No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
Analyzing human driving data an approach motivated by data science methods
Abstract
By analyzing a large data-base of car-driving data in a generic way, a few elementary facts on car-following have been found out. The inferences stem from the application of the mutual information to detect correlations to the data. Arguably, the most interesting fact is that the acceleration of the following vehicle depends mostly on the speed-difference to the lead vehicle. This seems to be a causal relationship, since acceleration follows speed-difference with an average delay of 0.5 s. Furthermore, the car-following process organizes itself in such a manner that there is a strong relation between speed and distance to the vehicle in front. In most cases, this is the dominant relationship in car-following. Additionally, acceleration depends only weakly on distance, which may be surprising and is at odds to a number of simple models that state an exclusive dependency between acceleration and distance.
... The former accounts for collision energy and probability with stationary obstacles, while the latter involves spatial overlap with neighbouring vehicles using predicted positions and stochastic accelerations. In stable highway driving, the longitudinal and lateral accelerations of neighbour follow a Gaussian distribution (Wagner et al., 2016;Ko et al., 2010). However, due to uncertainties and behavioural deviations, human drivers perceive risk differently, leading to a bias between objective and perceived risk. ...
Perceived risk is crucial in designing trustworthy and acceptable vehicle automation systems. However, our understanding of its dynamics is limited, and models for perceived risk dynamics are scarce in the literature. This study formulates a new computational perceived risk model based on potential collision avoidance difficulty (PCAD) for drivers of SAE level 2 driving automation. PCAD uses the 2D safe velocity gap as the potential collision avoidance difficulty, and takes into account collision severity. The safe velocity gap is defined as the 2D gap between the current velocity and the safe velocity region, and represents the amount of braking and steering needed, considering behavioural uncertainty of neighbouring vehicles and imprecise control of the subject vehicle. The PCAD predicts perceived risk both in continuous time and per event. We compare the PCAD model with three state-of-the-art models and analyse the models both theoretically and empirically with two unique datasets: Dataset Merging and Dataset Obstacle Avoidance. The PCAD model generally outperforms the other models in terms of model error, detection rate, and the ability to accurately capture the tendencies of human drivers' perceived risk, albeit at a longer computation time. Additionally, the study shows that the perceived risk is not static and varies with the surrounding traffic conditions. This research advances our understanding of perceived risk in automated driving and paves the way for improved safety and acceptance of driving automation systems.
... The risk considering the probable behavior of the neighbor vehicle is estimated by using a stochastic approach. The probability functions of acceleration variability can be estimated by treating acceleration signals as a random variable (Wagner et al., 2016). The acceleration variability is assumed to follow a Gaussian distribution (Ko et al., 2010). ...
: Surrogate measures of safety (SMoS) play an important role in detecting traffic conflicts and in traffic safety assessment. However, the underlying assumptions of SMoS are different and a certain SMoS may be adequate/inadequate for different applications. A comprehensive approach to evaluate the validity and applicability of SMoS is lacking in the literature. This study proposes such a framework that supports evaluating SMoS in multiple dimensions. We apply the framework to gain insights into the characteristics of six widely-used SMoS for longitudinal maneuvers, i.e., Time to Collision (TTC), single-step Probabilistic Driving Risk Field (S-PDRF), Deceleration Rate to Avoid a Crash (DRAC), Potential Index for Collision with Urgent Deceleration (PICUD), Proactive Fuzzy Surrogate Safety Metric (PFS), and the Critical Fuzzy Surrogate Safety Metric (CFS). To ensure comparability, all measures are calibrated with the same risk detection criterion. Four performance indicators, i.e., Prediction Accuracy, Timeliness, Robustness, and Efficiency are computed for all six SMoS and validated using naturalistic driving data. The strengths and weaknesses of all six measures are compared and analyzed elaborately. A key result is that not a single SMoS performs well in all performance dimensions. S-PDRF performs best in terms of Robustness but consumes the most time for computation. TTC is the most efficient but performs poorly in terms of Timeliness and Robustness. The proposed evaluation approach and the derived insights can support SMoS selection in active vehicle safety system design and traffic safety assessment.
... The probability of motion predictions is attributed to the underlying acceleration signal. The probability functions of acceleration variability can be estimated by treating acceleration signals as a random variable (Wagner et al., 2015). We assume acceleration variability to follow a normal distribution (Ko et al., 2010). ...
We present an approach to assess the risk taken by on-road vehicles within the framework of artificial field theory, envisioned for safety analysis and design of driving support/automation applications. Here, any obstacle (neighboring entity on the road) to the subject vehicle is treated as a finite scalar risk field that is formulated in the predicted configuration space of the subject vehicle. The driving risk estimate is the strength of the risk field at the subject vehicle's future location. This risk field is formulated as the product of two factors: collision probability and expected crash energy. The collision probability with neighboring vehicles is estimated based on probabilistic motion predictions. The risk can be assessed for a single time step or over multiple future time steps, depending on the required temporal resolution of the estimates. We verified the single step approach in three near-crash situations from a naturalistic dataset and in cut-in and hard-braking scenarios with simulation and showed the application of the multi-step approach in selecting the safest path in a lane-drop section. The risk descriptions from the proposed approach qualitatively reflect the narration of the situation and are in general consistent with Time To Collision. Compared to current surrogate measures of safety, the proposed risk estimate provides a better basis to assess the driving safety of an individual vehicle by considering the uncertainty over the future ambient traffic state and magnitude of expected crash consequences. The proposed driving risk model can be used as a component of intelligent vehicle safety applications and as a comprehensive surrogate measure for assessing traffic safety.
... In a safety assessment study, the surrogate safety metrics are extracted directly from the simulated trajectories and therefore the calibration might be restricted to microscopic variables [5]. High resolution trajectory datasets such as the one by Wagner et al. [42] provide opportunities for such calibration attempts. On the contrary, if one is interested in the performance evaluation of a steering control system, then the parameters related to submicroscopic variables should be calibrated. ...
Current lane-based microscopic traffic simulators combine car-following and lane changing logic to describe the (often discrete) lateral vehicle motion
on multi-lane road segments. However, the simulated lateral trajectories are physically unplausible and inside-lane behavior such as lane-keeping and curve negotiation cannot be modelled. In this work, we integrate lateral vehicle dynamics and yaw motion into a traffic simulation framework, aiming to describe lateral motion and vehicle interactions with more precision. The resulting framework consists of two coupled layers, an upper tactical level that plans maneuvers such as lane-changing; and a lower operational layer with a control module (steering and acceleration control) that operates in a closed loop with the bicycle model of vehicle dynamics. The feedback mechanism between the layers allows for dynamic trajectory re-planning. Unlike the microscopic traffic models, the proposed framework accounts for lateral vehicle dynamics and yaw motion; provides additional variables such as vehicle heading and front wheel steering angle; and is hence termed as submicroscopic. Case study results demonstrate the power of the framework to include lateral maneuvers such as curve negotiation, corrective steering, lane change abortion and fragmented lane changing. The framework was operationalized to model multi-lane traffic flow consisting of human-driven vehicles. At the macroscopic level, the traffic flow simulation can reproduce phenomena such as capacity drop. Thus the framework preserves the properties of the component models and at the same time describes the continuous 2-D planar movement of vehicles.
... Model fidelity can be adjusted through the quantisation step size ∆Q; blends between the coarse Traffic Cellular Automata and approaches based on differential equations can be selected. Other advantages are the modularity of the concept, the inherent randomness, the focus on observable variables and the lack of action points [71], [72]. ...
Microscopic traffic simulations capture the trajectories of individual drivers as responses to stimuli from their surroundings (i.e. other vehicles or road conditions). Mathematically, these models are usually designed with differential equations or as sets of integer-based rules. Since both approaches have disadvantages, we propose an in-between approach built with Timed Automata and Finite State Machines (FSM) to reproduce the human behaviour. The fundamental idea is to model the switches between a limited set of discrete acceleration levels with a FSM and derive all other trajectory features from there. The duration for which this constant acceleration is maintained is not fixed and is modelled by a (probabilistic) Timed Automaton (TA). With this arrangement, the complexity of CF behaviour can be represented with high computational efficiency in large-scale simulations without sacrificing model fidelity. It also captures the intrinsic randomness in human driving and enables the incorporation of directly observably statistical CF properties. This paper identifies the best-correlated stimulus-responses factors, analyses state machine properties of certain trajectory features and finally shows how several state machines can be hierarchically organised with the subsumption architecture.
... There, about 100 vehicles, most of them instrumented with sensors to measure position, speed, acceleration, distance, and speed-difference to the lead vehicles drove with about 1000 different drivers for three months in an area around Frankfurt/Main, Germany. A more detailed description of the data can be found else-where [12], here the data from the car-following episodes have been used. A first glimpse into the data can be gained from Fig. 1, where the distributions of the speed, the speed differences, the gaps, and the time headways are displayed. ...
Cellular automaton (CA) models of traffic flow are typically constructed to reproduce macroscopic features of traffic flow. Here, a few thoughts based on real car-following data are presented that show how to construct a discrete time / discrete space microscopic model of traffic flow. The question whether this can still be called a CA-model is left to the reader.
... Paper [90] presents an overview on resilience of interdependent networks to highlight the increasingly importance of analyzing the relations between systems as we move towards all sorts of smart technologies, like Smart Grids, Smart Cities, and Internet of Things (IOT). Paper [91] illustrates how to use data to estimate the efficiency of vehicle-to-vehicle and vehicle-to-infrastructure communication , the vehicles drove on pre-defined routes only, thereby covering an area of roughly 15 × 45 km around the German city of Frankfurt. The data have been recorded by four sensors, that were built into the vehicles: a GPS sensor, an acceleration sensor that was aligned with the cars geometry and therefore allowed the measurement of the longitudinal (in driving direction) and lateral acceleration (perpendicular to the driving direction), the distance and velocity difference to the lead vehicle by a radar/lidar sensor, and the speed from the traditional wheel sensors. ...
The ability to process and manage large data volumes has been proven to be not enough to tackle the current challenges presented by “Big Data”. Deep insight is required for understanding interactions among connected systems, space- and time- dependent heterogeneous data structures. Emergence of global properties from locally interacting data entities and clustering phenomena demand suitable approaches and methodologies recently developed in the foundational area of Data Science by taking a Complex Systems standpoint. Here, we deal with challenges that can be summarized by the question: “What can Complex Systems Science contribute to Big Data? ”. Such question can be reversed and brought to a superior level of abstraction by asking “What Knowledge can be drawn from Big Data?” These aspects constitute the main motivation behind this article to introduce a volume containing a collection of papers presenting interdisciplinary advances in the Big Data area by methodologies and approaches typical of the Complex Systems Science, Nonlinear Systems Science and Statistical Physics.
Extracted driving behavior of human driven vehicles can benefit the development of various applications like trajectory prediction or planning, abnormal driving detection, driving behavior classification, traffic simulation modeling, etc. In this paper, we focus on modeling human driving behavior in order to find simplifications for trajectory planning. Using a time-discrete kinematic bicycle model with the vehicle’s acceleration and steering rate as inputs, we model the human driven trajectories of an urban intersection drone dataset for different input sampling times. While most planning algorithms are using input sampling times below 0.33 s, we are able to model 98.2 % of the human driven trajectories of the investigated dataset with a sampling time of 0.6 s. Using longer input sampling times can result in smoother trajectories and longer planning horizons, and thus more efficient trajectories. In a next step, we analyze the correlations between the input of our model and the current state/last input. Such a priori knowledge could simplify common planning algorithms like model predictive control or tree-search based planners by limiting the action space of the ego-vehicle. We propose nonlinear transformations for steering rate and steering angle to represent correlations between speed, acceleration, steering angle and steering rate. In the transformed space the statistics are very well modeled by multivariate Gaussian distributions. Using a multivariate Gaussian, a fast usable behavior model is extracted which is independent of the environment.
We introduce a stochastic discrete automaton model to freeway traffic. Monte-Carlo simulations of the model show a transition from laminar traffic flow to start-stop-waves with increasing vehicle density, as is observed in real freeway traffic. For special cases analytical results can be obtained.
Unlabelled:
We introduce a novel implementation in ANSI C of the MINE family of algorithms for computing maximal information-based measures of dependence between two variables in large datasets, with the aim of a low memory footprint and ease of integration within bioinformatics pipelines. We provide the libraries minerva (with the R interface) and minepy for Python, MATLAB, Octave and C++. The C solution reduces the large memory requirement of the original Java implementation, has good upscaling properties and offers a native parallelization for the R interface. Low memory requirements are demonstrated on the MINE benchmarks as well as on large ( = 1340) microarray and Illumina GAII RNA-seq transcriptomics datasets.
Availability and implementation:
Source code and binaries are freely available for download under GPL3 licence at http://minepy.sourceforge.net for minepy and through the CRAN repository http://cran.r-project.org for the R package minerva. All software is multiplatform (MS Windows, Linux and OSX).
Since microscopic models are being heavily used in applications, the appropriate calibration and validation have been a recent concern. The contribution of this paper is to compare some of these models by calibrating and validating them with data from double-loop detectors on a multilane freeway. To simplify this task, the test of the models is done by simplifying the multilane reality to a simulation of only single lane. The results show that by simulating the multilane road with single lane models, calibration errors (Theil’s U, root mean squared error) of 14 % to 16 % can be obtained. A validation of the models –which means taking calibrated parameters of one data set to reproduce the other data sets– gives additional errors of about 0.5 to 2.5 percentage points. This is in good agreement with other calibration/validation approaches performed recently.
Microscopic simulation models are becoming increasingly important tools in modeling transport systems. There are a large number of available models used in many countries. the most difficult stage in the development and use of such models is the calibration and validation of the microscopic sub-models describing the traffic flow, such as the car following, lane changing and gap acceptance models. This difficulty is due to the lack of suitable methods for adapting models to empirical data. The aim of this paper is to present recent progress in calibratin a number of microscopic traffic flow models. By calibrating and validating various models using the same data sets, the models are directly comparable to each other. This sets the basis for a transparent benchmarking of those models. Furthermore, the advantages and disadvantages of each model can be analyzed better to develop a more realistic behavior of the simulated vehicles In this work various microscopic traffic flow models have been tested from a very microscopic point of view concerning the car-follwing behavior and gap-acceptance. The data used for calibration and validation is from car-following experiments performed in Japan in October 2001. The data have been collected by letting nine DGPS-equipped cars follow a lead car driving along a 3 km test track for about 15-30 minutes. So one gets the positions and speeds of each car in time intervals of 0.1 seconds. The experiment was repeated eight times letting the leading driver perform various driving in waves and emulating many acceleations/decelerations as they are typical at intersections. To minimize driver-dependent correlations between the data sets, the drivers were exchanged between the cars regularly after each experiment
In order to achieve autonomous operation of a vehicle in urban situations with unpredictable traffic, several realtime systems must interoperate, including environment perception, localization, planning, and control. In addition, a robust vehicle platform with appropriate sensors, computational hardware, networking, and software infrastructure is essential. We previously published an overview of Junior, Stanford's entry in the 2007 DARPA Urban Challenge. This race was a closed-course competition which, while historic and inciting much progress in the field, was not fully representative of the situations that exist in the real world. In this paper, we present a summary of our recent research towards the goal of enabling safe and robust autonomous operation in more realistic situations. First, a trio of unsupervised algorithms automatically calibrates our 64-beam rotating LIDAR with accuracy superior to tedious hand measurements. We then generate high-resolution maps of the environment which are subsequently used for online localization with centimeter accuracy. Improved perception and recognition algorithms now enable Junior to track and classify obstacles as cyclists, pedestrians, and vehicles; traffic lights are detected as well. A new planning system uses this incoming data to generate thousands of candidate trajectories per second, choosing the optimal path dynamically. The improved controller continuously selects throttle, brake, and steering actuations that maximize comfort and minimize trajectory error. All of these algorithms work in sun or rain and during the day or night. With these systems operating together, Junior has successfully logged hundreds of miles of autonomous operation in a variety of real-life conditions.
Identifying interesting relationships between pairs of variables in large data sets is increasingly important. Here, we present
a measure of dependence for two-variable relationships: the maximal information coefficient (MIC). MIC captures a wide range
of associations both functional and not, and for functional relationships provides a score that roughly equals the coefficient
of determination (R2) of the data relative to the regression function. MIC belongs to a larger class of maximal information-based nonparametric
exploration (MINE) statistics for identifying and classifying relationships. We apply MIC and MINE to data sets in global
health, gene expression, major-league baseball, and the human gut microbiota and identify known and novel relationships.
The development of autonomous vehicles for urban driving has seen rapid progress in the past 30 years. This paper provides a summary of the current state of the art in autonomous driving in urban environments, based primarily on the experiences of the authors in the 2007 DARPA Urban Challenge (DUC). The paper briefly summarizes the approaches that different teams used in the DUC, with the goal of describing some of the challenges that the teams faced in driving in urban environments. The paper also highlights the long-term research challenges that must be overcome in order to enable autonomous driving and points to opportunities for new technologies to be applied in improving vehicle safety, exploiting intelligent road infrastructure and enabling robotic vehicles operating in human environments.
The properties of vehicle time headways are fundamental in many traffic engineering applications, such as capacity and level of service studies on highways, unsignalized intersections, and roundabouts. The operation of modern vehicle-actuated traffic signals is based on the measurement of time headways in the arriving traffic flow. In addition, the vehicle generation in traffic flow simulation is usually based on some theoretical vehicle time headway model. The statistical analysis of vehicle time headways has been inadequate in three important aspects: 1) There has been no standard procedure to collect headway data and to describe their statistical properties. 2) The goodness-of-fit tests have been either powerless or infeasible. 3) Test results from multi-sample data have not been combined properly. A four-stage identification process is suggested to describe the headway data and to compare it with theoretical distributions. The process includes the estimation of the probability density function, the hazard function, the coefficient of variation, and the squared skewness and the kurtosis. The four-stage identification process effectively describes those properties of the distribution that are most helpful in selecting a theoretical headway model. One of the major problems in the headway studies has been the method for goodness-of-fit tests. The two most commonly used tests are the chi-square test and the nonparametric Kolmogorov-Smirnov test. The chi-square test is not very powerful. The nonparametric Kolmogorov-Smirnov test should be applied only, when the parameters of the distribution are known. If the parameters are estimated from the data, as in typical headway studies, the nonparametric Kolmogorov-Smirnov test gives too conservative results. These problems are addressed by parametric goodness-of-fit tests based on Monte Carlo methods. Another great problem has been the lack of theoretical foundation in dealing with multi-sample data. The headway data usually consist of several samples, and the null hypothesis is tested against each of them. Two methods are presented to strengthen the evidence of multi-sample tests: 1) The combined probability method gives a single significance probability based on several independent tests. 2) The moving probability method is used to describe the variation of combined probabilities against traffic volume. These methods were applied to time headway data from Finnish two-lane two-way roads. The independence of consecutive headways was tested using autocorrelation analysis, runs tests and goodness-of-fit tests for the geometric bunch size distribution. The results indicate that the renewal hypothesis should not be accepted in all traffic situations. This conclusion is partly supported by a further analysis of previous studies. Five theoretical distributions were tested for goodness of fit: the negative exponential distribution, the shifted exponential distribution, the gamma distribution, the lognormal distribution and the semi-Poisson distribution. None of these passed the tests. In the parameter estimation the maximum likelihood method was preferred. For distributions having a location (threshold) parameter, a modified maximum likelihood method was shown to give good estimates. The proposed procedures give a scientific foundation to identify and estimate statistical models for vehicle time headways, and to test the goodness of fit. It is shown that the statistical methods in the analysis of vehicle headways should be thoroughly revised following the guidelines presented here. Publication / Helsinki University of Technology, Transportation Engineering, ISSN 0781-5816; 87
Since the subject of traffic dynamics has captured the interest of physicists, many astonishing effects have been revealed and explained. Some of the questions now understood are the following: Why are vehicles sometimes stopped by so-called ``phantom traffic jams'', although they all like to drive fast? What are the mechanisms behind stop-and-go traffic? Why are there several different kinds of congestion, and how are they related? Why do most traffic jams occur considerably before the road capacity is reached? Can a temporary reduction of the traffic volume cause a lasting traffic jam? Under which conditions can speed limits speed up traffic? Why do pedestrians moving in opposite directions normally organize in lanes, while similar systems are ``freezing by heating''? Why do self-organizing systems tend to reach an optimal state? Why do panicking pedestrians produce dangerous deadlocks? All these questions have been answered by applying and extending methods from statistical physics and non-linear dynamics to self-driven many-particle systems. This review article on traffic introduces (i) empirically data, facts, and observations, (ii) the main approaches to pedestrian, highway, and city traffic, (iii) microscopic (particle-based), mesoscopic (gas-kinetic), and macroscopic (fluid-dynamic) models. Attention is also paid to the formulation of a micro-macro link, to aspects of universality, and to other unifying concepts like a general modelling framework for self-driven many-particle systems, including spin systems. Subjects such as the optimization of traffic flows and relations to biological or socio-economic systems such as bacterial colonies, flocks of birds, panics, and stock market dynamics are discussed as well. Comment: A shortened version of this article will appear in Reviews of Modern Physics, an extended one as a book. The 63 figures were omitted because of storage capacity. For related work see http://www.helbing.org/
Four headway models of increasing generality are considered from three points of view. We discuss (i) the value of the models for use as arrival processes in stochastic model building, (ii) some traffic situations where it is known from theoretical considerations, that the models are appropriate, and (iii) empirical evidence to support the models. It is shown that the two most general models have a sound rationale from viewpoints (ii) and (iii) and thus offer a realistic arrival assumption for stochastic modelling. Also, it is shown in two worked problems that these general models do not lead to mathematical difficulties when used as arrival processes. We conclude that these models offer a balanced compromise between realism and tractability for the stochastic model builder.
The world's data is growing more than 40% annually. Coupled withexponentially growing computing horsepower, this provides us withunprecedented basis for 'learning' useful things from the data throughstatistical induction without material human intervention and acting onthem. Philosophers have long debated the merits and demerits ofinduction as a scientific method, the latter being that conclusions arenot guaranteed to be certain and that multiple and numerous models canbe conjured to explain the observed data. I propose that 'big data'brings a new and important perspective to these problems in that itgreatly ameliorates historical concerns about induction, especially ifour primary objective is prediction as opposed to causal modelidentification. Equally significantly, it propels us into an era ofautomated decision making, where computers will make the bulk ofdecisions because it is infeasible or more costly for humans to do so.In this paper, I describe how scale, integration and most importantly,prediction will be distinguishing hallmarks in this coming era of DataScience.' In this brief monograph, I define this newly emerging fieldfrom business and research perspectives.
A time-discrete stochastic harmonic oscillator is presented as a model of human
car-following behaviour. This describes especially the non-continuous control of a human
driver – acceleration changes from time to time at so called action-points and is kept
constant in between. Analytical results can be derived which allow to classify the
different types of motion possible within this approach. These results show that with
weaker control by the human, unstable behaviour of the oscillator becomes more likely.
This is in line with common understanding about the causes of accidents. Finally, since
even the stochastic behaviour of this model is in parts analytically tractable, the width
of the speed-difference and distance fluctuations can be expressed as function of the
model’s parameter. This allows a fresh view on empirical car-following data and the
identification of parameters from real data in the context of the theory presented
here.
This work presents strong evidence that human car-following behaviour can be described by a linear model with no more than three parameters to an amazing degree of precision. From this result it can be inferred that any microscopic traffic flow model can be composed of the car-following behaviour plus a couple of rules that fixes boundaries of the behaviour in terms of limitations to speed, acceleration, and safety.
These limitations, however, usually have a clear physical meaning and understanding and are the only non-linearities needed to built a microscopic traffic flow model.
This contribution reports a recently recorded data-set that helps to understand the car-following process better. Since the empirical basis of most traffic flow models can be called weak, these findings may help to design better models. They demonstrate, that the process of car-following seems to have a very interestic stochastic dynamics. Especially, and different from most of the existing models the data show clearly that car following cannot be described by a noisy fixed point dynamics. This is because the acceleration of the cars is smooth and roughly constant for a certain time, with fast changes to a new value at so called action points.
Furthermore, the data can be used for calibration and validation purposes of the various models. This has been done with very interesting results indicating that all the models tested behave very similar and cannot describe the data better than with 15 % difference between models and data.
Many-particle simulations of vehicle interactions have been quite successful in the qualitative reproduction of observed traffic patterns. However, the assumed interactions could not be measured, as human interactions are hard to quantify compared to interactions in physical and chemical systems. We show that progress can be made by generalizing a method from equilibrium statistical physics we learned from random matrix theory. It allows one to determine the interaction potential via distributions of the netto distances s of vehicles. Assuming power-law interactions, we find that driver behavior can be approximated by a forwardly directed 1/s potential in congested traffic, while interactions in free traffic are characterized by an exponent of α≈4. This is relevant for traffic simulations and the assessment of telematic systems.
Certain aspects of traffic flow measurements imply the existence of a phase transition. Models known from chaos and fractals, such as nonlinear analysis of coupled differential equations, cellular automata, or coupled maps, can generate behavior which indeed resembles a phase transition in the flow behavior. Other measurements point out that the same behavior could be generated by geometrical constraints of the scenario. This paper looks at some of the empirical evidence, but mostly focuses on different modeling approaches. The theory of traffic jam dynamics is reviewed in some detail, starting from the well-established theory of kinematic waves and then veering into the area of phase transitions. One aspect of the theory of phase transitions is that, by changing one single parameter, a system can be moved from displaying a phase transition to not displaying a phase transition. This implies that models for traffic can be tuned so that they display a phase transition or not.
This paper focuses on microscopic modeling, i.e., coupled differential equations, cellular automata, and coupled maps. The phase transition behavior of these models, as far as it is known, is discussed. Similarly, fluid-dynamical models for the same questions are considered. A large portion of this paper is given to the discussion of extensions and open questions, which makes clear that the question of traffic jam dynamics is, albeit important, only a small part of an interesting and vibrant field. As our outlook shows, the whole field is moving away from a rather static view of traffic toward a dynamic view, which uses simulation as an important tool.
Thesis (Sc. D.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 1999. Includes bibliographical references (p. 185-189).
A very simple “car-following” rule is proposed wherein, if an nth vehicle is following an (n−1)th vehicle on a homogeneous highway, the time-space trajectory of the nth vehicle is essentially the same as the (n−1)th vehicle except for a translation in space and in time. It seems that such a rule is at least as accurate as any of the more elaborate rules of car-following that have been proposed over the last 50 years or so. Actually, the proposed model could be interpreted as a special case of existing models but with fewer parameters and a different logic. At least this should form a reasonable starting point for investigating other phenomena.
We present a dynamical model of traffic congestion based on the equation of motion of each vehicle. In this model, the legal velocity function is introduced, which is a function of the headway of the preceding vehicle. We investigate this model with both analytic and numerical methods. The stability of traffic flow is analyzed, and the evolution of traffic congestion is observed with the development of time.
In this paper, we give an elaborate and understandable review of traffic cellular automata (TCA) models, which are a class of computationally efficient microscopic traffic flow models. TCA models arise from the physics discipline of statistical mechanics, having the goal of reproducing the correct macroscopic behaviour based on a minimal description of microscopic interactions. After giving an overview of cellular automata (CA) models, their background and physical setup, we introduce the mathematical notations, show how to perform measurements on a TCA model's lattice of cells, as well as how to convert these quantities into real-world units and vice versa. The majority of this paper then relays an extensive account of the behavioural aspects of several TCA models encountered in literature. Already, several reviews of TCA models exist, but none of them consider all the models exclusively from the behavioural point of view. In this respect, our overview fills this void, as it focusses on the behaviour of the TCA models, by means of time-space and phase-space diagrams, and histograms showing the distributions of vehicles' speeds, space, and time gaps. In the report, we subsequently give a concise overview of TCA models that are employed in a multi-lane setting, and some of the TCA models used to describe city traffic as a two-dimensional grid of cells, or as a road network with explicitly modelled intersections. The final part of the paper illustrates some of the more common analytical approximations to single-cell TCA models.
In the so-called "microscopic" models of vehicular traffic, attention is paid explicitly to each individual vehicle each of which is represented by a "particle"; the nature of the "interactions" among these particles is determined by the way the vehicles influence each others' movement. Therefore, vehicular traffic, modeled as a system of interacting "particles" driven far from equilibrium, offers the possibility to study various fundamental aspects of truly nonequilibrium systems which are of current interest in statistical physics. Analytical as well as numerical techniques of statistical physics are being used to study these models to understand rich variety of physical phenomena exhibited by vehicular traffic. Some of these phenomena, observed in vehicular traffic under different circumstances, include transitions from one dynamical phase to another, criticality and self-organized criticality, metastability and hysteresis, phase-segregation, etc. In this critical review, written from the perspective of statistical physics, we explain the guiding principles behind all the main theoretical approaches. But we present detailed discussions on the results obtained mainly from the so-called "particle-hopping" models, particularly emphasizing those which have been formulated in recent years using the language of cellular automata. Comment: 170 pages, Latex, figures included
Traffic Simulation and Data -Validation Methods and Applications
- Winnie Daamen
- Christine Buisson
- Serge P Hoogendoorn
Winnie Daamen, Christine Buisson, and Serge P. Hoogendoorn, editors.
Traffic Simulation and Data -Validation Methods and Applications. Taylor
and Francis, CRC Press, 2014.
R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing
- R Development
- Core Team
R Development Core Team. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria,
2011. ISBN 3-900051-07-0.
Simulation of bottlenecks in single lane traffic flow
- W Helly
W. Helly. Simulation of bottlenecks in single lane traffic flow. In Proceedings
of the symposium on theory of traffic flow., pages 207-238, 1959.