arXiv subjects

Michael Schreckenberg

Publications and source records attributed to Michael Schreckenberg.

At least 19 recordsLinked to original sources

arXiv2026

An improved car-oriented mean-field theory for stochastic traffic flow models

We propose an improved mean-field analysis of cellular automata models of single-lane vehicular traffic. By combining aspects of the Car-Oriented-Mean-Field (COMF) theory and the 2-site cluster method, which have been previously successfully applied to similar models, we aim to capture both short- and long-range correlations more accurately. In contrast to classical mean-field theories, the improved method is well suited for models with inhomogeneous stationary states and able to capture the essential properties of phase separation, e.g. in models with slow-to-start rules. The improved accuracy and new physical insights are illustrated through an application to the VDR model with $v_{\text{max}}=1$.

cond-mat.stat-mech↗

arXiv2024

Spatiotemporal statistical features of velocity responses to traffic congestions in a local motorway network

The causal connection between congestions and velocity changes at different locations induces various statistical features, which we identify and measure in detail. We carry out an empirical analysis of large-scale traffic data on a local motorway network around the Breitscheid intersection in the North Rhine-Westphalia, Germany. We put forward a response function which measures the velocity change at a certain location versus time conditioned on a congestion at another location. We use a novel definition of the corresponding congestion indicator to ensure causality. We find that the response of velocities to the congestion exhibits phase changes in time. A negative response at smaller time lags transforms into positive one at larger time lags, implying a certain traffic mechanism. The response decays as a power law with the distance. We also identify a scaling property leading to a collapse of the response functions on one curve.

physics.soc-ph↗

arXiv2024

How much longer do you have to drive than the crow has to fly?

When traveling by car from one location to another, our route is constrained by the road network. The network distance between the two locations is generally longer than the geodetic distance as the crow flies. We report a systematic relation between the statistical properties of these two distances. Empirically, we find a robust scaling between network and geodetic distance distributions for a variety of large motorway networks. A simple consequence is that we typically have to drive $1.3\pm0.1$ times longer than the crow flies. This scaling is not present in standard random networks; rather, it requires non-random adjacency. We develop a set of rules to build a realistic motorway network, also consistent with the above scaling. We hypothesize that the scaling reflects a compromise between two societal needs: high efficiency and accessibility on the one hand, and limitation of costs and other burdens on the other.

physics.soc-ph↗

arXiv2024

Correlations in Motion: A Simple Response-Based Analysis of Traffic Flow

Why does a traffic jams form out of nowhere, and why does it stretch for kilometers even after the initial cause is passed? This study examines how congestion moves and spreads across motorways using a surprisingly simple method: response functions. These functions are based purely on data and show how changes in traffic flow, density, and velocity are connected over time and space. Using real-world data from German motorways, we track how traffic reacts to earlier disturbances, capturing the waves of slowing and accelerating that drivers experience in stop-and-go traffic. The results demonstrate how congestion propagates and how its rhythm can be measured and predicted. Unlike complex traffic models, this approach requires no simulations or assumptions about driver behavior. It works directly from the information provided by the road. The goal is clear: to understand congestion better so that we can manage it more effectively and perhaps spend less time stuck in it.

physics.soc-ph↗

arXiv2024

A Methodology of Cooperative Driving based on Microscopic Traffic Prediction

We present a methodology of cooperative driving in vehicular traffic, in which for short-time traffic prediction rather than one of the statistical approaches of artificial intelligence (AI), we follow a qualitative different microscopic traffic prediction approach developed recently [Phys. Rev. E 106 (2022) 044307]. In the microscopic traffic prediction approach used for the planning of the subject vehicle trajectory, no learning algorithms of AI are applied; instead, microscopic traffic modeling based on the physics of vehicle motion is used. The presented methodology of cooperative driving is devoted to application cases in which microscopic traffic prediction without cooperative driving cannot lead to a successful vehicle control and trajectory planning. For the understanding of the physical features of the methodology of cooperative driving, a traffic city scenario has been numerically studied, in which a subject vehicle, which requires cooperative driving, is an automated vehicle. Based on microscopic traffic prediction, in the methodology first a cooperating vehicle(s) is found; then, motion requirements for the cooperating vehicle(s) and characteristics of automated vehicle control are predicted and used for vehicle motion; to update predicted characteristics of vehicle motion, calculations of the predictions of motion requirements for the cooperating vehicle and automated vehicle control are repeated for each next time instant at which new measured data for current microscopic traffic situation are available. With the use of microscopic traffic simulations, the evaluation of the applicability of this methodology is illustrated for a simple case of unsignalized city intersection, when the automated vehicle wants to turn right from a secondary road onto the priority road.

physics.soc-ph↗

arXiv2023

Congestions and Spectral Transition in Time-Lagged Correlations of Motorway Traffic

The congestion of a motorway section is propagated to its neighbouring sections, leading to correlations. The resulting correlation matrix encodes the information on congestion. Here, we study symmetrized time-lagged correlations and show how their spectral properties reveal congestion durations. We carry out an empirical analysis and find a transition behavior for the dominant eigenvalue as function of the time lag. Furthermore, we set up a numerical simulation model for indicator time series of traffic phases as well as a simplified model that we treat analytically. We consider various scenarios. Our results reveal a nonlinear relation between the spectral transition and the congestion duration. In our simplified model, we derive this relation analytically.

physics.soc-ph↗

arXiv2023

Transitions between quasi-stationary states in traffic systems: Cologne orbital motorways as an example

Traffic systems can operate in different modes. In a previous work, we identified these modes as different quasi-stationary states in the correlation structure. Here, we analyze the transitions between such quasi-stationary states, i.e., how the system changes its operational mode. In the longer run this might be helpful to forecast the time evolution of correlation patterns in traffic. We take Cologne orbital motorways as an example, we construct a state transition network for each quarter of 2015 and find a seasonal dependence for those quasi-stationary states in the traffic system. Using the PageRank algorithm, we identify and explore the dominant states which occur frequently within a moving time window of 60 days in 2015. To the best of our knowledge, this is the first study of this type for traffic systems.

physics.soc-ph↗

arXiv2022

Response functions as a new concept to study local dynamics in traffic networks

Vehicle velocities in neighbouring road sections are correlated with memory effects. We explore the response of the velocities in the sequence of sections to a congestion in a given section and its dynamic characteristics. To this end, we transfer the concept of response functions from previous applications in finance to traffic systems. The dynamical characteristics are of particular interest. We identify two phases, a phase of transient response and a phase of long-term response. The transient response is pronounced when considering the backward propagation of heavy congestions but almost vanishes for forward propagation. For each response phase, we find a linear relation between the velocity response and the congestion correlator, implying that the correlation of congestion is most likely the cause for the velocity response. We also construct a susceptible-decelerated-withdrawing model mathematically inspired by the susceptible-infectious-recovered (SIR) model in epidemiology to describe the transient response. We find that the heavy congestion on a section propagates forward and backward at a similar rate, but the forward sections are more likely to recover from the effect of heavy congestion than the backward sections.

physics.soc-ph↗

arXiv2022

Sensitivity of principal components to system changes in the presence of non-stationarity

Non-stationarity affects the sensitivity of change detection in correlated systems described by sets of measurable variables. We study this by projecting onto different principal components. Non-stationarity is modeled as multiple normal states that exist in the system even before a change occurs. The studied changes occur in mean values, standard deviations or correlations of the variables. Monte Carlo simulations are performed to test the sensitivity for change detection with and without knowledge about the non-stationarity for different system dimensions and numbers of normal states. A comparison clearly shows that the knowledge about the non-stationarity of the system greatly improves change detection sensitivity for all principal components. This improvement is largest for those components that already provide the greatest possibility for change detection in the stationary case. We illustrate our results with an example using real traffic flow data, in which we detect a weekend and a bank holiday start as anomalies.

physics.data-an↗

arXiv2022

Identifying subdominant collective effects in a large motorway network

In a motorway network, correlations between parts or, more precisely, between the sections of (different) motorways, are of considerable interest. Knowledge of flows and velocities on individual motorways is not sufficient, rather, their correlations determine or reflect, respectively, the functionality of and the dynamics on the network. These correlations are time-dependent as the dynamics on the network is highly non-stationary. Apart from the conceptual importance, correlations are also indispensable to detect risks of failure in a traffic network. Here, we proceed with revealing a certain hierarchy of correlations in traffic networks that is due to the presence and to the extent of collectivity. In a previous study, we focused on the collectivity motion present in the entire traffic network, i.e. the collectivity of the system as a whole. Here, we manage to subtract this dominant effect from the data and identify the subdominant collectivities which affect different, large parts of the traffic network. To this end, we employ a spectral analysis of the correlation matrix for the whole system. We thereby extract information from the virtual network induced by the correlations and map it on the true topology, i.e. on the real motorway network. The uncovered subdominant collectivities provide a new characterization of the traffic network. We carry out our study for the large motorway network of North Rhine-Westphalia (NRW), Germany.

physics.soc-ph↗

arXiv2022

Collective behavior in the North Rhine-Westphalia motorway network

To understand the dynamics on complex networks, measurement of correlations is indispensable. In a motorway network, it is not sufficient to collect information on fluxes and velocities on all individual links, i.e. parts of the freeways between ramps and highway crosses. The interdependencies and mutual connections are also of considerable interest. We analyze correlations in the complete motorway network in North Rhine-Westphalia, the most populous state in Germany. We view the motorway network as a complex system consisting of road sections which interact via the motion of vehicles, implying structures in the corresponding correlation matrices. In particular, we focus on collective behavior, i.e. coherent motion in the whole network or in large parts of it. To this end, we study the eigenvalue and eigenvector statistics and identify significant sections in the motorway network. We find collective behavior in these significant sections and further explore its causes. We show that collectivity throughout the network cannot directly be related to the traffic states (free, synchronous and congested) in Kerner's three-phase theory. Hence, the degree of collectivity provides a new, complementary observable to characterize the motorway network.

physics.soc-ph↗

arXiv2021

Spatial Correlation Analysis of Traffic Flow on Parallel Motorways in Germany

With the widely used method of correlation matrix analysis, this study reveals the change of traffic states on parallel motorways in North Rhine-Westphalia, Germany. In terms of the time series of traffic flow and velocity, we carry out a quantitative analysis in correlations and reveal a high level of strongly positive traffic flow correlation and rich structural features in the corresponding correlation matrices. The strong correlation is mainly ascribed to the daily time evolution of traffic flow during the periods of rush hours and non-rush hours. In terms of free flow and congestion, the structural features are able to capture the average traffic situation we derive from our data. Furthermore, the structural features in correlation matrices for individual time periods corroborate our results from the correlation matrices regarding a whole day. The average correlations in traffic flows and velocities over all pairwise sections disclose the traffic behavior during each individual time period. Our contribution uncovers the potential application of correlation analysis on the study of traffic networks as a complex system.

physics.soc-ph↗

arXiv2020

Quasi-stationary states in temporal correlations for traffic systems: Cologne orbital motorway as an example

Traffic systems are complex systems that exhibit non-stationary characteristics. Therefore, the identification of temporary traffic states is significant. In contrast to the usual correlations of time series, here we study those of position series, revealing structures in time, i.e. the rich non-Markovian features of traffic. Considering the traffic system of the Cologne orbital motorway as a whole, we identify five quasi-stationary states by clustering reduced rank correlation matrices of flows using the $k$-means method. The five quasi-stationary states with nontrivial features include one holiday state, three workday states and one mixed state of holidays and workdays. In particular, the workday states and the mixed state exhibit strongly correlated time groups shown as diagonal blocks in the correlation matrices. We map the five states onto reduced-rank correlation matrices of velocities and onto traffic states where free or congested states are revealed in both space and time. Our study opens a new perspective for studying traffic systems. This contribution is meant to provide a proof of concept and a basis for further study.

physics.soc-ph↗

arXiv2019

System-of-Systems Modeling, Analysis and Optimization of Hybrid Vehicular Traffic

While the development of fully autonomous vehicles is one of the major research fields in the Intelligent Transportation Systems (ITSs) domain, the upcoming longterm transition period - the hybrid vehicular traffic - is often neglected. However, within the next decades, automotive systems with heterogeneous autonomy levels will share the same road network, resulting in new problems for traffic management systems and communication network infrastructure providers. In this paper, we identify key challenges of the upcoming hybrid traffic scenario and present a system-of-systems model, which brings together approaches and methods from traffic modeling, data science, and communication engineering in order to allow data-driven traffic flow optimization. The proposed model consists of data acquisition, data transfer, data analysis, and data exploitation and exploits real world sensor data as well as simulative optimization methods. Based on the results of multiple case studies, which focus on individual challenges (e.g., resource-efficient data transfer and dynamic routing of vehicles), we point out approaches for using the existing infrastructure with a higher grade of efficiency.

cs.NI↗

arXiv2018

Performance comparison of dynamic vehicle routing methods for minimizing the global dwell time in upcoming smart cities

Traffic jams in urban scenarios are often caused by bottlenecks related to the street topology and road infrastructure, e.g. traffic lights and merging of lanes. Instead of addressing traffic flow optimization in a static way by extending the road capacity through constructing additional streets, upcoming smart cities will exploit the availability of modern communication technologies to dynamically change the mobility behavior of individual vehicles. The underlying overall goal is to minimize the total dwell time of the vehicles within the road network. In this paper, different bottleneck-aware methods for dynamic vehicle routing are compared in comprehensive simulations. As a realistic evaluation scenario, the inner city of Dusseldorf is modeled and the mobility behavior of the cars is represented based on real-world traffic flow data. The simulation results show, that the consideration of bottlenecks in a routing method decreased the average travel time by around 23%. Based on these results a new routing method is created which further reduces the average travel time by around 10%. The simulations further show, that the implementation of dynamic lanes in inner cities most of the time only shift traffic congestion to following bottlenecks without reducing the travel times.

physics.soc-ph↗

arXiv2018

Lightweight Joint Simulation of Vehicular Mobility and Communication with LIMoSim

The provision of reliable and efficient communication is a key requirement for the deployment of autonomous cars as well as for future Intelligent Transportation Systems (ITSs) in smart cities. Novel communications technologies will have to face highly-complex and extremely dynamic network topologies in a Vehicle-to-Everything (V2X)-context and will require the consideration of mobility information into decision processes for routing, handover and resource allocation. Consequently, researches and developers require simulation tools that are capable of providing realistic representations for both components as well as means for leveraging the convergence of mobility and communication. In this paper, we present a lightweight framework for the simulation of vehicular mobility, which has a communications-oriented perspective by design and is intended to be used in combination with a network simulator. In contrast to existing approaches, it works without requiring Interprocess Communication (IPC) using an integrated approach and is therefore able to reduce the complexity of simulation setups dramatically. Since mobility and communication share the same codebase, it is able to model scenarios with a high level of interdependency between those two components. In a proof-of-concept study, we evaluate the proposed simulator in different example scenarios in an Long Term Evolution (LTE)- context using real-world map data.

cs.NI↗

arXiv2018

Radio-based Traffic Flow Detection and Vehicle Classification for Future Smart Cities

Intelligent Transportation Systems (ITSs) providing vehicle-related statistical data are one of the key components for future smart cities. In this context, knowledge about the current traffic flow is used for travel time reduction and proactive jam avoidance by intelligent traffic control mechanisms. In addition, the monitoring and classification of vehicles can be used in the field of smart parking systems. The required data is measured using networks with a wide range of sensors. Nevertheless, in the context of smart cities no existing solution for traffic flow detection and vehicle classification is able to guarantee high classification accuracy, low deployment and maintenance costs, low power consumption and a weather-independent operation while respecting privacy. In this paper, we propose a radiobased approach for traffic flow detection and vehicle classification using signal attenuation measurements and machine learning algorithms. The results of comprehensive measurements in the field prove its high classification success rate of about 99%.

cs.NI↗

arXiv2017

The Importance of Antipersistence for Traffic Jams

Universal characteristics of road networks and traffic patterns can help to forecast and control traffic congestion. The antipersistence of traffic flow time series has been found for many data sets, but its relevance for congestion has been overseen. Based on empirical data from motorways in Germany, we study how antipersistence of traffic flow time-series impacts the duration of traffic congestion on a wide range of time scales. We find a large number of short lasting traffic jams, which implies a large risk for rear-end collisions.

physics.soc-ph↗