arXiv subjects

Martin Treiber

Publications and source records attributed to Martin Treiber.

At least 55 records · Page 3Linked to original sources

arXiv2009

Enhanced Intelligent Driver Model to Access the Impact of Driving Strategies on Traffic Capacity

With an increasing number of vehicles equipped with adaptive cruise control (ACC), the impact of such vehicles on the collective dynamics of traffic flow becomes relevant. By means of simulation, we investigate the influence of variable percentages of ACC vehicles on traffic flow characteristics. For simulating the ACC vehicles, we propose a new car-following model that also serves as basis of an ACC implementation in real cars. The model is based on the Intelligent Driver Model [Treiber et al., Physical Review E 62, 1805 (2000)] and inherits its intuitive behavioural parameters: desired velocity, acceleration, comfortable deceleration, and desired minimum time headway. It eliminates, however, the sometimes unrealistic behaviour of the Intelligent Driver Model in cut-in situations with ensuing small gaps that regularly are caused by lane changes of other vehicles in dense or congested traffic. We simulate the influence of different ACC strategies on the maximum capacity before breakdown, and the (dynamic) bottleneck capacity after breakdown. With a suitable strategy, we find sensitivities of the order of 0.3, i.e., 1% more ACC vehicles will lead to an increase of the capacities by about 0.3%. This sensitivity multiplies when considering travel times at actual breakdowns.

physics.soc-ph↗

arXiv2009

Reconstructing the Traffic State by Fusion of Heterogeneous Data

We present an advanced interpolation method for estimating smooth spatiotemporal profiles for local highway traffic variables such as flow, speed and density. The method is based on stationary detector data as typically collected by traffic control centres, and may be augmented by floating car data or other traffic information. The resulting profiles display transitions between free and congested traffic in great detail, as well as fine structures such as stop-and-go waves. We establish the accuracy and robustness of the method and demonstrate three potential applications: 1. compensation for gaps in data caused by detector failure; 2. separation of noise from dynamic traffic information; and 3. the fusion of floating car data with stationary detector data.

physics.data-an↗

arXiv2009

Theoretical vs. Empirical Classification and Prediction of Congested Traffic States

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.

physics.soc-ph↗

arXiv2008

Approximate Hamiltonian Statistics in One-dimensional Driven Dissipative Many-Particle Systems

This contribution presents a derivation of the steady-state distribution of velocities and distances of driven particles on a onedimensional periodic ring. We will compare two different situations: (i) symmetrical interaction forces fulfilling Newton's law of "actio = reactio" and (ii) asymmetric, forwardly directed interactions as, for example in vehicular traffic. Surprisingly, the steady-state velocity and distance distributions for asymmetric interactions and driving terms agree with the equilibrium distributions of classical many-particle systems with symmetrical interactions, if the system is large enough. This analytical result is confirmed by computer simulations and establishes the possibility of approximating the steady state statistics in driven many-particle systems by Hamiltonian systems. Our finding is also useful to understand the various departure time distributions of queueing systems as a possible effect of interactions among the elements in the respective queue [D. Helbing et al., Physica A 363, 62 (2006)].

physics.data-an↗

arXiv2008

Agents for Traffic Simulation

Vehicular traffic is a classical example of a multi-agent system in which autonomous drivers operate in a shared environment. The article provides an overview of the state-of-the-art in microscopic traffic modeling and the implications for simulation techniques. We focus on the short-time dynamics of car-following models which describe continuous feedback control tasks (acceleration and braking) and models for discrete-choice tasks as a response to the surrounding traffic. The driving style of an agent is characterized by model parameters such as reaction time, desired speed, desired time gap, anticipation etc. In addition, internal state variables corresponding to the agent's "mind" are used to incorporate the driving experiences. We introduce a time-dependency of some parameters to describe the frustration of drivers being in a traffic jam for a while. Furthermore, the driver's behavior is externally influenced by the neighboring vehicles and also by environmental input such as limited motorization and braking power, visibility conditions and road traffic regulations. A general approach for dealing with discrete decision problems in the context of vehicular traffic is introduced and applied to mandatory and discretionary lane changes. Furthermore, we consider the decision process whether to brake or not when approaching a traffic light turning from green to amber. Another aspect of vehicular traffic is related to the heterogeneity of drivers. We discuss a hybrid system of coupled vehicle and information flow which can be used for developing and testing applications of upcoming inter-vehicle communication techniques.

physics.soc-ph↗

arXiv2008

Estimating Acceleration and Lane-Changing Dynamics Based on NGSIM Trajectory Data

The NGSIM trajectory data sets provide longitudinal and lateral positional information for all vehicles in certain spatiotemporal regions. Velocity and acceleration information cannot be extracted directly since the noise in the NGSIM positional information is greatly increased by the necessary numerical differentiations. We propose a smoothing algorithm for positions, velocities and accelerations that can also be applied near the boundaries. The smoothing time interval is estimated based on velocity time series and the variance of the processed acceleration time series. The velocity information obtained in this way is then applied to calculate the density function of the two-dimensional distribution of velocity and inverse distance, and the density of the distribution corresponding to the ``microscopic'' fundamental diagram. Furthermore, it is used to calculate the distributions of time gaps and times-to-collision, conditioned to several ranges of velocities and velocity differences. By simulating virtual stationary detectors we show that the probability for critical values of the times-to-collision is greatly underestimated when estimated from single-vehicle data of stationary detectors. Finally, we investigate the lane-changing process and formulate a quantitative criterion for the duration of lane changes that is based on the trajectory density in normalized coordinates. Remarkably, there is a very noisy but significant velocity advantage in favor of the targeted lane that decreases immediately before the change due to anticipatory accelerations.

physics.soc-ph↗

arXiv2008

Calibrating Car-Following Models using Trajectory Data: Methodological Study

The car-following behavior of individual drivers in real city traffic is studied on the basis of (publicly available) trajectory datasets recorded by a vehicle equipped with an radar sensor. By means of a nonlinear optimization procedure based on a genetic algorithm, we calibrate the Intelligent Driver Model and the Velocity Difference Model by minimizing the deviations between the observed driving dynamics and the simulated trajectory when following the same leading vehicle. The reliability and robustness of the nonlinear fits are assessed by applying different optimization criteria, i.e., different measures for the deviations between two trajectories. The obtained errors are in the range between~11% and~29% which is consistent with typical error ranges obtained in previous studies. In addition, we found that the calibrated parameter values of the Velocity Difference Model strongly depend on the optimization criterion, while the Intelligent Driver Model is more robust in this respect. By applying an explicit delay to the model input, we investigated the influence of a reaction time. Remarkably, we found a negligible influence of the reaction time indicating that drivers compensate for their reaction time by anticipation. Furthermore, the parameter sets calibrated to a certain trajectory are applied to the other trajectories allowing for model validation. The results indicate that ``intra-driver variability'' rather than ``inter-driver variability'' accounts for a large part of the calibration errors. The results are used to suggest some criteria towards a benchmarking of car-following models.

physics.soc-ph↗

arXiv2006

Autonomous detection and anticipation of jam fronts from messages propagated by inter-vehicle communication

In this paper, a minimalist, completely distributed freeway traffic information system is introduced. It involves an autonomous, vehicle-based jam front detection, the information transmission via inter-vehicle communication, and the forecast of the spatial position of jam fronts by reconstructing the spatiotemporal traffic situation based on the transmitted information. The whole system is simulated with an integrated traffic simulator, that is based on a realistic microscopic traffic model for longitudinal movements and lane changes. The function of its communication module has been explicitly validated by comparing the simulation results with analytical calculations. By means of simulations, we show that the algorithms for a congestion-front recognition, message transmission, and processing predict reliably the existence and position of jam fronts for vehicle equipment rates as low as 3%. A reliable mode of operation already for small market penetrations is crucial for the successful introduction of inter-vehicle communication. The short-term prediction of jam fronts is not only useful for the driver, but is essential for enhancing road safety and road capacity by intelligent adaptive cruise control systems.

physics.data-an↗

arXiv2006

Jam-avoiding adaptive cruise control (ACC) and its impact on traffic dynamics

Adaptive-Cruise Control (ACC) automatically accelerates or decelerates a vehicle to maintain a selected time gap, to reach a desired velocity, or to prevent a rear-end collision. To this end, the ACC sensors detect and track the vehicle ahead for measuring the actual distance and speed difference. Together with the own velocity, these input variables are exactly the same as in car-following models. The focus of this contribution is: What will be the impact of a spreading of ACC systems on the traffic dynamics? Do automated driving strategies have the potential to improve the capacity and stability of traffic flow or will they necessarily increase the heterogeneity and instability? How does the result depend on the ACC equipment level? We discuss microscopic modeling aspects for human and automated (ACC) driving. By means of microscopic traffic simulations, we study how a variable percentage of ACC-equipped vehicles influences the stability of traffic flow, the maximum flow under free traffic conditions until traffic breaks down, and the dynamic capacity of congested traffic. Furthermore, we compare different percentages of ACC with respect to travel times in a specific congestion scenario. Remarkably, we find that already a small amount of ACC equipped cars and, hence, a marginally increased free and dynamic capacity, leads to a drastic reduction of traffic congestion.

physics.soc-ph↗

arXiv2005

Understanding widely scattered traffic flows, the capacity drop, platoons, and times-to-collision 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. Single-vehicle data generated by several 'virtual detectors' show a semi-quantitative agreement with microscopic data from the Dutch freeway A9. This includes the observed distributions of the net time headways and times-to-collision for free and congested traffic. While the times-to-collision show a nearly universal distribution in free and congested traffic, the modal value of the time headway distribution is shifted by a factor of about two in congested conditions. Macroscopically, this corresponds to the 'capacity drop' at the transition from free to congested traffic. Finally, we explain the wide scattering of one-minute flow-density data by a self-organized variance-driven process that leads to the spontaneous formation and decay of long-lived platoons even for deterministic dynamics on a single lane.

physics.soc-ph↗

arXiv2005

Analytical investigation of oscillations in intersecting flows of pedestrian and vehicle traffic

In two intersecting many-particle streams, one can often find the emergence of oscillatory patterns. Here, we investigate the interaction of pedestrians with vehicles, when they try to cross a road. A numerical study of this coupled pedestrian-vehicle delay problem has been presented in a previous paper. Here, we focus on the analytical treatment of the problem, which requires to use a simplified car-following model. Our analytical results for the phase transition to oscillatory pedestrian and traffic flows and the average waiting times are well supported by numerical evaluations and give a detailed picture of the collective dynamics emerging when pedestrians try to cross a road. The mathematical expressions allow one to identify the dependence on model parameters such as the vehicle or pedestrian arrival rate, and the safety factor of pedestrian gap acceptance. We also calculate a formula for the vehicle time gap distribution, which corresponds to the departure time distribution of a M/D/1 queue.

physics.soc-ph↗

arXiv2005

Analytical Investigation of Innovation Dynamics Considering Stochasticity in the Evaluation of Fitness

We investigate a selection-mutation model for the dynamics of technological innovation,a special case of reaction-diffusion equations. Although mutations are assumed to increase the variety of technologies, not their average success ("fitness"), they are an essential prerequisite for innovation. Together with a selection of above-average technologies due to imitation behavior, they are the "driving force" for the continuous increase in fitness. We will give analytical solutions for the probability distribution of technologies for special cases and in the limit of large times. The selection dynamics is modelled by a "proportional imitation" of better technologies. However, the assessment of a technology's fitness may be imperfect and, therefore, vary stochastically. We will derive conditions, under which wrong assessment of fitness can accelerate the innovation dynamics, as it has been found in some surprising numerical investigations.

cond-mat.stat-mech↗

arXiv2005

Delays, Inaccuracies and Anticipation in Microscopic Traffic Models

We generalize a wide class of time-continuous microscopic traffic models to include essential aspects of driver behaviour not captured by these models. Specifically, we consider (i) finite reaction times, (ii) estimation errors, (iii) looking several vehicles ahead (spatial anticipation), and (iv) temporal anticipation. The estimation errors are modelled as stochastic Wiener processes and lead to time-correlated fluctuations of the acceleration. We show that the destabilizing effects of reaction times and estimation errors can essentially be compensated for by spatial and temporal anticipation, that is, the combination of stabilizing and destabilizing effects results in the same qualitative macroscopic dynamics as that of the respectively underlying simple car-following model. In many cases, this justifies the use of simplified, physics-oriented models with a few parameters only. Although the qualitative dynamics is unchanged, multi-anticipation increase both spatial and temporal scales of stop-and-go waves and other complex patterns of congested traffic in agreement with real traffic data. Remarkably, the anticipation allows accident-free smooth driving in complex traffic situations even if reaction times exceed typical time headways.

cond-mat.soft↗

arXiv2004

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.

cond-mat.stat-mech↗

arXiv2003

Fokker-Planck equation approach to vehicle statistics

This contribution presents a derivation of the steady-state distribution of velocities and distances of vehicles in freeway traffic which has been suggested for the evaluation of interaction potentials among vehicles (see preprint cond-mat/0301484). Despite the forwardly directed interactions and the additional driving terms in vehicle traffic, the steady-state velocity and distance distributions agree with the equilibrium distributions of classical many-particle systems with symmetrical interactions, if the system is large enough. Finally, this analytical result is confirmed by computer simulations.

cond-mat.stat-mech↗

arXiv2003

Memory effects in microscopic traffic models and wide scattering in flow-density data

By means of microscopic simulations we show that non-instantaneous adaptation of the driving behaviour to the traffic situation together with the conventional measurement method of flow-density data can explain the observed inverse-$λ$ shape and the wide scattering of flow-density data in ``synchronized'' congested traffic. We model a memory effect in the response of drivers to the traffic situation for a wide class of car-following models by introducing a new dynamical variable describing the adaptation of drivers to the surrounding traffic situation during the past few minutes (``subjective level of service'') and couple this internal state to parameters of the underlying model that are related to the driving style. % For illustration, we use the intelligent-driver model (IDM) as underlying model, characterize the level of service solely by the velocity and couple the internal variable to the IDM parameter ``netto time gap'', modelling an increase of the time gap in congested traffic (``frustration effect''), that is supported by single-vehicle data. % We simulate open systems with a bottleneck and obtain flow-density data by implementing ``virtual detectors''. Both the shape, relative size and apparent ``stochasticity'' of the region of the scattered data points agree nearly quantitatively with empirical data. Wide scattering is even observed for identical vehicles, although the proposed model is a time-continuous, deterministic, single-lane car-following model with a unique fundamental diagram.

cond-mat.stat-mech↗

arXiv2002

Microsimulations of Freeway Traffic Including Control Measures

Using a recently developed microscopic traffic model, we simulate how speed limits, on-ramp controls, and vehicle-based driver-assistance systems influence freeway traffic. We present results for a section of the German Autobahn A8-East. Both, a speed limit and an on-ramp control could considerably reduce the severeness of the originally observed and simulated congestion. Introducing 20% vehicles equipped with driver-assistance systems eliminated the congestion almost completely

cond-mat.dis-nn↗

arXiv2002

An adaptive smoothing method for traffic state identification from incomplete information

We present a new method to obtain spatio-temporal information from aggregated data of stationary traffic detectors, the ``adaptive smoothing method''. In essential, a nonlinear spatio-temporal lowpass filter is applied to the input detector data. This filter exploits the fact that, in congested traffic, perturbations travel upstream at a constant speed, while in free traffic, information propagates downstream. As a result, one obtains velocity, flow, or other traffic variables as smooth functions of space and time. Applications include traffic-state visualization, reconstruction of traffic situations from incomplete information, fast identification of traffic breakdowns (e.g., in incident detection), and experimental verification of traffic models. We apply the adaptive smoothing method to observed congestion patterns on several German freeways. It manages to make sense out of data where conventional visualization techniques fail. By ignoring up to 65% of the detectors and applying the method to the reduced data set, we show that the results are robust. The method works well if the distances between neighbouring detector cross sections do not exceed 3 km.

cond-mat.stat-mech↗