paper aims at investigating analytically how different car-following combinations (i.e. the following type) influence the overall stability of heterogeneous traffic flow dynamics. More specifically, we will consider the four types of car-following behaviour such as car–car, car–truck, truck–car, and truck–truck. The effect of such car-following types on the overall linear stability condition of the heterogeneous traffic flow will be studied using a generalised multi-class car-following model in which the optimal speed function is not only dependent on the the space headway between two consecutive vehicles as in previous study of Mason and Woods [1997. “Car-following Model of Multispecies Systems of Road Traffic.” Physical Review E: 2203–2214] but also on the and the relative speed between those two consecutive vehicles.

Effects of comprehensive information of the nearest following vehicle on traffic flow instability

Based on the condition of inhibiting traffic flow instability, this paper studies the effects of comprehensive information of the nearest following vehicle obtained by drivers' rear view behavior on traffic flow instability. Research shows that in the real practice the probability of paying attention to the information of the preceding vehicle is greater than that of paying attention to the information of the following vehicle, and the drivers' sensitive coefficient is assumed to be greater than 0, many conclusions such as the following can be obtained: 1) the information of the nearest following vehicle headway may reduce traffic flow instability, and the larger the attention probability, the smaller the traffic flow instability; on the contrary, the information of the velocity difference between the vehicle and the nearest following vehicle may increase the traffic flow instability, so the larger the attention probability, the bigger the traffic flow instability; 2) the instability reduction effect due to the comprehensive information from the nearest following vehicle is greater than the increasing effect on the traffic flow instability; 3) the bigger the driver's sensitive coefficient of the distance difference, the bigger the reducing effect of the information of the nearest following vehicle on traffic flow instability; 4) the bigger the driver's sensitive coefficient of the velocity difference, the bigger the increasing effect of the information of the nearest following vehicle on traffic flow instability.

Analytical studies on the instabilities of heterogeneous intelligent traffic flow

It has been widely reported in literature that a small perturbation in traffic flow such as a sudden deceleration of a vehicle could lead to the formation of traffic jams without a clear bottleneck. These traffic jams are usually related to instabilities in traffic flow. The applications of intelligent traffic systems are a potential solution to reduce the amplitude or to eliminate the formation of such traffic instabilities. A lot of research has been conducted to theoretically study the effect of intelligent vehicles, for example adaptive cruise control vehicles, using either computer simulation or analytical method. However, most current analytical research has only applied to single class traffic flow. To this end, the main topic of this paper is to perform a linear stability analysis to find the stability threshold of heterogeneous traffic flow using microscopic models, particularly the effect of intelligent vehicles on heterogeneous (or multi-class) traffic flow instabilities. The analytical results will show how intelligent vehicle percentages affect the stability of multi-class traffic flow.

Instability of cooperative adaptive cruise control traffic flow: A macroscopic approach

This paper proposes a macroscopic model to describe the operations of cooperative adaptive cruise control (CACC) traffic flow, which is an extension of adaptive cruise control (ACC) traffic flow. In CACC traffic flow a vehicle can exchange information with many preceding vehicles through wireless communication. Due to such communication the CACC vehicle can follow its leader at a closer distance than the ACC vehicle. The stability diagrams are constructed from the developed model based on the linear and nonlinear stability method for a certain model parameter set. It is found analytically that CACC vehicles enhance the stabilization of traffic flow with respect to both small and large perturbations compared to ACC vehicles. Numerical simulation is carried out to support our analytical findings. Based on the nonlinear stability analysis, we will show analytically and numerically that the CACC system better improves the dynamic equilibrium capacity over the ACC system. We have argued that in parallel to microscopic models for CACC traffic flow, the newly developed macroscopic will provide a complete insight into the dynamics of intelligent traffic flow.

Effect of driver behaviours on the formation and dissipation of traffic flow instabilities

This paper extends a non-local second order continuum traffic model to take into account the timid or aggressive driver behaviours. Based on the proposed model, we derive analytically the effect of timid or aggressive driver behaviours on the instability of traffic dynamics. Simulation results are presented to show how the timid or aggressive driver behaviours influence the formation and dissipation of stop-and-go waves. It is found theoretically and numerically that aggressive drivers tend to stabilize traffic flow whereas timid drivers tend to destabilize traffic flow.

THE INFLUENCE OF INDIVIDUAL DRIVER CHARACTERISTICS ON CONGESTION FORMATION

Previous works have pointed out that one of the reasons for the formation of traffic congestion is instability in traffic flow. In this study, we investigate theoretically how the characteristics of individual drivers influence the instability of traffic flow. The discussions are based on the optimal velocity model, which has three parameters related to individual driver characteristics. We specify the mappings between the model parameters and driver characteristics in this study. With linear stability analysis, we obtain a condition for when instability occurs and a constraint about how the model parameters influence the unstable traffic flow. Meanwhile, we also determine how the region of unstable flow densities depends on these parameters. Additionally, the Langevin approach theoretically validates that under the constraint, the macroscopic characteristics of the unstable traffic flow becomes a mixture of free flows and congestions. All of these results imply that both overly aggressive and overly conservative drivers are capable of triggering traffic congestion.

Ultradiscrete optimal velocity model: A cellular-automaton model for traffic flow and linear instability of high-flux traffic

In this paper, we propose the ultradiscrete optimal velocity model, a cellular-automaton model for traffic flow, by applying the ultradiscrete method for the optimal velocity model. The optimal velocity model, defined by a differential equation, is one of the most important models; in particular, it successfully reproduces the instability of high-flux traffic. It is often pointed out that there is a close relation between the optimal velocity model and the modified Korteweg-de Vries (mkdV) equation, a soliton equation. Meanwhile, the ultradiscrete method enables one to reduce soliton equations to cellular automata which inherit the solitonic nature, such as an infinite number of conservation laws, and soliton solutions. We find that the theory of soliton equations is available for generic differential equations and the simulation results reveal that the model obtained reproduces both absolutely unstable and convectively unstable flows as well as the optimal velocity model.

Influence of Reaction Times and Anticipation on Stability of Vehicular Traffic Flow

Two causes for the instability of traffic flow are investigated: the time lag caused by finite accelerations of vehicles and the delay caused by finite reaction times of drivers. Furthermore, the degree to which drivers may compensate for these delays is simulated by looking several vehicles ahead and anticipating future traffic situations. Since vehicular traffic flow is an extended multiparticle system with many degrees of freedom, two concepts of linear stability have to be considered: (a) local stability of a car following a leader that drives at constant velocity and (b) string (chain) stability of a platoon of several vehicles following each other. Typically, string stability is a much more restrictive criterion than local stability. Both types of stability are simulated with the human driver model of M. Treiber et al. [Physica A, Vol. 360, No. 1, 2006, pp. 71-88], which includes all the foregoing features. Several interesting results were found: (a) with a suitable anticipation, string stability for reaction times exceeding the safety time gap was obtained (to the authors' knowledge, this result had not yet been achieved for any other car-following model); (b) parameter changes that destabilize the model variant with zero reaction time may stabilize the model with finite reaction times, and vice versa; and (c) distributed reaction times (every driver has a different reaction time) can stabilize the system compared with the case of drivers with identical reaction times that are equal to the mean.

INFLUENCE OF REACTION TIMES AND ANTICIPATION ON THE STABILITY OF VEHICULAR TRAFFIC FLOW

We investigate two causes for the instability of traffic flow: The time lag caused by finite accelerations of the vehicles, and the delay caused by the finite reaction times of the drivers. Furthermore, we simulate to which degree drivers may compensate for these delays by looking several vehicles ahead and anticipate future traffic situations. Since vehicular traffic flow is a multi-particle system with many degrees of freedom, two concepts of linear stability have to be considered: Local stability of a car following a leader that drives at constant velocity, and string (chain) stability of a “platoon” of several vehicles following each other. Typically, string stability is a much more restrictive criterion than local stability. We simulate both types of stability with the human driver model (HDM)[M. Treiber et al., Physica A, Vol. 360 (1), 71–88 (2006)], which includes all the features above. We found several remarkable results: (i) with a suitable anticipation, we obtained string stability for reaction times exceeding the “safe time headway”, which, to date, has not yet been obtained for any other car-following model; (ii) parameter changes that destabilize the model variant with zero reaction time may stabilize the model with finite reaction times and vice versa, (iii) distributed reaction times (every driver has a different reaction time) can stabilize the system compared to drivers with identical reaction times that are equal to the mean.

On spacing policies for highway vehicle automation

This paper develops a framework for the design and evaluation of spacing policies for adaptive cruise control. Spacing policies are evaluated from the point of view of string stability, traffic flow stability and traffic flow capacity. The standard constant time-gap spacing policy can guarantee string stability but is shown to suffer from poor traffic capacity and traffic flow instability. An "ideal" spacing policy is proposed that evolves naturally from the evaluation framework. The proposed spacing policy is a nonlinear function of speed. It provides string stability and traffic flow stability as well as a higher traffic flow capacity compared to the standard time-gap controller. An associated result proved in the paper is that traffic flow stability implies string stability for flow volumes up to a described maximum value.

A car-following model with stochastically considering the relative velocity in a traffic flow

In this paper, the car-following model with stochastically considering the relative velocity in a traffic flow is presented through investigating the vehicle a cceleration process with uncertainty. The stability criterion superior to the Ba ndo's model is derived by the linear stability analysis. The density wave is inv estigated analytically with the perturbation method. The results show that the o ccurrence of traffic jamming transitions can be described by the kink solution o f the modified Korteweg-de Vries equation. The effects of stochastic relative ve locity on the traffic flow are simulated and analyzed. It is shown that the chan ge rate of velocity in the new model is smaller than that of the Bando's model u nder the same condition and depends on the probability p. As the probability p i ncreases, a small initial disturbance does not magnify and influence on the traf fic flow, but fades away for a long time. The stable region in the new model is larger than in the Bando's model in the phase diagram. The existent initial hyst eresis in the new model will approach to a small region with the increase of tim e in the headway-velocity plot, which is exactly different from that in the Band o's model.In contrast,the hysteresis region in Bando's model will be continuousl y extended to cause traffic flow instability.