arXiv subjects

Michael Schreckenberg

Publications and source records attributed to Michael Schreckenberg.

At least 37 records · Page 2Linked to original sources

arXiv2015

Velocity Statistics of the Nagel-Schreckenberg Model

The statistics of velocities in the cellular automaton model of Nagel and Schreckenberg for traffic are studied. From numerical simulations, we obtain the probability distribution function (PDF) for vehicle velocities and the velocity-velocity (vv) correlation function. We identify the probability to find a standing vehicle as a potential order parameter that signals nicely the transition between free congested flow for sufficiently large number of velocity states. Our results for the vv correlation function resemble features of a second order phase transition. We develop a 3-body approximation that allows us to relate the PDFs for velocities and headways. Using this relation, an approximation to the velocity PDF is obtained from the headway PDF observed in simulations. We find a remarkable agreement between this approximation and the velocity PDF obtained from simulations.

nlin.CG↗

arXiv2013

Statistical Analysis of High-Flow Traffic States

The relation between the fundamental observables of traffic flow (i.e., vehicle density, flow rate, and average velocity) is of great importance for the study of traffic phenomena. Probably the most common source of such data are inductive loop detectors, which count the number of passing vehicles and measure their speed. We will present an analysis of detector data collected by more than 3000 loop detectors during the past three years on the motorway network of the state of North Rhine-Westphalia. Besides presenting some general aspects of traffic flow, our analysis focuses on the characteristics of so-called high-flow states, i.e. traffic states where the flow rate exceeds 50 vehicles per minute and lane (3000 veh/h/lane). We investigate the duration, frequency and other statistics of such states, the viability of the data and we study the conditions under which they occur. The factors that influence the existence of high-flow states in traffic are, for instance, the fraction of slow vehicles (namely trucks), the motorway's general topology (e.g. number of lanes), the hour of the day and day of the week. This information is directly accessible from the detector data.

stat.AP↗

arXiv2013

The comfortable driving model revisited: Traffic phases and phase transitions

We study the spatiotemporal patterns resulting from different boundary conditions for a microscopic traffic model and contrast it with empirical results. By evaluating the time series of local measurements, the local traffic states are assigned to the different traffic phases of Kerner's three-phase traffic theory. For this classification we use the rule-based FOTO-method, which provides `hard' rules for this assignment. Using this approach, our analysis shows that the model is indeed able to reproduce three qualitatively different traffic phases: free flow (F), synchronized traffic (S), and wide moving jams (J). In addition, we investigate the likelihood of transitions between the three traffic phases. We show that a transition from free flow (F) to a wide moving jam (J) often involves an intermediate transition; first from free flow F to synchronized flow S and then from synchronized flow to a wide moving jam. This is supported by the fact that the so called F->S transition (from free flow to synchronized traffic) is much more likely than a direct F->J transition. The model under consideration has a functional relation between traffic flow and traffic density. The fundamental hypothesis of the three-phase traffic theory, however, postulates that the steady states of synchronized flow occupy a two-dimensional region in the flow-density plane. Due to the obvious discrepancy between the model investigated here and the postulate of the three-phase traffic theory, the good agreement that we found could not be expected. For a more detailed analysis, we also studied the vehicle dynamics at a microscopic level and provide a comparison of real detector data with simulated data of the identical highway segment.

physics.soc-ph↗

arXiv2012

On the reproducibility of spatiotemporal traffic dynamics with microscopic traffic models

Traffic flow is a very prominent example of a driven non-equilibrium system. A characteristic phenomenon of traffic dynamics is the spontaneous and abrupt drop of the average velocity on a stretch of road leading to congestion. Such a traffic breakdown corresponds to a boundary-induced phase transition from free flow to congested traffic. In this paper, we study the ability of selected microscopic traffic models to reproduce a traffic breakdown, and we investigate its spatiotemporal dynamics. For our analysis, we use empirical traffic data from stationary loop detectors on a German Autobahn showing a spontaneous breakdown. We then present several methods to assess the results and compare the models with each other. In addition, we will also discuss some important modeling aspects and their impact on the resulting spatiotemporal pattern. The investigation of different downstream boundary conditions, for example, shows that the physical origin of the traffic breakdown may be artificially induced by the setup of the boundaries.

physics.soc-ph↗

arXiv2009

Exact matrix-product states for parallel dynamics: Open boundaries and excess mass on the ring

In this paper it is shown that the steady-state weights of the asymmetric simple exclusion process (ASEP) with open boundaries and parallel update can be written as a product of a scalar pair-factorized and a matrix-product state. This type of state is also obtained for an ASEP on a ring in which particles can move one or two sites. The dynamics leads to the formation of an excess hole that plays the role of a defect. We expect the process to play a similar role for parallel dynamics as the well-known ASEP with a single defect-particle (that is obtained in the continuous-time limit) especially for the study of shocks. The process exhibits a first-order phase transition between two phases with different defect velocities. These are calculated exactly from the process-generating function.

cond-mat.stat-mech↗

arXiv2009

Headway oscillations and phase transitions for diffusing particles with increased velocity

An asymmetric exclusion process with $N$ particles on $L$ sites is considered where particles can move one or two sites per infinitesimal time-step. An exact analysis for N=2 and a mean-field theory in comparison with simulations show even/odd oscillations in the headway distribution of particles. Oscillations become maximal if particles try to move as far as possible with regard to their maximum velocity and particle exclusion. A phase transition separates two density profiles around a generated perturbation that plays the role of a defect. The matrix-product ansatz is generalized to obtain the exact solution for finite $N$ and $L$. Thermodynamically, the headway distribution yields the mean-field result as $N^{-1}\to 0$ while it is not described generally by a product measure.

cond-mat.stat-mech↗

arXiv2008

Counterflow Extension for the F.A.S.T.-Model

The F.A.S.T. (Floor field and Agent based Simulation Tool) model is a microscopic model of pedestrian dynamics, which is discrete in space and time. It was developed in a number of more or less consecutive steps from a simple CA model. This contribution is a summary of a study on an extension of the F.A.S.T-model for counterflow situations. The extensions will be explained and it will be shown that the extended F.A.S.T.-model is capable of handling various counterflow situations and to reproduce the well known lane formation effect.

cs.MA↗

arXiv2008

The F.A.S.T.-Model

A discrete model of pedestrian motion is presented that is implemented in the Floor field- and Agentbased Simulation Tool (F.A.S.T.) which has already been applicated to a variety of real life scenarios.

cs.MA↗

arXiv2008

Moore and more and symmetry

In any spatially discrete model of pedestrian motion which uses a regular lattice as basis, there is the question of how the symmetry between the different directions of motion can be restored as far as possible but with limited computational effort. This question is equivalent to the question ''How important is the orientation of the axis of discretization for the result of the simulation?'' An optimization in terms of symmetry can be combined with the implementation of higher and heterogeniously distributed walking speeds by representing different walking speeds via different amounts of cells an agent may move during one round. Therefore all different possible neighborhoods for speeds up to v = 10 (cells per round) will be examined for the amount of deviation from radial symmetry. Simple criteria will be stated which will allow find an optimal neighborhood for each speed. It will be shown that following these criteria even the best mixture of steps in Moore and von Neumann neighborhoods is unable to reproduce the optimal neighborhood for a speed as low as 4.

cs.MA↗

arXiv2006

Experimental study of pedestrian flow through a bottleneck

In this work the results of a bottleneck experiment with pedestrians are presented in the form of total times, fluxes, specific fluxes, and time gaps. A main aim was to find the dependence of these values from the bottleneck width. The results show a linear decline of the specific flux with increasing width as long as only one person at a time can pass, and a constant value for larger bottleneck widths. Differences between small (one person at a time) and wide bottlenecks (two persons at a time) were also found in the distribution of time gaps.

physics.soc-ph↗

arXiv2006

Experimental study of pedestrian counterflow in a corridor

In this work the results of a pedestrian counterflow experiment in a corridor of a width of 2 meter are presented. 67 participants were divided into two groups with varying relative and absolute size and walked in opposite direction through a corridor. The video footage taken from the experiment was evaluated for passing times, walking speeds, fluxes and lane-formation including symmetry breaking. The results include comparatively large fluxes and speeds as well as a maximal asymmetry between left- and right-hand traffic. The sum of flow and counterflow in any case turns out to be larger than the flow in all situations without counterflow.

cond-mat.stat-mech↗

arXiv2006

F.A.S.T. - Floor field- and Agent-based Simulation Tool

In this paper a model of pedestrian motion is presented. As application its parameters are fitted to one run in a primary school evacuation exercise. Simulations with these parameters are compared to further runs during the same exercise.

physics.comp-ph↗

arXiv2006

Characterizing correlations of flow oscillations at bottlenecks

"Oscillations" occur in quite different kinds of many-particle-systems when two groups of particles with different directions of motion meet or intersect at a certain spot. We present a model of pedestrian motion that is able to reproduce oscillations with different characteristics. The Wald-Wolfowitz test and Gillis' correlated random walk are shown to hold observables that can be used to characterize different kinds of oscillations.

cond-mat.stat-mech↗

arXiv2005

Asymmetric exclusion processes with shuffled dynamics

The asymmetric simple exclusion process (ASEP) with periodic boundary conditions is investigated for shuffled dynamics. In this type of update, in each discrete timestep the particles are updated in a random sequence. Such an update is important for several applications, e.g. for certain models of pedestrian flow in two dimensions. For the ASEP with shuffled dynamics and a related truncated process exact results are obtained for deterministic motion (p=1). Since the shuffled dynamics is intrinsically stochastic, also this case is nontrivial. For the case of stochastic motion (0<p<1) it is shown that, in contrast to all other updates studied previously, the ASEP with shuffled update does not have a product measure steady state. Approximative formulas for the steady state distribution and fundamental diagram are derived that are in very good agreement with simulation data.

cond-mat.stat-mech↗

arXiv2004

Discretisation effects and the influence of walking speed in cellular automata models for pedestrian dynamics

We study discretisation effects in cellular automata models for pedestrian dynamics by reducing the cell size. Then a particle occupies more than one cell which leads to subtle effects in the dynamics, e.g. non-local conflict situations. Results from computer simulations of the floor field model are compared with empirical findings. Furthermore the influence of increasing the maximal walking speed $v_{\rm max}$ is investigated by increasing the interaction range beyond nearest neighbour interactions. The extension of the model to $v_{\rm max}>1$ turns out to be a severe challenge which can be solved in different ways. Four major variants are discussed that take into account different dynamical aspects. The variation of $v_{\rm max}$ has strong influence on the shape of the flow-density relation. We show that walking speeds $v_{\rm max}>1$ lead to results which are in very good agreement with empirical data.

cond-mat.stat-mech↗

arXiv2004

An 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 new light on the relevant interactions in traffic flow.

cond-mat.stat-mech↗

arXiv2004

Mechanical restriction versus human overreaction triggering congested traffic states

A new cellular automaton (CA) traffic model is presented. The focus is on mechanical restrictions of vehicles realized by limited acceleration and deceleration capabilities. These features are incorporated into the model in order to construct the condition of collision-free movement. The strict collision-free criterion imposed by the mechanical restrictions is softened in certain traffic situations, reflecting human overreaction. It is shown that the present model reliably reproduces most empirical findings including synchronized flow, the so-called {\it pinch effect}, and the time-headway distribution of free flow. The findings suggest that many free flow phenomena can be attributed to the platoon formation of vehicles ({\it platoon effect})

cond-mat.stat-mech↗

arXiv2002

Optimization potential of a real highway network: an empirical study

Empirical observations and theoretical studies indicate that the overall travel-time of vehicles in a traffic network can be optimized by means of ramp metering control systems. Here, we present an analysis of traffic data of the highway network of North-Rhine-Westfalia in order to identify and characterize the sections of the network which limit the performance, i.e., the bottlenecks. It is clarified whether the bottlenecks are of topological nature or if they are constituted by on-ramps. This allows to judge possible optimization mechanisms and reveals in which areas of the network they have to be applied.

cond-mat.stat-mech↗