Arne Kesting

General Lane-Changing Model MOBIL for Car-Following Models

A general model (minimizing overall braking induced by lane change, MOBIL) is proposed to derive lane-changing rules for discretionary and mandatory lane changes for a wide class of car-following models. Both the utility of a given lane and the risk associated with lane changes are determined in terms of longitudinal accelerations calculated with microscopic traffic models. This determination allows for the formulation of compact and general safety and incentive criteria for both symmetric and asymmetric passing rules. Moreover, anticipative elements and the crucial influence of velocity differences of these car-following models are automatically transferred to the lane-changing rules. Although the safety criterion prevents critical lane changes and collisions, the incentive criterion takes into account the advantages and disadvantages of other drivers associated with a lane change via the “politeness factor.” The parameter allows one to vary the motivation for lane changing from purely egoistic to more cooperative driving behavior. This novel feature allows one first to prevent lane changes for a marginal advantage if they obstruct other drivers and second to let an aggressive driver induce the lane change of a slower driver ahead in order to no longer be obstructed. This phenomenon is common for asymmetric passing rules with a dedicated lane for passing. The model is applied to traffic simulations of cars and trucks with the intelligent driver model as the underlying car-following model. An open system with an on-ramp is studied, and the resulting lane-changing rate is investigated as a function of the spatial coordinate as well as a function of traffic density.

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.

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 the basis of an ACC implementation in real cars. The model is based on the intelligent driver model (IDM) 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 IDM 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 per cent more ACC vehicles will lead to an increase in the capacities by about 0.3 per cent. This sensitivity multiplies when considering travel times at actual breakdowns.

Estimating Acceleration and Lane-Changing Dynamics from Next Generation Simulation Trajectory Data

The Next Generation Simulation (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 because the noise in the NGSIM positional information is greatly increased by the necessary numerical differentiations. A smoothing algorithm is proposed for positions, velocities, and accelerations that can also be applied near the boundaries. The smoothing time interval is estimated on the basis of 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. It is also 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, it is shown that the probability for critical values of the times to collision is greatly underestimated when estimated from single-vehicle data of stationary detectors. Finally, the lane-changing process is investigated, and a quantitative criterion is formulated for the duration of lane changes that is based on the trajectory density in normalized coordinates. There is a noisy but significant velocity advantage in favor of the targeted lane that decreases immediately before the change due to anticipatory accelerations.

Calibrating Car-Following Models by 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 data sets recorded by a vehicle equipped with a radar sensor. By means of a nonlinear optimization procedure based on a genetic algorithm, the intelligent driver model and the velocity difference model are calibrated by minimizing the deviations between the observed driving dynamics and the simulated trajectory in following the same leading vehicle. The reliability and robustness of the nonlinear fits are assessed by applying different optimization criteria, that is, different measures for the deviations between two trajectories. The obtained errors are between 11% and 29%, which is consistent with typical error ranges obtained in previous studies. It is also found that the calibrated parameter values of the velocity difference model depend strongly on the optimization criterion, whereas the intelligent driver model is more robust. The influence of a reaction time is investigated by applying an explicit delay to the model input. A negligible influence of the reaction time is found and indicates that drivers compensate for their reaction time by anticipation. Furthermore, the parameter sets calibrated to a certain trajectory are applied to the other trajectories; this step allows for model validation. The results indicate that intradriver variability rather than interdriver variability accounts for a large part of the calibration errors. The results are used to suggest some criteria toward a benchmarking of car-following models.

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.

How Reaction Time, Update Time, and Adaptation Time Influence the Stability of Traffic Flow

When modeling the acceleration and decel- eration of drivers, there are three characteristic time con- stants that influence the dynamics and stability of traffic flow: The reaction time of the drivers, the velocity adap- tation time needed to accelerate to a new desired velocity, and the numerical update time. By means of numerical simulations with a time-continuous car-following model, we investigate how these times interplay with each other and effectively influence the longitudinal instability mech- anisms for a platoon of vehicles. The long-wavelength string instability is mainly driven by the velocity adapta- tion time while short-wavelength local instabilities arise for sufficiently high reaction and update times. Further- more, we investigate the relation between large update time steps and finite reaction times as they both introduce delays in the reaction to the traffic situation. Remarkably, the numerical update time is dynamically equivalent to about half the reaction time, which clarifies the meaning of the time step in models formulated as iterated maps such as the Newell and the Gipps model. Furthermore, with respect to stability, there is an optimal adaptation time as a function of the reaction time.

Theoretical vs. empirical classification and prediction of congested traffic states

Abstract 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.

Connectivity Statistics of Store-and-Forward Intervehicle Communication

Intervehicle communication (IVC) enables vehicles to exchange messages within a limited broadcast range and thus self-organize into dynamical vehicular ad hoc networks. For the foreseeable future, however, a direct connectivity between equipped vehicles in one direction is rarely possible. We therefore investigate an alternative mode in which messages are stored by relay vehicles traveling in the opposite direction and forwarded to vehicles in the original direction at a later time. The wireless communication consists of two ¿transversal¿ message hops across driving directions. Since direct connectivity for transversal hops and a successful message transmission to vehicles in the destination region are only a matter of time, the quality of this IVC strategy can be described in terms of the distribution function for the total transmission time. Assuming a Poissonian distance distribution between equipped vehicles, we derive analytical probability distributions for message transmission times and related propagation speeds for a deterministic and a stochastic model of the maximum range of direct communication. By means of integrated microscopic simulations of communication and bidirectional traffic flows, we validated the theoretical expectation for multilane roadways. We found little deviation of the analytical result for multilane scenarios but significant deviations for a single lane. This can be explained by vehicle platooning. We demonstrate the efficiency of the transverse hopping mechanism for a congestion-warning application in a microscopic traffic-simulation scenario. Messages are created on an event-driven basis by equipped vehicles getting into and out of a traffic jam. This application is operative for penetration levels as low as 1%.

Reconstructing the Traffic State by Fusion of Heterogeneous Data

This paper presents 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 the “adaptive smoothing method” which takes as input stationary detector data as typically collected by traffic control centers. The authors generalize this method to allow for fusion with 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. The authors 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.