Single-vehicle data of highway traffic: a statistical analysis

The effect of an occlusion-induced delay on braking behavior in critical situations: A driving simulator study

OBJECTIVE

To share results of an experiment that used visual occlusion for a new purpose: inducing a waiting time.

BACKGROUND

Senders was a leading figure in human factors. In his research on the visual demands of driving, he used occlusion techniques.

METHODS

In a simulator experiment, we examined how drivers brake for different levels of urgency and different visual conditions. In three blocks (1 = brake lights, 2 = no brake lights, 3 = occlusion), drivers followed a vehicle at 13.4 or 33.4 m distance. At certain moments, the lead vehicle decelerated moderately (1.7 m/s2) or strongly (6.5 m/s2). In the occlusion condition, the screens blanked for 0.4 s (if 6.5 m/s2) or 2.0 s (if 1.7 m/s2) when the lead vehicle started to decelerate. Participants were instructed to brake only after the occlusion ended.

RESULTS

The lack of brake lights caused a delayed response. In the occlusion condition, drivers adapted to the instructed late braking by braking harder. However, adaptation was not always possible: In the most urgent condition, most participants collided with the lead vehicle because the ego-vehicle's deceleration limits were reached. In non-urgent conditions, some drivers braked unnecessarily hard. Furthermore, while waiting until the occlusion cleared, some drivers lightly touched the brake pedal.

CONCLUSION

This experimental design demonstrates how drivers (sometimes fail to) adjust their braking behavior to the criticality of the situation.

APPLICATION

The phenomena of biomechanical readiness and (inappropriate) dosing of the brake pedal may be relevant to safety, traffic flow, and ADAS design.

Autonomous Vehicles for Enhancing Expressway Capacity: A Dynamic Perspective

With rapidly developing communication and autonomous-driving technology, traffic flow on road networks will change from homogeneous human-driven vehicle (HDV) traffic flow to heterogeneous mixed traffic flow (MTF) comprising HDVs, autonomous vehicles (AVs), and connective-and-autonomous vehicles (CAVs). To understand the changes in the MTF of transportation engineering, we investigated the reserved capacity (RC) and right-of-way (ROW) reallocation policy that should be utilized under MTF scenarios. We established an MTF-based theoretical model to calculate the expressway segment capacity, theoretically analyzed the influence of the market penetration rate (MPR) on capacity and validated the model through numerical analysis. The results showed that the MPR of AVs and CAVs can enhance the MTF RC that is within 0–200% and that the platooning rate of CAVs positively influences the MTF RC. CAV popularization does not necessarily lead to a rapid increase in the transportation system efficiency when the MPR is <40% but significantly improves the efficiency of existing urban transportation facilities. When the MPR is >40%, the greatest enhancement is 4800 pcu/h/lane in terms of RC. A ROW reallocation policy that equips CAV-dedicated lanes according to the MPR of AVs and CAVs can enhance the capacity of expressway systems by 500 pcu/h/lane in terms of RC.

Investigation of Merge Assist Policies to Improve Safety of Drone Traffic in a Constrained Urban Airspace

Package delivery via autonomous drones is often presumed to hold commercial and societal value when applied to urban environments. However, to realise the benefits, the challenge of safely managing high traffic densities of drones in heavily constrained urban spaces needs to be addressed. This paper applies the principles of traffic segmentation and alignment to a constrained airspace in efforts to mitigate the probability of conflict. The study proposes an en-route airspace concept in which drone flights are directly guided along a one-way street network. This one-way airspace concept uses heading-altitude rules to vertically segment cruising traffic as well as transitioning flights with respect to their travel direction. However, transition flights trigger a substantial number of merging conflicts, thus negating a large part of the benefits gained from airspace structuring. In this paper, we aim to reduce the occurrence of merging conflicts and intrusions by using a delay-based and speed-based merge-assist strategy, both well-established methods from road traffic research. We apply these merge assistance strategies to the one-way airspace design and perform simulations for three traffic densities for the experiment area of Manhattan, New York. The results indicate, at most, a 9–16% decrease in total number of intrusions with the use of merge assistance. By investigating mesoscopic features of the urban street network, the data suggest that the relatively low efficacy of the merge strategies is mainly caused by insufficient space for safe manoeuvrability and the inability for the strategies to fully respond and thus resolve conflicts on short-distance streets.

Using empirical traffic trajectory data for crash risk evaluation under three-phase traffic theory framework

This study employed surrogate safety measures to evaluate the crash risks in different traffic phases and phase transitions according to the three-phase theory. The analysis was conducted from a microscopic perspective based on empirical vehicle trajectory data collected from the Interstate 80 in California, USA, and the Yingtian Expressway in Nanjing, China. Traffic phases were identified based on traffic flow variables and their correlations. Two advanced crash risk indexes from vehicle trajectories were conducted to evaluate the safety performance in each traffic state. The effects of various traffic flow variables (i.e. flow rate, density, average speed) on crash risks were explored based on speed-density plane, speed-flow plane and flow-density plane. Three regression models were developed to quantify the effects of traffic flow variables and traffic states on crash risks. The results show significant disparities of safety performance among different traffic states. Synchronized flow and wide moving jam are found to be the most dangerous phases. High density and low speed are associated with high crash risk. The best crash risk prediction performance is achieved when integrating both traffic phases and traffic parameters.

Dynamic behavior of elevators under random inflow of passengers

Elevators can be regarded as oscillators driven by the calls of passengers who arrive randomly. We study the dynamic behavior of elevators during the down peak period numerically and analytically. We assume that new passengers arrive at each floor according to a Poisson process and call the elevators to go down to the ground floor. We numerically examine how the round-trip time of a single elevator depends on the inflow rate of passengers at each floor and reproduce it by a self-consistent equation considering the combination of floors where the call occurs. By setting an order parameter, we show that the synchronization of two elevators occurs irrespective of final destination (whether the elevators did or did not go to the top floor). It indicates that the spontaneous ordering of elevators emerges from the Poisson noise. We also reproduce the round-trip time of two elevators by a self-consistent equation considering the interaction through the existence of passengers and the absence of volume exclusion. Those results suggest that such interaction stabilizes and characterizes the spontaneous ordering of elevators.

Further We Travel the Faster We Go

The average travelling speed increases in a nontrivial manner with the travel distance. This leads to scaling-like relations on quite extended spatial scales, for all mobility modes taken together and also for a given mobility mode in part. We offer a wide range of experimental results, investigating and quantifying this universal effect and its measurable causes. The increasing travelling speed with the travel distance arises from the combined effects of: choosing the most appropriate travelling mode; the structure of the travel networks; the travel times lost in the main hubs, starting or target cities; and the speed limit of roads and vehicles.

Hopf bifurcation analysis for a dissipative system with asymmetric interaction: Analytical explanation of a specific property of highway traffic

A dissipative system with asymmetric interaction, the optimal velocity model, shows a Hopf bifurcation concerned with the transition from a homogeneous motion to the formation of a moving cluster, such as the emergence of a traffic jam. We investigate the properties of Hopf bifurcation depending on the particle density, using the dynamical system for the traveling cluster solution of the continuum system derived from the original discrete system of particles. The Hopf bifurcation is revealed as a subcritical one, and the property explains well the specific phenomena in highway traffic: the metastability of jamming transition and the hysteresis effect in the relation of car density and flow rate.

Safety performance of traffic phases and phase transitions in three phase traffic theory

Crash risk prediction models were developed to link safety to various phases and phase transitions defined by the three phase traffic theory. Results of the Bayesian conditional logit analysis showed that different traffic states differed distinctly with respect to safety performance. The random-parameter logit approach was utilized to account for the heterogeneity caused by unobserved factors. The Bayesian inference approach based on the Markov Chain Monte Carlo (MCMC) method was used for the estimation of the random-parameter logit model. The proposed approach increased the prediction performance of the crash risk models as compared with the conventional logit model. The three phase traffic theory can help us better understand the mechanism of crash occurrences in various traffic states. The contributing factors to crash likelihood can be well explained by the mechanism of phase transitions. We further discovered that the free flow state can be divided into two sub-phases on the basis of safety performance, including a true free flow state in which the interactions between vehicles are minor, and a platooned traffic state in which bunched vehicles travel in successions. The results of this study suggest that a safety perspective can be added to the three phase traffic theory. The results also suggest that the heterogeneity between different traffic states should be considered when estimating the risks of crash occurrences on freeways.

Multifractal nature of particulate matters (PMs) in Hong Kong urban air

In this study, we investigate the persistent variation and the multifractal nature of particulate matter (PM) concentrations from vehicle emissions at a typical traffic intersection of street canyon in Hong Kong. Six size groups of PMs are measured and collected during rush hour sessions on different dates respectively. A recently developed model, namely multifractal detrended fluctuation analysis (MF-DFA), is employed to decompose and analyze the collected database. Through estimating the scaling exponent, it is found that the PM levels from vehicular emissions display long-term correlation characters. By employing MF-DFA method to calculate the generalized Hurst exponent and discuss the multifractal spectrums of all size groups, it is noticed that the fine particulate matters in grain diameter of 0.3-0.499 μm present strong multifractal nature, intensive oscillations of concentration variations, and long-term persistence. For fine particulate matters in the grain diameter ranges from 0.5 μm to 4.99 μm, their similar and weak multifractal natures reflect the self-similarity behaviors among these groups and the gradual decreases of the lasting effects. For large size particulate matters, i.e., grain diameter above 5 μm, certain mono-fractal nature and sharp decay of long-term persistence are obtained, even for intermittent effects. It can therefore be concluded that the fine particulate matter diffuses anomaly and persists for a long time.

Experimental study of short-range interactions in vehicular traffic

Single vehicle data obtained from magnetic loops on an expressway allowed us to measure velocity correlations and velocity differences between non-neighbor vehicles on the same lane, showing some strong correlations even for platoons of 7 or 8 vehicles. The corresponding time headway distribution for non-neighbor vehicles is also presented. We were also able to get some informations about interlane structures, through crossed time headway distributions. It should be noticed that these last results on crossed time headways are meaningful only because the subset of data we used corresponds to a unique stationary traffic state and still contains a large amount of data, with a large fraction of short time headways. The link with passing maneuvers is discussed.

Long-range correlations of density fluctuations in the Kerner-Klenov-Wolf cellular automata three-phase traffic flow model

Detrended fluctuation analysis (DFA) is a useful tool to measure the long-range power-law correlations in 1f noise. In this paper, we investigate the power-law dynamics behavior of the density fluctuation time series generated by the famous Kerner-Klenov-Wolf cellular automata model in road traffic. Then the complexities of spatiotemporal, average speed, and the average density have been analyzed in detail. By introducing the DFA method, our main observation is that the free flow and wide moving jam phases correspond to the long-range anticorrelations. On the contrary, at the synchronized flow phase, the long-range correlated property is observed.

Gradient mechanism in a communication network

We study the efficiency of the gradient mechanism of message transfer in a two-dimensional communication network of regular nodes and randomly distributed hubs. Each hub on the network is assigned some randomly chosen capacity and hubs with lower capacities are connected to the hubs with maximum capacity. The average travel times of single messages traveling on the lattice decrease rapidly as the number of hubs increase. The functional dependence of the average travel times on the hub density shows q-exponential behavior with a power-law tail. We also study the relaxation behavior of the network when a large number of messages are created simultaneously at random locations and travel on the network toward their designated destinations. For this situation, in the absence of the gradient mechanism, the network can show congestion effects due to the formation of transport traps. We show that if hubs of high betweenness centrality are connected by the gradient mechanism, efficient decongestion can be achieved. The gradient mechanism is less prone to the formation of traps than other decongestion schemes. We also study the spatial configurations of transport traps and propose minimal strategies for their elimination.

Modeling highway-traffic headway distributions using superstatistics

We study traffic clearance distributions (i.e., the instantaneous gap between successive vehicles) and time-headway distributions by applying the Beck and Cohen superstatistics. We model the transition from free phase to congested phase with the increase of vehicle density as a transition from the Poisson statistics to that of the random-matrix theory. We derive an analytic expression for the spacing distributions that interpolates from the Poisson distribution and Wigner's surmise and apply it to the distributions of the net distance and time gaps among the succeeding cars at different densities of traffic flow. The obtained distribution fits the experimental results for single-vehicle data of the Dutch freeway A9 and the German freeway A5.

Cellular-automaton model with velocity adaptation in the framework of Kerner's three-phase traffic theory

In this paper, we propose a cellular automata (CA) model for traffic flow in the framework of Kerner's three-phase traffic theory. We mainly consider the velocity-difference effect on the randomization of vehicles. The presented model is equivalent to a combination of two CA models, i.e., the Kerner-Klenov-Wolf (KKW) CA model and the Nagel-Schreckenberg (NS) CA model with slow-to-start effect. With a given probability, vehicle dynamical rules are changed over time randomly between the rules of the NS model and the rules of the KKW model. Due to the rules of the KKW model, the speed adaptation effect of three-phase traffic theory is automatically taken into account and our model can show synchronized flow. Due to the rules of the NS model, our model can show wide moving jams. The effect of "switching" from the rules of the KKW model to the rules of the NS model provides equivalent effects to the "acceleration noise" in the KKW model. Numerical simulations are performed for both periodic and open boundaries conditions. The results are consistent with the well-known results of the three-phase traffic theory published before.

Understanding widely scattered traffic flows, the capacity drop, and platoons as effects of variance-driven time gaps

We investigate the adaptation of the time headways in car-following models as a function of the local velocity variance, which is a measure of the inhomogeneity of traffic flow. We apply this mechanism to several car-following models and simulate traffic breakdowns in open systems with an on-ramp as bottleneck and in a closed ring road. Single-vehicle data and one-minute aggregated data generated by several virtual detectors show a semiquantitative agreement with microscopic and flow-density data from the Dutch freeway A9. This includes the observed distributions of the net time headways for free and congested traffic, the velocity variance as a function of density, and the fundamental diagram. The modal value of the time headway distribution is shifted by a factor of about 2 under congested conditions. Macroscopically, this corresponds to the capacity drop at the transition from free to congested traffic. The simulated fundamental diagram shows free, synchronized, and jammed traffic, and a wide scattering in the congested traffic regime. We explain this by a self-organized variance-driven process that leads to the spontaneous formation and decay of long-lived platoons even for a deterministic dynamics on a single lane.

Microscopic features of moving traffic jams

Empirical and numerical microscopic features of moving traffic jams are presented. Based on a single vehicle data analysis, it is found that within wide moving jams, i.e., between the upstream and downstream jam fronts there is a complex microscopic spatiotemporal structure. This jam structure consists of alternations of regions in which traffic flow is interrupted and flow states of low speeds associated with "moving blanks" within the jam. Moving blanks within a wide moving jam resemble electron holes in the valence band of semiconductors: As the moving blanks that propagate upstream appear due to downstream vehicle motion within the jam, so appearance of electron holes moving with the electric field results from electron motion against the electric field in the valence band of semiconductors. Empirical features of moving blanks are found. Based on microscopic models in the context of the Kerner's three-phase traffic theory, physical reasons for moving blanks emergence within wide moving jams are disclosed. Microscopic nonlinear effects of moving jam emergence, propagation, and dissolution as well as a diverse variety of hysteresis effects in freeway traffic associated with phase transitions and congested traffic propagation are numerically investigated. Microscopic structure of moving jam fronts is numerically studied and compared with empirical results.

Empirical test for cellular automaton models of traffic flow

Based on a detailed microscopic test scenario motivated by recent empirical studies of single-vehicle data, several cellular automaton models for traffic flow are compared. We find three levels of agreement with the empirical data: (1) models that do not reproduce even qualitatively the most important empirical observations, (2) models that are on a macroscopic level in reasonable agreement with the empirics, and (3) models that reproduce the empirical data on a microscopic level as well. Our results are not only relevant for applications, but also shed light on the relevant interactions in traffic flow.

Steady-state solutions of hydrodynamic traffic models

We investigate steady-state solutions of hydrodynamic traffic models in the absence of any intrinsic inhomogeneity on roads such as on-ramps. It is shown that typical hydrodynamic models possess seven different types of inhomogeneous steady-state solutions. The seven solutions include those that have been reported previously only for microscopic models. The characteristic properties of wide jam such as moving velocity of its spatiotemporal pattern and/or out-flux from wide jam are shown to be uniquely determined and thus independent of initial conditions of dynamic evolution. Topological considerations suggest that all of the solutions should be common to a wide class of traffic models. The results are discussed in connection with the universality conjecture for traffic models. Also the prevalence of the limit-cycle solution in a recent study of a microscopic model is explained in this approach.

Interpreting the wide scattering of synchronized traffic data by time gap statistics

Based on the statistical evaluation of experimental single-vehicle data, we propose a quantitative interpretation of the erratic scattering of flow-density data in synchronized traffic flows. A correlation analysis suggests that the dynamical flow-density data are well compatible with the so-called jam line characterizing fully developed traffic jams, if one takes into account the variation of their propagation speed due to the large variation of the netto time gaps (the inhomogeneity of traffic flow). The form of the time gap distribution depends not only on the density, but also on the measurement cross section: The most probable netto time gap in congested traffic flow upstream of a bottleneck is significantly increased compared to uncongested freeway sections. Moreover, we identify different power-law scaling laws for the relative variance of netto time gaps as a function of the sampling size. While the exponent is -1 in free traffic corresponding to statistically independent time gaps, the exponent is about -2/3 in congested traffic flow because of correlations between queued vehicles.

Cellular automata model simulating complex spatiotemporal structure of wide jams

According to the empirical observation of highway traffic, inside wide moving jams there is a complex spatiotemporal structure: jam is not compact and relatively large values of the time and the distance headway are visible. We present a cellular automata model by introducing "jam headway" and "jammed status" to simulate that complex structure. Using computer simulations, the fundamental diagram, the space-time plots, the time series of the density in the jams, and the 1-min average data of this model are analyzed. It is shown that compared to other existing models, this model can display the experimental characteristics of the wide moving jams.

Open boundaries in a cellular automaton model for traffic flow with metastable states

The effects of open boundaries in the velocity-dependent randomization (VDR) model, a modified version of the well-known Nagel-Schreckenberg (NaSch) cellular automaton model for traffic flow, are investigated. In contrast to the NaSch model, the VDR model exhibits metastable states and phase separation in a certain density regime. A proper insertion strategy allows us to investigate the whole spectrum of possible system states and the structure of the phase diagram by Monte Carlo simulations. We observe an interesting microscopic structure of the jammed phases, which is different from the one of the NaSch model. For finite systems, the existence of high flow states in a certain parameter regime leads to a special structure of the fundamental diagram measured in the open system. Apart from that, the results are in agreement with an extremal principle for the flow, which has been introduced for models with a unique flow-density relation. Finally, we discuss the application of our findings for a systematic flow optimization. Here some surprising results are obtained, e.g., a restriction of the inflow can lead to an improvement of the total flow through a bottleneck.

Long-lived states in synchronized traffic flow: empirical prompt and dynamical trap model

The present paper proposes an interpretation of the widely scattered states (called synchronized traffic) stimulated by Kerner's hypothesis about the existence of a multitude of metastable states in the fundamental diagram. Using single-vehicle data collected at the German highway A1, temporal velocity patterns have been analyzed to show a collection of certain fragments with approximately constant velocities and sharp jumps between them. The particular velocity values in these fragments vary in a wide range. In contrast, the flow rate is more or less constant because its fluctuations are mainly due to the discreteness of traffic flow. Subsequently, we develop a model for synchronized traffic that can explain these characteristics. Following previous work [I. A. Lubashevsky and R. Mahnke, Phys. Rev. E 62, 6082 (2000)] the vehicle flow is specified by car density, mean velocity, and additional order parameters h and a that are due to the many-particle effects of the vehicle interaction. The parameter h describes the multilane correlations in the vehicle motion. Together with the car density it determines directly the mean velocity. The parameter a, in contrast, controls the evolution of h only. The model assumes that a fluctuates randomly around the value corresponding to the car configuration optimal for lane changing. When it deviates from this value the lane change is depressed for all cars forming a local cluster. Since exactly the overtaking maneuvers of these cars cause the order parameter a to vary, the evolution of the car arrangement becomes frozen for a certain time. In other words, the evolution equations form certain dynamical traps responsible for the long-time correlations in the synchronized mode.

Probabilistic description of traffic breakdowns

We analyze the characteristic features of traffic breakdown. To describe this phenomenon we apply the probabilistic model regarding the jam emergence as the formation of a large car cluster on a highway. In these terms, the breakdown occurs through the formation of a certain critical nucleus in the metastable vehicle flow, which enables us to confine ourselves to one cluster model. We assume that, first, the growth of the car cluster is governed by attachment of cars to the cluster whose rate is mainly determined by the mean headway distance between the car in the vehicle flow and, maybe, also by the headway distance in the cluster. Second, the cluster dissolution is determined by the car escape from the cluster whose rate depends on the cluster size directly. The latter is justified using the available experimental data for the correlation properties of the synchronized mode. We write the appropriate master equation converted then into the Fokker-Planck equation for the cluster distribution function and analyze the formation of the critical car cluster due to the climb over a certain potential barrier. The further cluster growth irreversibly causes jam formation. Numerical estimates of the obtained characteristics and the experimental data of the traffic breakdown are compared. In particular, we draw a conclusion that the characteristic intrinsic time scale of the breakdown phenomenon should be about 1 min and explain the case why the traffic volume interval inside which traffic breakdown is observed is sufficiently wide.

Optimization of congested traffic by controlling stop-and-go waves

We propose a new optimization strategy based on inducing stop-and-go waves on the main road and controlling their wavelength. Using numerical simulations of a recent stochastic car-following model we show that this strategy yields optimization of traffic flow when implemented in systems with a localized periodic inhomogeneity, such as signalized intersections and entry ramps. The optimization process is explained by our finding of a generalized fundamental diagram (GFD) for traffic, namely a flux-density-wavelength relation. Projecting the GFD on the density-flux plane yields a two-dimensional region of stable states, qualitatively similar to that found empirically [Kerner, Phys. Rev. Lett. 81, 3797 (1998)] in synchronized traffic.

Single-vehicle data of highway traffic: microscopic description of traffic phases

We present a detailed analysis of single-vehicle data, which sheds some light on the microscopic interaction of the vehicles. Besides the analysis of free flow and synchronized traffic the data sets especially provide information about wide jams that persist for a long time. The data have been collected at a location far away from ramps and in the absence of speed limits, which allows a comparison with idealized traffic simulations. We also resolve some open questions concerning the time-headway distribution.

Empirical macroscopic features of spatial-temporal traffic patterns at highway bottlenecks

Results of an empirical study of congested patterns measured during 1995-2001 at German highways are presented. Based on this study, various types of congested patterns at on and off ramps have been identified, their macroscopic spatial-temporal features have been derived, and an evolution of those patterns and transformations between different types of the patterns over time has been found out. It has been found that at an isolated bottleneck (a bottleneck that is far enough from other effective bottlenecks) either the general pattern (GP) or the synchronized flow pattern (SP) can be formed. In GP, synchronized flow occurs and wide moving jams spontaneously emerge in that synchronized flow. In SP, no wide moving jams emerge, i.e., SP consists of synchronized flow only. An evolution of GP into SP when the flow rate to the on ramp decreases has been found and investigated. Spatial-temporal features of complex patterns that occur if two or more effective bottlenecks exist on a highway have been found out. In particular, the expanded pattern where synchronized flow covers two or more effective bottlenecks can be formed. It has been found that the spatial-temporal structure of congested patterns possesses predictable, i.e., characteristic, unique, and reproducible features, for example, the most probable types of patterns that are formed at a given bottleneck. According to the empirical investigations the cases of the weak and the strong congestion should be distinguished. In contrast to the weak congestion, the strong congestion possesses the following characteristic features: (i) the flow rate in synchronized flow is self-maintaining near a limit flow rate; (ii) the mean width of the region of synchronized flow in GP does not depend on traffic demand; (iii) there is a correlation between the parameters of synchronized flow and wide moving jams: the higher the flow rate out from a wide moving jam is, the higher is the limit flow rate in the synchronized flow. The strong congestion often occurs in GP whereas the weak congestion is usual for SP. The weak congestion is often observed at off ramps whereas the strong congestion much more often occurs at on ramps. Under the weak congestion diverse transformations between different congested patterns can occur.

Human behavior as origin of traffic phases

It is shown that the desire for smooth and comfortable driving is directly responsible for the occurrence of synchronized traffic in highway traffic. This desire goes beyond the avoidance of accidents, which so far has been the main focus of microscopic modeling and that is mainly responsible for the other two phases observed empirically, free flow and wide moving jams. These features have been incorporated into a microscopic model based on stochastic cellular automata by means of event-driven anticipation. The results of computer simulations are compared with empirical data. It turns out that anticipation effects are responsible for the stabilization of the traffic phases and even reproduce the empirically observed coexistence of wide moving jams with both free flow and synchronized traffic.

Headways in traffic flow: remarks from a physical perspective

Traffic flow can be understood as a realization of a broad class of one dimensional physical systems, where a hard core repulsive interaction competes with a longer ranged attraction between the particles. It can be shown rigorously that the statistical properties of such systems in thermal equilibrium are well described by a family of distributions that stems from the random matrix theory. Analyzing the traffic data from different sources, we show that traffic on real roads belongs to that class of random matrix distributions. Also, various traffic simulation models show a similar behavior. It is demonstrated in such a way that the headway distribution of a highway traffic, that serves usually as a paradigm of systems driven far from equilibrium, is reasonably well described by a distribution originating from equilibrium statistical physics.

Macroscopic traffic models from microscopic car-following models

We present a method to derive macroscopic fluid-dynamic models from microscopic car-following models via a coarse-graining procedure. The method is first demonstrated for the optimal velocity model. The derived macroscopic model consists of a conservation equation and a momentum equation, and the latter contains a relaxation term, an anticipation term, and a diffusion term. Properties of the resulting macroscopic model are compared with those of the optimal velocity model through numerical simulations, and reasonable agreement is found although there are deviations in the quantitative level. The derivation is also extended to general car-following models.

Noise-assisted traffic of spikes through neuronal junctions

The presence of noise, i.e., random fluctuations, in the nervous system raises at least two different questions. First, is there a constructive role noise can play for signal transmission in a neuron channel? Second, what is the advantage of the power spectra observed for the neuron activity to be shaped like 1/f(k)? To address these questions a simple stochastic model for a junction in neural spike traffic channels is presented. Side channel traffic enters main channel traffic depending on the spike rate of the latter one. The main channel traffic itself is triggered by various noise processes such as Poissonian noise or the zero crossings of Gaussian 1/f(k) noise whereas the variation of the exponent k gives rise to a maximum of the overall traffic efficiency. It is shown that the colored noise is superior to the Poissonian and, in certain cases, to deterministic, periodically ordered traffic. Further, if this periodicity itself is modulated by Gaussian noise with different spectral exponents k, then such modulation can lead to noise-assisted traffic as well. The model presented can also be used to consider car traffic at a junction between a main and a side road and to show how randomness can enhance the traffic efficiency in a network. (c) 2001 American Institute of Physics.

Order-parameter model for unstable multilane traffic flow

We discuss a phenomenological approach to the description of unstable vehicle motion on multilane highways that explains in a simple way the observed sequence of the "free flow <--> synchronized mode <--> jam" phase transitions as well as the hysteresis in these transitions. We introduce a variable called an order parameter that accounts for possible correlations in the vehicle motion at different lanes. So, it is principally due to the "many-body" effects in the car interaction in contrast to such variables as the mean car density and velocity being actually the zeroth and first moments of the "one-particle" distribution function. Therefore, we regard the order parameter as an additional independent state variable of traffic flow. We assume that these correlations are due to a small group of "fast" drivers and by taking into account the general properties of the driver behavior we formulate a governing equation for the order parameter. In this context we analyze the instability of homogeneous traffic flow that manifested itself in the above-mentioned phase transitions and gave rise to the hysteresis in both of them. Besides, the jam is characterized by the vehicle flows at different lanes which are independent of one another. We specify a certain simplified model in order to study the general features of the car cluster self-formation under the "free flow <--> synchronized motion" phase transition. In particular, we show that the main local parameters of the developed cluster are determined by the state characteristics of vehicle motion only.

Phase diagram of congested traffic flow: An empirical study

We analyze traffic data from a highway section containing one effective on-ramp. Based on two criteria, local velocity variation patterns and expansion (or nonexpansion) of congested regions, three distinct congested traffic states are identified. These states appear at different levels of the upstream flux and the on-ramp flux, thereby generating a phase digram of the congested traffic flow. Observed traffic states are compared with recent theoretical analyses and both agreeing and disagreeing features are found.

Asymmetric exclusion process with next-nearest-neighbor interaction: some comments on traffic flow and a nonequilibrium reentrance transition

We study the steady-state behavior of a driven nonequilibrium lattice gas of hard-core particles with next-nearest-neighbor interaction. We calculate the exact stationary distribution of the periodic system and for a particular line in the phase diagram of the system with open boundaries where particles can enter and leave the system. For repulsive interactions the dynamics can be interpreted as a two-speed model for traffic flow. The exact stationary distribution of the periodic continuous-time system turns out to coincide with that of the asymmetric exclusion process (ASEP) with discrete-time parallel update. However, unlike in the (single-speed) ASEP, the exact flow diagram for the two-speed model resembles in some important features the flow diagram of real traffic. The stationary phase diagram of the open system obtained from Monte Carlo simulations can be understood in terms of a shock moving through the system and an overfeeding effect at the boundaries, thus confirming theoretical predictions of a recently developed general theory of boundary-induced phase transitions. In the case of attractive interaction we observe an unexpected reentrance transition due to boundary effects.

Synchronized traffic flow from a modified lighthill-whitman model

A simple macroscopic argument leading to a diffusively corrected form of the classical kinematic-wave (Lighthill-Whitham) model of the flow of vehicular traffic is described. An example of a diffusively corrected kinematic-wave model displays a diffusion coefficient that is negative, for sufficiently large densities. It is shown that such a diffusively corrected kinematic-wave model is capable of reproducing elements of the synchronized flow reported by Kerner and Rehborn.