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Experimental properties of complexity in traffic flow
Abstract
Experimental investigations of a complexity in traffic flow are presented. It is shown that this complexity is linked to space-time transitions between three qualitative different kinds of traffic: ``free'' traffic flow, ``synchronized'' traffic flow, and traffic jams. Peculiarities of ``synchronized'' traffic flow and jams that are responsible for a complex behavior of traffic are found.
... According to traffic flow data analyzed recently by Kerner & Rehborn [11,12,13], Kerner [14,15], and also Neubert et al. [16] there are three distinctive states of multilane traffic flow, the free flow (F ), the synchronized mode (S), and wide moving jams (J). This endows the multilane traffic flow with a variety of properties. ...
... Both of them are of the first order, i.e. exhibiting breakdown, hysteresis, and nucleation effects [13]. The present paper focuses its attention on a unique property of the synchronized mode itself, its complexity [12]. In contrast to the free flow, the synchronized mode matches a two-dimensional domain on the ρq-plane rather than a curve on it (Fig. 1). ...
... In this regard the synchronized mode is also referred to as a widely scattered traffic state for which a fundamental diagram in the form of a one-dimensional curve did not exist. [12] showing possible states of the free flow and the synchronized mode in the ρq-plane. ...
The present paper proposes a novel interpretation of the widely scattered states (called synchronized traffic) stimulated by Kerner's hypotheses about the existence of a multitude of metastable states in the fundamental diagram. Using single vehicle data collected at the German highway A1, temporal velocity patterns have been analyzed to show a collection of certain fragments with approximately constant velocities and sharp jumps between them. The particular velocity values in these fragments vary in a wide range. In contrast, the flow rate is more or less constant because its fluctuations are mainly due to the discreteness of traffic flow. Subsequently, we develop a model for synchronized traffic that can explain these characteristics. Following previous work (I.A.Lubashevsky, R.Mahnke, Phys. Rev. E v. 62, p. 6082, 2000) the vehicle flow is specified by car density, mean velocity, and additional order parameters h and a that are due to the many-particle effects of the vehicle interaction. The parameter h describes the multilane correlations in the vehicle motion. Together with the car density it determines directly the mean velocity. The parameter a, in contrast, controls the evolution of h only. The model assumes that a fluctuates randomly around the value corresponding to the car configuration optimal for lane changing. When it deviates from this value the lane change is depressed for all cars forming a local cluster. Since exactly the overtaking manoeuvres of these cars cause the order parameter a to vary, the evolution of the car arrangement becomes frozen for a certain time. In other words, the evolution equations form certain dynamical traps responsible for the long-time correlations in the synchronized mode.
... The theoretical equilibrium flow rate can therefore be computed as q = ρv ∞ (number of vehicles passing a location per unit time). As shown in Figure 1(b), this model successfully reproduces the three phases of traffic [22,23]. Specifically, the flow rate increases from 0 to q * ≡ max(q) as ρ increases from 0 to ρ * , representing the free flow phase; the flow rate then decreases as ρ increases to ρ jam ≡ arg min ρ>0 q(ρ) = 0, representing the synchronized flow; the system enters the traffic jam phase when ρ = ρ jam , as the headway of each vehicle becomes smaller than the minimal headway d. ...
... Additionally, ρ jam = 134 vehicles per kilometer. These values are in good agreement with prior experimental results [22,23]. ...
This paper develops a computational framework based on a car-following model to study traffic instability and lane changes. Building upon Newell's classical first-order car-following model, we show that, both analytically and numerically, there exists a vehicle-density-dependent critical reaction time that determines the stability of single-lane traffic. Specifically, perturbations to the equilibrium system decay with time for low reaction time and grow for high reaction time. This critical reaction time converges to Newell's original result in the continuum limit. Additionally, we propose a psychology-based lane-changing mechanism that builds a quantitative connection between the driver's psychological factor (frustration level) and the driving condition. We show that our stochastic lane-changing model can faithfully reproduce interesting phenomena like load-balancing of different lanes. Our model supports the result that more frequent lane changes only marginally benefit the driver's overall velocity.
... The three phases of this theory are "free traffic", "wide moving jams", and "synchronized flow". While a characteristic feature of "synchronized flow" is the wide scattering of flow-density data (Kerner and Rehborn, 1996b), many microscopic and macroscopic traffic models neglect noise effects and the heterogeneity of drivervehicle units for the sake of simplicity, and they possess a unique flow-density or speed-distance relationship under stationary and spatially homogeneous equilibrium conditions. Therefore, Appendix A discusses some issues concerning the wide scattering of congested traffic flows and how it can be treated within the framework of such models. ...
... The source of probably most controversies in traffic theory is an observed spatiotemporal structure called the "pinch effect" or "general pattern" (Kerner and Rehborn, 1996b), see Kerner (2004) for details and Fig. 1 of Schönhof and Helbing (2009) for a typical example of the spatiotemporal evolution. From the perspective of the above list, this pattern relates to stylized facts 6 and 8, i.e., it has the following features: (i) relatively stationary congested traffic (pinch region) near the downstream front, (ii) small perturbations that grow to oscillatory structures as they travel further upstream, (iii) some of these structures grow to form "wide jams", thereby suppressing other small jams, which either merge or dissolve. ...
Despite the availability of large empirical data sets and the long history of traffic modeling, the theory of traffic congestion on freeways is still highly controversial. In this contribution, we compare Kerner's three-phase traffic theory with the phase diagram approach for traffic models with a fundamental diagram. We discuss the inconsistent use of the term "traffic phase" and show that patterns demanded by three-phase traffic theory can be reproduced with simple two-phase models, if the model parameters are suitably specified and factors characteristic for real traffic flows are considered, such as effects of noise or heterogeneity or the actual freeway design (e.g. combinations of off- and on-ramps). Conversely, we demonstrate that models created to reproduce three-phase traffic theory create similar spatiotemporal traffic states and associated phase diagrams, no matter whether the parameters imply a fundamental diagram in equilibrium or non-unique flow- density relationships. In conclusion, there are different ways of reproducing the empirical stylized facts of spatiotemporal congestion patterns summarized in this contribution, and it appears possible to overcome the controversy by a more precise definition of the scientific terms and a more careful comparison of models and data, considering effects of the measurement process and the right level of detail in the traffic model used.
... The effect of bottlenecks on a flow in a lane is relevant in many applied contexts such as traffic [1,2] and pedestrian [3,4,5,6,7] flows, motion in biological systems [9,8], but also in more abstract problems such as the study of the effect of blockage in stationary states [10,11,12] or the effect of obstacles on two-dimensional particle flows [13,14,15]. ...
... In Z (1) L,N the sum extends to the finite value T , thus the factorial can be approximated as The estimate of the sum in (3.10) is more delicate since the index k can be arbitrarily large when the thermodynamic limit is considered. To evaluate the behavior of the partition function in the above limit, it is useful to introduce the function I(k) by rewriting (3.10) as Z (2) L,N = ∑ N k=0 exp{LI(k)}. ...
We investigate the appearance of trapping states in pedestrian flows through bottlenecks as a result of the interplay between the geometry of the system and the microscopic stochastic dynamics. We model the flow trough a bottleneck via a Zero Range Process on a one dimensional periodic lattice. Particle are removed from the lattice sites with rates proportional to the local occupation numbers. The bottleneck is modelled by a particular site of the lattice where the updating rate saturates to a constant value as soon as the local occupation number exceeds a fixed threshold. We show that, for any finite value of such threshold, the stationary particle current saturates to the limiting bottleneck rate when the total particle density in the system exceeds the bottleneck rate itself.
... These traits make complex systems unique in their ability to display emergent properties, in which the collective interactions can give rise to novel, unexpected, and self-organised phenomena that cannot be easily predicted by examining the individual parts in isolation. Examples of this abound in ecology [1], economics [2], neuroscience [3], and even in situations from everyday life such as traffic jams [4]. ...
... 3. Repeat the previous step N times for many sampled q i , obtaining a null distribution of each PID atom. 4. The relative amount of synergistic, unique, or redundant information of p can be quantified by tak- synergy-dominated, with large values of either redundancy or unique information becoming less likely. ...
A key feature of information theory is its universality, as it can be applied to study a broad variety of complex systems. However, many information-theoretic measures can vary significantly even across systems with similar properties, making normalisation techniques essential for allowing meaningful comparisons across datasets. Inspired by the framework of Partial Information Decomposition (PID), here we introduce Null Models for Information Theory (NuMIT), a null model-based non-linear normalisation procedure which improves upon standard entropy-based normalisation approaches and overcomes their limitations. We provide practical implementations of the technique for systems with different statistics, and showcase the method on synthetic models and on human neuroimaging data. Our results demonstrate that NuMIT provides a robust and reliable tool to characterise complex systems of interest, allowing cross-dataset comparisons and providing a meaningful significance test for PID analyses.
... Moreover, we use an anthropomorphic design for CAVs; that is, all car-following behaviors for different vehicles (i.e., RVs, CVs, and CAVs) were described by the same car-following model (Talebpour and Mahmassani, 2016;Yao et al., 2021). In the existing research, the car-following model can be divided into five types: stimulus-response model (Helbing, 2001), safe distance model (Kerner and Rehborn, 1996), social force model (Kerner and Klenov, 2003), optimal velocity model (Kerner, 2002(Kerner, , 1998Kerner and Rehborn, 1996) and low-order linear model (Helbing, 2001). As a kind of social force model, the Intelligent Driver Model (IDM) (Kesting et al., 2010;Treiber et al., 2000) can well capture the driving habits of experienced drivers and has a wide range of applications. ...
... Moreover, we use an anthropomorphic design for CAVs; that is, all car-following behaviors for different vehicles (i.e., RVs, CVs, and CAVs) were described by the same car-following model (Talebpour and Mahmassani, 2016;Yao et al., 2021). In the existing research, the car-following model can be divided into five types: stimulus-response model (Helbing, 2001), safe distance model (Kerner and Rehborn, 1996), social force model (Kerner and Klenov, 2003), optimal velocity model (Kerner, 2002(Kerner, , 1998Kerner and Rehborn, 1996) and low-order linear model (Helbing, 2001). As a kind of social force model, the Intelligent Driver Model (IDM) (Kesting et al., 2010;Treiber et al., 2000) can well capture the driving habits of experienced drivers and has a wide range of applications. ...
With the development of connected vehicles and automated driving technologies, connected automated vehicle (CAV) can not only provide its own trajectory, but also obtain the exact trajectories of vehicles within its detection range. However, trajectory data collected by this method is minimal due to the low penetration rates (PRs) of CAVs, and fail to capture the characteristics of traffic flow. This study proposes a fully sampled trajectory reconstruction method for mixed traffic flow with regular vehicles (RVs), connected vehicles (CVs), and CAVs based on car-following behavior. Firstly, considering the minimum safety distance constraints between vehicles, an optimization model for minimizing the impact on the acceleration of the known vehicles is developed to obtain the number of inserted RVs. Secondly, the speed of the inserted RVs is estimated based on the traffic flow model. Then, an optimization model is proposed to determine the position of each inserted RV. Finally, numerical simulation is designed to investigate the influence of traffic density and PRs of CAVs and CVs. Results show that the proposed method can better reconstruct the vehicle trajectory on the freeway under the different traffic densities in a congested state. The MAPE of the number and position of inserted RVs is less than 10.7% and 0.37%, respectively. In addition, the proposed method performs well even if the PRs of CAVs and CVs are extremely low.
... This section aims at presenting congestion patterns according to their characteristics to receive a more accurate ground truth. Kerner et al. [10] [11] [12] [13] distinguish between three traffic phases: free-flow, synchronized flow, and wide moving jam, two of which involve congested areas. Helbing et al. [14] extended the prevailing traffic conditions in congestion to five phases. ...
... Congestion type hot spots based on Floating Car Data (FCD)[13] ...
This paper presents an approach that increases the resilience of a freeway network while
differentiating patterns of freeway congestion events and investigating hot spots of each
pattern both spatially and temporally. Based on an automated pattern recognition, an
emerging congestion event can be identified and classified into one of four predefined
congestion patterns. Determining the spatial and temporal extensions of several congestion events, hot spots of each pattern can be localized. Additionally, possible traffic management and control measures are compiled and evaluated by expert statements to mitigate and dissolve the found congestion hot spots. This approach provides a helpful toolbox for freeway operators to classify occurring congestion into predefined categories and to select appropriate countermeasures based on the hot spot analysis to increase the resilience of the overall system. By applying the presented methodology, optimized traffic information is provided to the operator in time-critical situations, which enables an improved decisionmaking process in traffic management. The data base is three large-scale data sets from stationary detectors, vehicle re-identification sensors, and floating car data collected on a German freeway in 2019.
... However, those traditional models have been questioned in the last two decades. Based on the empirical data [36][37][38][39][40][41], Kerner claimed that jam (J) should be regarded as an independent phase, in which the average speed is very low (~0 km/h) and the density is very high (~ρ jam ). Congested flow excluding jam is named as synchronized flow (S). Figure 1 shows an example of the NGSIM trajectory data on Lane 1 (the leftmost lane) and Lane 4 on the US 101 highway. ...
Traffic breakdown refers to the first-order transition from free flow to synchronized flow. It is characterized by a rapid decrease in speed, suddenly increasing density, and abruptly plummeting capacity in most of the relevant observations. To understand its cause and model its empirical observations, a multi-regime car-following model is proposed, which classifies the car-following state into four regimes, i.e., Free driving, High-speed following, Low-speed following, and Emergency. Simulation results demonstrate that traffic breakdown and spontaneous jam formation can be reproduced simultaneously by the new model. Experimental verification has shown that the new model can successfully simulate the observed concave growth pattern of traffic oscillations.
... Based on the empirical observations accumulated on highways in different countries for nearly 8 decades (see for instance the Refs. (Pedersen and et.al., 2011;Kerner and Rehborn, 1996;Daganzo, 2002;Cassidy, 1998)), one important empirical feature of the so called fundamental diagram of traffic flow is the inverse-λ shape (Edie, 1961;Drake and Schofer, 1967;Payne, 1984;Hall et al., 1992) accompanying with capacity drop (Banks, 1990(Banks, , 1991Hall, 1991). The inverse-λ implies discontinuity of the flow as a function of vehicle density which occurs in the vicinity of the maximum of the flow. ...
In this work, we show that the inverse- shape in the fundamental diagram of traffic flow can be produced dynamically by a simple nonlinear mesoscopic model with stochastic noises. The proposed model is based on the gas-kinetic theory of the traffic system. In our approach, the nonlinearity leads to the coexistence of different traffic states. The scattering of the data is thus attributed to the noise terms introduced in the stochastic differential equations and the transition among the various traffic states. Most importantly, the observed inverse- shape and the associated sudden jump of physical quantities arise due to the effect of stochastic noises on the stability of the system. The model parameters are calibrated, and a qualitative agreement is obtained between the data and the numerical simulations.
... There is no general agreement if measurements show 1-phase/1-state or 2-phase/3-state traffic (or possibly even three phases (22)). There is some evidence for hysteresis in Germany (23), manifesting itself in transitions from high to lower flow values at the same density. ...
There is discussion if traffic displays multiple phases (e.g. laminar, jammed, synchronized) or not. This paper presents evidence that a stochastic car following model, by changing one of its parameters, can be moved from showing two phases (laminar and jammed) to showing only one phase. Models with two phases show three states: two being homogeneous states corresponding to each phase, and a third state which consists of a mix between the two phases (phase coexistence). Although the gas-liquid analogy to traffic models has been widely discussed, no traffic-related model ever displayed a completely understood stochastic version of that transition. Having a stochastic model is however important to understand the potentially probabilistic nature of the transition. Most importantly, if indeed 2-phase models describe certain aspects correctly, then this leads to predictions for breakdown probabilities. Alternatively, if 1-phase models describe these aspects better, then there is no breakdown.Interestingly, such 1-phase models can still allow for jam formation on small scales, which may give the impression of having a 2-phase dynamics.
... In the meantime, empirical observations indicate that there are different phases of traffic. According to Kerner [1][2][3][4][5][6][7][8], these are (see Fig. 1): ...
Traffic flow at low densities (free traffic) is characterized by a quasi-one-dimensional relation between traffic flow and vehicle density, while no such fundamental diagram exists for `synchronized' congested traffic flow. Instead, a two-dimensional area of widely scattered flow-density data is observed as a consequence of a complex traffic dynamics. For an explanation of this phenomenon and transitions between the different traffic phases, we propose a new class of molecular-dynamics-like, microscopic traffic models based on times to collisions and discuss the properties by means of analytical arguments. Similar models may help to understand the laminar and turbulent phases in the dynamics of stock markets as well as the transitions among them.
... Kerner's traffic flow theory (Kerner and Rehborn, 1996;Kerner, 2001Kerner, , 2004Kerner et al., 2004;Kerner, 2009;Palmer et al., 2011) describes the phenomenon of traffic congestion in detail. This theory distinguishes three phases of traffic: free-flow, synchronized flow, and wide moving jam. ...
... Emerging freeway congestion on the roads follow certain patterns and can therefore be classified into only few types. A basic and well-known traffic state classification is the three-phase traffic theory developed by Kerner et al. [15]- [20]. This theory distinguishes three phases of traffic: freeflow, synchronized flow, and wide moving jam. ...
This paper investigates the detection rate of various freeway congestion patterns and compares them across different traffic sensor technologies. Congestion events can be categorized into multiple types, ranging from short traffic disruptions (referred to as Jam Wave) to Stop and Go patterns and severe congestion scenarios like Wide Jam. We analyze multiple traffic data sets, including speed data from loop detectors, travel time measurements from Bluetooth sensors, and floating car data (FCD) collected from probe vehicles. Each combination of congestion pattern and detection technology is thoroughly examined and evaluated in terms of its capability and suitability for identifying specific traffic congestion patterns. For our experimental site, we selected the freeway A9 in Germany, which spans a length of 157 km . Our findings reveal that Bluetooth sensors, which record travel times between two locations, are barely suited for detecting short traffic incidents such as Jam Waves due to their downstream detection direction, contrasting with the upstream congestion propagation. Segment-based speed calculations prove more effective in identifying significant congestion events. FCD tend to recognize Stop and Go patterns more frequently than loop detectors but often underestimate severe congestion due to their sensitivity to penetration rates and data availability.
... Millimetre wave radar equipment along the northern cross channel is deployed at 2 points in the lower channel, and the deployment points are installed in the western section of the northern cross channel lower levels at K4+733 and K4+908 as shown in Fig. 1 Table 1 and Table 2, respectively. [34][35] . At present, mainstream traffic congestion is often divided into 3-5 states according to the congestion index currently applied by AMAP, which uses a congestion delay index to divide the traffic state into 4 states: smooth, slow, congested and severely congested. ...
Lane changing behavior is a more complex driving behavior among driving behaviors. The lane changing behavior of drivers may exacerbate congestion, however, driver behavioral characteristics are difficult to be accurately acquired and quantified, and thus tend to be simplified or ignored in existing lane changing models. In this paper, the Bik-means clustering algorithm is used to analyze the urban road congestion state discrimination method. Then, simulated driving scenarios under different traffic congestion conditions for simulated driving tests. Through the force feedback system and infrared camera, the data of driver lane-changing behaviors at different traffic congestion levels are obtained separately, and the definitions of the starting and ending points of a vehicle changing lanes are determined. Furthermore, statistical analysis and discussion of key feature parameters including driver lane-changing behavior data and visual data under different levels of traffic congestion were conducted. It is found that the average lane change intention times in each congestion state are 2s, 4s, 6s and 7s, while the turn signal duration and the number of rearview mirror observations have similar patterns of change to the data on lane-changing intention duration. Moreover, drivers’ pupil diameters become smaller during the lane-changing intention phase, and then relatively enlarge during lane-changing, the range of pupil variation is roughly 3.5-4 mm. The frequency of observing the vehicle in front of the target lane increased as the level of congestion increased, and the frequency of observation in the driver's mirrors while changing lanes approximately doubled compared to driving straight ahead, and this ratio increased as the level of congestion increased.
... Furthermore, jamming is a natural phenomenon that illustrates spontaneous evolution from a freely flowing state to a jammed state with no change in the external forcing. Similar issues are important for understanding the flow of suspensions and emulsions [19][20][21][22][23][24][25][26] through constrictions, where the hydrodynamics of the flowing fluid as well as the capillary effects must be taken into account, e.g., the flow of vortices through an array of pinning sites in superconductors [27], as well as automotive [28] and pedestrian [29] traffic. In spite of many simulations [17,30] and experiments in both two-and three-dimensional hoppers [12,18,31,32], the ability to predict or control clogging is still lacking [33]. ...
... (Sciences and Board 2022) employed six levels of service (LOS) to represent different traffic flow levels. (Kerner and Rehborn 1996) proposed a three-phase theory with three phases and four phase transitions. (Courbon and Leclercq 2011) created the fundamental diagram, which depicts the relationship among space-mean flow, density, and speed. ...
The utilization of traffic conflict indicators is crucial for assessing traffic safety, especially when the crash data is unavailable. To identify traffic conflicts based on traffic flow characteristics across various traffic states, we propose a framework that utilizes unsupervised learning to automatically establish surrogate safety measures (SSM) thresholds. Different traffic states and corresponding transitions are identified with the three-phase traffic theory using high-resolution trajectory data. Meanwhile, the SSMs are mapped to the corresponding traffic states from the perspectives of time, space, and deceleration. Three models, including k-means, GMM, and Mclust, are investigated and compared to optimize the identification of traffic conflicts. It is observed that Mclust outperforms the others based on the evaluation metrics. According to the results, there is a variation in the distribution of traffic conflicts among different traffic states, wide moving jam (phase J) has the highest conflict risk, followed by synchronous flow (phase S), and free flow (phase F). Meanwhile, the thresholds of traffic conflicts cannot be fully represented by the same value through different traffic states. It reveals that the heterogeneity of thresholds is exhibited across traffic state transitions, which justifies the necessity of dynamic thresholds for traffic conflict analysis.
... The synchronized state includes three sub-classes: nearly both stationary and homogeneous state, state where average speed is stable while density noticeably changes, and essentially nonstationary and nonhomogeneous state. Following the work of Kerner and Rehborn (15), Banks (16) further investigated the characteristics of congested flow and reported that there may be a congested-flow regime for which the slopes of the flow-concentration transferences are not merely random but rather predominately positive. ...
Reliable real-time traffic state identification (TSI) provides key support for traffic management and control. Although substantial efforts have been devoted to TSI, considering the high dynamics and stochasticity of traffic flows, there remain challenges in providing reliable and consistent TSI results, especially in online network–level applications. In this study, we propose a time series clustering-based offline-online modeling framework for reliable TSI using high-resolution traffic data. Specifically, in the proposed framework, the offline module extracts representative traffic state patterns from massive historical data, which serve as the state references in the online module when performing real-time TSI with streaming information. Instead of point data, the proposed framework uses high-resolution traffic data in the form of time series, providing rich information on traffic flows and details on their short-term fluctuations and stable long-term trends. In the offline module, considering the fuzziness of traffic states, we introduce a fuzzy c-means based clustering method for offline traffic flow series clustering and traffic state pattern extraction, within which the dynamic time warping algorithm is adopted for measuring the similarity between different time series, and the optimal number of clusters is determined by a proposed critical segment–based method to reach consistent TSI in network-wide applications. In the online module, a dynamic programming–based real-time TSI approach is developed to produce reliable and smooth identification results. Extensive numerical experiments on a 20-mi-long freeway corridor in California, USA, were performed to validate the proposed framework. Results demonstrate the effectiveness of the proposed framework.
... Particularly, regarding microscopic models, Gipps [2] proposed a car-following model and used it to reproduce some characteristics of real trafc fow, while Nagel and Schreckenberg [3] constructed a basic cellular automaton trafc fow model (i.e., the NaSch model). Moreover, Kerner and Rehborn [4,5] developed the threephase trafc fow theory based on real trafc observation data, and a number of similar models were put forward based on this theory [6,7]. In addition, the rapid development of technology gave birth to the concept of intelligent vehicles (e.g., connected and autonomous vehicles), and such vehicles have entered specifc markets. ...
On-ramps are considered to be one of the common traffic bottlenecks. In order to improve the operation efficiency of on-ramps, scholars worldwide have proposed various vehicle merging strategies. In this study, we designed different rules to express three collaborative strategies and studied their impact on on-ramp systems. Cellular automata models were used to simulate the systems under different situations, and the average speed and traffic flow rate of both the main roads and ramps were analyzed. The results show that (1) all the three merging strategies give excessive “priority” to the merging vehicle, leading to a severe reduction in the traffic performance of the main road; (2) nevertheless, these strategies have different effects on the entire system with a one-lane or two-lane main road. Due to the lane-changing behavior, the system with a two-lane main road has more advantages than that featured with a one-lane road, making the former system performing better than the latter under the same strategies; (3) the vehicles on the ramp and main road affect each other, and as the vehicle entering probabilities become large, the traffic flow rate on the main road decreases whereas that on the ramp increases. However, the effect is not unlimited, the flow rate on both roads finally reaches a stable level (forming a “platform”); and (4) large values of the merging safety distance parameter decrease the flow rate of the entire system. All the previous results provide a deep understanding of the impact of the three merging strategies on traffic flow, contributing to the design of on-ramp systems that have better operation efficiency and low levels of congestion.
... 3.3. Module C: Spatial-temporal traffic pattern tracking and prediction Rehborn (1996a, 1996b), through empirical traffic data, distinguished two qualitatively different traffic phases within the congested traffic regime: synchronized flow and wide-moving jam which formed the basis for their proposed threephase traffic flow theory (Kerner & Rehborn, 1996a, 1996b. Based on this theory, forecasting of traffic objects (FOTO) and automatic tracking of moving traffic jams (ASDA) models were developed to effectively reconstruct the spatiotemporal traffic patterns on real-world highway corridors (Kerner 2004). ...
Traffic state prediction forms the basis for effective and efficient traffic control and management strategies. A model-based traffic state prediction approach based on a stochastic microscopic three-phase model is developed to predict traffic flow, speed, and travel time in short prediction horizons consisting of multiple time steps ahead. The proposed model utilizes connected vehicles’ trajectory data including location and speed information and fuses this information with detector measurements using an Adaptive Kalman filter. Stochastic driver behaviors in merging, lane-changing, and over-acceleration are considered in the three-phase microscopic model, which allows for a precise prediction of macroscopic parameters for a relatively long stretch of freeway. Traffic flow and speed predictions are conducted for each lane individually and, for a whole segment. Per-lane predictions provide valuable information regarding different speed fluctuations in each lane for identifying congestion and applying proactive freeway controls. Predicted traffic parameters are used for tracking and predicting the spatial-temporal traffic patterns in real-time. The accuracy of the proposed model is examined and validated for various penetration rates of connected vehicles and prediction horizons and outperforms the baseline prediction methods.
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... Previous research has investigated the cause of capacity drop using aggregated traffic data from loop detectors. Kerner proposed the "three-phase traffic" theory and the concept of "phase transition" [13][14][15] and believed that the "phase transition" process of traffic flow caused the "breakdown phenomenon" of a sudden decrease in vehicle speed, resulting in capacity drop. Studies have observed capacity drop in areas where lane changing often occurs, near weaving segments [16,17], merging [18][19][20], diverging [21], and lane-drop [22] bottlenecks. ...
Capacity drop is the critical phenomenon that triggers traffic congestion, while traffic evolution is very complex during a capacity drop. This study applied the empirical vehicle trajectory data to explore the traffic characteristics during the capacity drop at the tunnel bottleneck section. We first construct a capacity drop analysis model using image processing technology to extract high-precision vehicle trajectories. We then analyze the characteristics of the evolution process of the capacity drop at the bottleneck area. The results show that the capacity drop is a dynamic evolution process from free flow to congested flow where traffic operation is distinct. The capacity drop shows the difference between congested flow and non-congested flow. The driving characteristics of drivers in the two states are also different. The influence of lane-changing behavior on the capacity drop is estimated. In the free flow state, the disturbance caused by lane-changing can be quickly eliminated. With the increase in vehicle numbers in the area, the frequent lane-changing behavior accumulates disturbance. When the disturbance reaches a certain degree, congestion will occur, and the vehicle’s speed will drop sharply, resulting in a capacity drop.
... Sometimes the congested state is divided into synchronised flow in which cars are following each other at a relatively constant speed, and stop-and-go motion (the name explains the concept) at even higher densities [117]. Some authors go further into dividing the synchronised flow depending on whether the speed and separation of the vehicles is stationary or not [118]. ...
Recent decades have seen a rise in the use of physics methods to study different societal phenomena. This development has been due to physicists venturing outside of their traditional domains of interest, but also due to scientists from other disciplines taking from physics the methods that have proven so successful throughout the 19th and the 20th century. Here we characterise the field with the term ‘social physics’ and pay our respect to intellectual mavericks who nurtured it to maturity. We do so by reviewing the current state of the art. Starting with a set of topics that are at the heart of modern human societies, we review research dedicated to urban development and traffic, the functioning of financial markets, cooperation as the basis for our evolutionary success, the structure of social networks, and the integration of intelligent machines into these networks. We then shift our attention to a set of topics that explore potential threats to society. These include criminal behaviour, large-scale migration, epidemics, environmental challenges, and climate change. We end the coverage of each topic with promising directions for future research. Based on this, we conclude that the future for social physics is bright. Physicists studying societal phenomena are no longer a curiosity, but rather a force to be reckoned with. Notwithstanding, it remains of the utmost importance that we continue to foster constructive dialogue and mutual respect at the interfaces of different scientific disciplines.
... For example, the deviation from the maximal section velocity δv section =v ego − v maxSet is discretized into: over the maximal allowed velocity, in range of the maximal allowed velocity, slower than the allowed velocity and much slower than the allowed velocity. The lane velocity is discretized after The Three Phases Traffic of Kerner [77] into free-flow, synchronized-flow and wide-moving-jam. ...
One important aspect of autonomous driving lies in the selection of maneuver sequences. Here, the objective is to optimize the driving comfort and travel-duration, while always keeping within the safety limits. Human drivers analyze and try to anticipate the traffic situation choosing their actions not only based on current information but also based on experience. Different from assistance systems, where the last decision and the responsibility still falls back on the driver, on a highly automated driving vehicle, the driver does not have continuous control. Thus, the system has to guarantee the safety during the autonomous driving phase. The challenge is to perform the driving activity based on the only partially available knowledge of the situation. Even if the observed data can be complemented by back-end information, the sensor range is still limited. Besides, the behavior of other road members is only partially predictable for a short time horizon. Therefore, the planning system is forced to deal with uncertainties and partial knowledge. The ability to react to unexpected situations should be ensured under defined constraints. The system needs to: • Present robustness over uncertainties and traffic evolutions.
• Provide feasible solutions regarding the dynamic limitations of the vehicle, the weather conditions and meeting real-time requirements.
• Handle complexity in a traceable way, remaining intuitive for the driver.
This thesis proposes a planning system that ensures driving safety on short horizons and integrates previous experiences to optimize the expected reward. The planner presents a multi-level architecture, similar to the human reasoning process, which combines continuous planning with semantical information. This allows the planning system to deal with the complexity of the problem in a computationally efficient way and also provides an intuitive interface to communicate the decisions to the driver. A qualitative analysis of the different parameters that influence the passenger perception of comfort and safety is presented. The planner clusters the different options, assesses them and selects the best policy based on the expected reward over the time. The integration of different abstraction levels allows to deal with the increasing time horizon as well as with the increasing uncertainties. This approach takes not only the information provided by the environment into account, but also the observed and learned values from past situations.
... Sometimes the congested state is divided into synchronised flow in which cars are following each other at a relatively constant speed, and stop-and-go motion (the name explains the concept) at even higher densities [117]. Some authors go further into dividing the synchronised flow depending on whether the speed and separation of the vehicles is stationary or not [118]. ...
Recent decades have seen a rise in the use of physics-inspired or physics-like methods in attempts to resolve diverse societal problems. Such a rise is driven both by physicists venturing outside of their traditional domain of interest, but also by scientists from other domains who wish to mimic the enormous success of physics throughout the 19th and 20th century. Here, we dub the physics-inspired and physics-like work on societal problems "social physics", and pay our respect to intellectual mavericks who nurtured the field to its maturity. We do so by comprehensively (but not exhaustively) reviewing the current state of the art. Starting with a set of topics that pertain to the modern way of living and factors that enable humankind's prosperous existence, we discuss urban development and traffic, the functioning of financial markets, cooperation as a basis for civilised life, the structure of (social) networks, and the integration of intelligent machines in such networks. We then shift focus to a set of topics that explore potential threats to humanity. These include criminal behaviour, massive migrations, contagions, environmental problems, and finally climate change. The coverage of each topic is ended with ideas for future progress. Based on the number of ideas laid out, but also on the fact that the field is already too big for an exhaustive review despite our best efforts, we are forced to conclude that the future for social physics is bright. Physicists tackling societal problems are no longer a curiosity, but rather a force to be reckoned with, yet for reckoning to be truly productive, it is necessary to build dialog and mutual understanding with social scientists, environmental scientists, philosophers, and more.
... Note that the aforementioned works do not have a universal and concrete theoretical framework to explain space-temporal traffic flow features, which may lead to problems in the transferability of the results throughout the world. In recent decades, Kerner proposed the three-phase traffic theory based on systematic empirical investigations [15][16][17] and theoretical studies [18,19]. According to Kerner's concept, a macroscopic traffic flow can be classified into three phases, including free flow (F), synchronized flow (S), and wide moving jam (J) phases. ...
Driving safety is considered to have a strong relationship with traffic flow characteristics. However, very few studies have addressed the safety impacts in the three-phase traffic theory that has been demonstrated to be an advancement in explaining the empirical features of traffic flow. Another important issue affecting safety is driver experience heterogeneity, especially in developing countries experiencing a dramatic growth in the number of novice drivers. Thus, the primary objective of the current study is to develop a microsimulation environment for evaluating safety performance considering the presence of novice drivers in the framework of three-phase theory. First, a car-following model is developed by incorporating human physiological factors into the classical Intelligent Driver Model (IDM). Moreover, a surrogate safety measure based on the integration concept is modified to evaluate rear-end crashes in terms of probability and severity simultaneously. Based on a vehicle-mounted experiment, the field data of car-following behavior are collected by dividing the subjects into a novice group and an experienced group. These data are used to calibrate the proposed car-following model to explain driver experience heterogeneity. The results indicate that our simulation environment is capable of reproducing the three-phase theory, and the changes in the modified surrogate safety measure are highly correlated with traffic phases. We also discover that the presence of novice drivers leads to different safety performance outcomes across various traffic phases. The effect of driver experience heterogeneity is found to increase the probability of the rear-end crashes as well as the corresponding severity. The results of this study are expected to provide a scientific understanding of the mechanisms of crash occurrences and to provide application suggestions for improving traffic safety performance.
Granular material flowing through bottlenecks like the openings of silos tend to clog and to inhibit further flow. We study this phenomenon in a three-dimensional hopper for spherical and shape-anisotropic particles by means of X-ray tomography. The X-ray tomograms provide information on the bulk of the granular filling, and allows to determine the particle positions and orientations inside the silo. In addition, it allows to calculate local packing densities in different parts of the container. We find that in the flowing zone of the silo particles show a preferred orientation and thereby a higher order. Similarly to simple shear flows, the average orientation of the particles is not parallel to the streamlines but encloses a certain angle with it. In most parts of the hopper, the angular distribution of the particles did not reach the one corresponding to stationary shear flow, thus the average orientation angle in the hopper deviates more from the streamlines than in stationary shear flows. In the flowing parts of the silo shear induced dilation is observed, which is more pronounced for elongated grains than for nearly spherical particles. The clogged state is characterized by a dome, i. e. the geometry of the layer of grains blocking the outflow. The shape of the dome depends on the particle shape.
In this chapter, we present a classification of traffic flow models aimed at capturing various physical phenomena and representing different traffic flow conditions, followed by an in-depth discussion of microscopic models. Example models are provided that account for individual vehicle dynamics from both deterministic and stochastic perspectives. Experimental studies and examples of simulation tools are surveyed. The chapter concludes with notes and relevant references.
An asymmetric dissipative system of particles is directly applicable to vehicular traffic. Actually, the one-dimensional OV model was developed primarily to analyse the phenomena of traffic flow such as the occurrence of jam formation.
In order to unravel the physical and mathematical mystery of synchronized-flow mechanism and to reveal the fundamental mechanism and origin of synchronized flow produced by nonlinear stochastic processes, we have produced simple stochastic traffic flow models (the gradual-NaSch, Phoenix and mPhoenix models) with nonlinear safe speeds. In the mNaSch model and our gradual-NaSch model, the [Formula: see text]th vehicle’s speed is the same as or different from the [Formula: see text]th vehicle’s speed because they are discrete values. In the mNaSch and gradual-NaSch models, the same discrete values of the [Formula: see text]th and [Formula: see text]th states make it easy to identify synchronized flow with speed-synchronized phase of the [Formula: see text]th and [Formula: see text]th states. On the other hand, when we deal with synchronized flow in continuous traffic flow models, we face a problem. Continuous values cause the difficulty in identification of synchronization. In order to definitely clarify whether or not synchronized flow occurs in continuous models, we have established a novel idea of Exchange approach to recognizing synchronized flow as speed-synchronized phase. Our idea is generated from the analogical image that the whole system of synchronized metronomes does not change even if the [Formula: see text]th and [Formula: see text]th synchronized metronomes are exchanged. The Exchange approach (exchanging the [Formula: see text]th vehicle’s state for any [Formula: see text]th vehicle’s state in the whole system of traffic flow), which causes distortion such as a collision if non-synchronized vehicle’s states are exchanged and makes it possible to definitely clarify whether or not synchronized flow occurs in continuous models, is applied to our simple stochastic continuous model (the mPhoenix model). On the basis of the Exchange approach, we can recognize that the mPhoenix model surely reproduces synchronized flow. In addition, we have proposed mathematical approach to deriving nonlinear safe speeds which guarantee collision free driving and reproduce synchronized flow.
Reliable real-time traffic state identification (TSI) is one of the critical foundations in traffic operation management and control systems. Although extensive efforts have been devoted to TSI, due to the high dynamics and stochasticity of traffic flows, there are still some challenges in providing reliable and consistent TSI results, especially in online network-level applications. In this study, we propose a new time series clustering based offline-online modeling framework for reliable TSI using high-resolution traffic data. Specifically, in the proposed framework, the offline module extracts representative traffic state patterns from massive historical data, which serve as the state references in the online module when performing real-time TSI with streaming information. Instead of point data, the proposed framework utilizes high-resolution traffic data in the form of time series, providing rich information on traffic flows in terms of detailed short-term fluctuations and stable long-term trends. In the offline module, considering the fuzziness of traffic states, we introduce a fuzzy c-means based clustering method for offline traffic flow series clustering and traffic state pattern extraction, within which the dynamic time warping algorithm is adopted for measuring the similarity between different time series, the optimal number of clusters is determined by a critical segment based method to reach consistent TSI in network-wide applications. In the online module, a dynamic programming based real-time TSI approach is developed to produce reliable and smooth identification results using streaming data. Extensive numerical experiments on a real-world freeway corridor are performed to examine the effectiveness of the proposed framework.
The speed limit signs can be used to enhance traffic safety, nevertheless, the large differences between the speed of vehicles provoked by the speed limit zone (SLZ) may increase the dissipation of energy caused by the deceleration of vehicles. In this paper, the effect of the SLZ on traffic flow and energy dissipation is investigated based on a cellular automaton model that considers the three traffic phases (free flow, synchronized flow and wide moving jams). It is found that the throughput and the energy dissipation depend strongly on the length of the SLZ as well as on the speed adopted inside the SLZ. The microscopic effect of the SLZ is also studied. The dependence of the density and the length of platoons induced by the SLZ were evaluated. The characteristic of the traffic flow can be also evaluated with the energy dissipation. For high densities, the effect of the SLZ becomes seldom on the flow, however, the energy dissipation shows salient features, which can be used as an indicator of traffic phases.
The recent extension of a macroscopic fundamental diagram (MFD) into a bi-modal MFD (or 3D-MFD) provides the relationship among the total network circulating flows and the accumulations of private vehicles and public buses. 3D-MFD reveals the contribution of large occupancy vehicles such as buses in improving urban transportation efficiency. A lot of bi-modal traffic management techniques are introduced based on 3D-MFD to improve the urban traffic efficiency without using detailed origin-destination (OD) information. However, similar to MFD, 3D-MFD is also highly affected by the heterogeneity of a road network. In order to form 3D-MFDs with low scatter to be utilized for further bi-modal traffic management, this paper proposes a partition method to cluster road links into several homogeneous regions for a bi-modal urban network. It is comprised of three layers named as initial partition, merging, and boundary adjusting. At the initial partition layer, Seeded Region Growing (SRG) and the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) are integrated to obtain a number of subregions. A modified Genetic Algorithm (GA) is developed to merge the subregions into larger regions at the merging layer. Then, boundary adjusting is performed by changing the region to which a boundary is clustered to optimize the result. Multi-sensor data collected from Shenzhen in China are utilized to verify the effectiveness of the proposed partition method.
Achieving high-level, anthropomorphic lane-changing control for autonomous vehicles is an important method for promoting the safe and efficient operation of autonomous vehicles. According to existing lane-changing models, the important phenomenon that frequent acceleration and deceleration cause a poor riding experience and thus induce the intention of lane-changing needs to be given more attention. In this study, a discretionary lane-changing control method for autonomous vehicles is designed based on anti-interference ability (AIA, where AIA is the number of decelerations per unit time of an autonomous vehicle) to extract the traffic flow variation characteristics of autonomous vehicles with AIA and to determine methods to improve the driving efficiency and stability of autonomous vehicles. AIA is introduced to the lane-changing decision-making process of autonomous vehicles to simulate the phenomenon of lane-changing intention caused by poor riding experience. A control model that can evaluate the lane-changing conditions is then proposed. NetLogo software was selected to construct a one-way, two-lane scenario for autonomous vehicle operation, and the impacts of the proposed decision-making method in each scenario were tested. The experimental results show that autonomous vehicles are more likely to produce frequent deceleration behaviors under large-traffic and small-space operating conditions. A traffic flow composed of autonomous vehicles that use AIA to induce lane-changing intentions has a more obvious phase transition process. An autonomous vehicle whose AIA induces lane-changing intention can improve the speed and stability for a certain traffic volume (a saturation of less than approximately 0.45). Although lane-changing behavior breaks the stable state of two-lane traffic flow, it will also successfully suppress the aggravation of traffic congestion. Lane-changing has an impact on the local oscillation of traffic flow, and a stable traffic flow operation state and reduction in the AIA clearing frequency are mutually reinforcing.
As the important spatiotemporal state of traffic flow discovered by Kerner’s three-phase traffic theory, the synchronized traffic flow describes a new traffic phase in congested traffic. However, until now most models within the standard traffic theories cannot reproduce it. The average space gap model (ASGM) is a simple cellular automaton model aimed to reproduce various empirical findings discovered by Kerner’s three-phase traffic theory by incorporating the influence of the multi-anticipative effect on vehicle’s deceleration. However, this paper shows that the simulated synchronized flow by ASGM is not consistent with the reality. To this end, the Multi-Anticipative Model (MAM) based on ASGM is proposed, which describes the influence of the multi-anticipative effect on both the accelerations and the decelerations. Simulations indicate that the empirical consistent synchronized flow and related congested patterns can be well reproduced by MAM. Moreover, MAM can reproduce the speed drop in the car following vehicle platoons reported by the empirical observations. Generally, MAM indicates that the multi-anticipative effect can shed light on the understanding and capturing the complex characteristics of traffic flow especially reported by Kerner’s three-phase traffic theory.
In this paper, a cellular automata model with dual cruise-control limit is refined where the length of each cell is set to 1.5 m and each vehicle can still occupy five cells. The prominent feature of this new model is that these vehicles with low-speed and high-speed are not affected by noise and the slow start rule of the Takayasu and Takayasu model is introduced if there is an empty cell in front of the stationary vehicle. Based on the computer simulation results, one obtains that the new refined model can successfully reproduce the empirical characteristics of three-phase traffic flow theory. In the fundamental diagram, there are three-phase traffic states: Free flow, synchronized flow and wide moving jam. In particular, 2[Formula: see text]-characteristic for phase transitions can be presented. Furthermore, the propagation speed of the downstream front of the moving synchronized pattern (MSP) and wide moving jam is within the range of empirical observation data or close to the range of empirical observation data.
Nowadays, in order to improve the traffic conditions in mountainous areas, the demand of climbing lanes is increasing. In this paper, car–truck heterogeneous traffic flow characteristics on the highway with a climbing lane are studied up based on an improved Kerner–Klenov–Schreckenberg–Wolf (KKSW) cellular automation (CA) model. To depict the speed characteristics of vehicle’s climbing and lane-changing behaviors, additional evolution rules for trucks are introduced into the KKSW model. Specifically, the motion of trucks climbing on the slope is described as a deceleration process and an equilibrium process. Furthermore, we define the probability of a truck driver using the climbing lane as a function of the observed real-time occupancy on it. We have found that in accordance with Kerner’s theory, traffic breakdown is an F→S transition that occurs in metastable free flow with respect to the F→S transition. When the traffic demand increases, the bottleneck appears due to the merging of trucks from the climbing lane to the inner lane. Localized synchronized flow patterns (LSP) emerge on both the inner and outer lanes. When traffic demand increases further, wide moving jams emerge in synchronized flow and general pattern (GP) appears on the inner lane, whereas synchronized flow patterns remain on the outer lane only. In addition, the macroscopic traffic flow characteristics under varying truck percentages are analyzed. We have found that the improving effect of climbing lane on traffic efficiency is closely related to the truck percentage.
In this study, a new dual cruise-control limit cellular automaton model with a refined cell length, where vehicles moving with high or low velocity are not affected by noise and the slow-to-start rule is incorporated for standing vehicles with just one free cell in front, is established. In the new refined model, one sets each cell and each vehicle to 2.5 m and 7.5 m in length, respectively. Computer simulation results have shown that the new refined model can successfully reproduce the empirical features of three-phase traffic flow theory including 2Z-characteristic for phase transitions, whether vehicles are uniformly distributed, densely distributed or randomly distributed on the road first. Furthermore, one also finds that the slope tgα of the linear synchronous flow varies with the delay probability p and the maximum value of low velocity vLM in the synchronized flow region. Under homogeneous distribution, the linear synchronous flow with double slopes (tgα, tgβ) is first discovered for the case of 3 ≤ vLM ≤ 5. Under random distribution, all possible co-existence phases of three-phase traffic flow are presented in the fundamental diagram.
Being able to estimate future velocity on a road network has applications from vehicle navigation systems to emergency vehicle dispatching systems. The existence of traffic congestion can severely impact travelers’ travel time and in this paper we explore methods to take it into account in velocity forecasting models. Using a data approach, different traffic observations can be classified into classes with and without congestion. Our research shows that using congestion as an attribute can reduce the prediction error when implementing machine learning models, such as random forest or multi-layer perceptron. Furthermore, training separate models for each class performs better than using congestion as an extra attribute. A methodology for the congestion pattern identification is proposed, based only in the velocity and volume values.
Traffic status recognition and classification is an important prerequisite for traffic management and control. Based on the idea of weight optimal, a weighted fuzzy c-means clustering method for improving the accuracy of traffic classification is proposed in this study to ease traffic congestion. First, since there are many indexes that affect the traffic flow state classification, three commonly used indexes namely, volume, speed and occupancy are chosen as the main parameters for the traffic flow state classification in this paper. Second, in order to quantitatively analyze the influence degree of different traffic flow parameters on traffic flow state division, based on the principle of weight optimization, the objective function of weight optimization is established. Then the weight of each attribute index is obtained by using the branch and bound algorithm. Finally, since the traditional fuzzy c-means clustering method will not consider the influence of different traffic flow parameter weights on the traffic flow state classification results, the classification effect needs to be further improved. A fuzzy weighted c-means classification method which uses weighted Euclidean distance instead of Euclidean distance is proposed to classify the traffic flow states. Based on the same traffic flow data sample on the same road section, the traffic state classification results with different methods show that it is helpful to improve the traffic flow state classification accuracy by weighting the clustering index. Because the influence of different parameters on the traffic flow state classification is considered in the process of clustering, it is more conducive to improve the classification accuracy. Moreover, it can provide more accurate classification information for traffic control and decision making.
This study employed surrogate safety measures to evaluate the crash risks in different traffic phases and phase transitions according to the three-phase theory. The analysis was conducted from a microscopic perspective based on empirical vehicle trajectory data collected from the Interstate 80 in California, USA, and the Yingtian Expressway in Nanjing, China. Traffic phases were identified based on traffic flow variables and their correlations. Two advanced crash risk indexes from vehicle trajectories were conducted to evaluate the safety performance in each traffic state. The effects of various traffic flow variables (i.e. flow rate, density, average speed) on crash risks were explored based on speed-density plane, speed-flow plane and flow-density plane. Three regression models were developed to quantify the effects of traffic flow variables and traffic states on crash risks. The results show significant disparities of safety performance among different traffic states. Synchronized flow and wide moving jam are found to be the most dangerous phases. High density and low speed are associated with high crash risk. The best crash risk prediction performance is achieved when integrating both traffic phases and traffic parameters.
We investigate a probabilistic cellular automaton model which has been introduced recently. This model describes single-lane traffic flow on a ring and generalizes the asymmetric exclusion process models. We study the equilibrium properties and calculate the so-called fundamental diagrams (flow vs.\ density) for parallel dynamics. This is done numerically by computer simulations of the model and by means of an improved mean-field approximation which takes into account short-range correlations. For cars with maximum velocity 1 the simplest non-trivial approximation gives the exact result. For higher velocities the analytical results, obtained by iterated application of the approximation scheme, are in excellent agreement with the numerical simulations. Comment: Revtex, 30 pages, full postscript version (including figures) available by anonymous ftp from "fileserv1.mi.uni-koeln.de" in the directory "pub/incoming/" paper accepted for publication in Phys.Rev.E
Many researchers have reported on the occurence of gaps in freeway speed-density and flow-density data and have suggested that discontinuous functions are necessary to properly describe “observed” traffic behavior. This paper investigates the flow-occupancy (spot-density) relationship using an extensive data set collected on the Queen Elizabeth Way in Ontario. Daily time-traced plots of 5-minute average flow rates versus occupancy were analyzed. Results indicate that there is another interpretation of gaps in data, which does not imply a discontinuous function, but rather, an inverted V shape (continuous, but not continuously differentiable). Three conclusions were reached: (a) it is essential to provide details of data collection locations if one is to know whether a particular pattern in resulting data represents a “true” relationship, or just the specifics of a particular place; (b) there are clear advantages to examining daily time traces of traffic behavior, rather than relying on scatter diagrams of numerous days of accumulated data; and, (c) previously documented arguments for a discontinuous flow-occupancy relationship do not seem convincing, because knowledge of daily operations at a particular location could easily explain the occurence of gaps in the data.
It is shown that, in an initially homogeneous traffic flow, a region of high density and low average velocity of cars can spontaneously appear, if the density of cars in the flow exceeds some critical value. This region-a cluster of cars-can move with constant velocity in the opposite direction or in the direction of the flow, depending on the selected parameters and the initial conditions of the traffic flow. Based on numerical simulations, the kinetics of cluster formation and the shape of stationary moving clusters are found. The results presented can explain the appearance of a ``phantom traffic jam,'' which is observed in real traffic flow.
The nonlinear theory of the cluster effect in a traffic flow [B. S. Kerner and P. Konhäuser, Phys. Rev. E 48, 2335 (1993)], i.e., the effect of the appearance of a region of high density and low average velocity of vehicles in an initially homogeneous flow, is presented. The structures of a stationary moving cluster are derived. It is found that the density, the average velocities of vehicles inside and outside the cluster, and also the velocity of the cluster are the characteristic parameters of the traffic flow. The dependencies of the cluster structure and parameters on the density of vehicles in the initially homogeneous flow and on the length of the road are investigated. It is found that the cluster can appear within regions of density of vehicles which correspond to a stable homogeneous flow. It is shown that an appearance of a localized perturbation, having a finite amplitude, in the stable homogeneous flow can lead to a self-formation of a local cluster of vehicles which is surrounded by the homogeneous traffic flow. The parameters of the local cluster do not depend on the amplitude of this perturbation but only on the parameters of the flow.
We study a single-lane traffic model that is based on human driving behavior. The outflow from a traffic jam self-organizes to a critical state of maximum throughput. Small perturbations of the outflow far downstream create emergent traffic jams with a power law distribution of lifetimes, t. On varying the vehicle density in a closed system, this critical state separates lamellar and jammed regimes, and exhibits 1/f noise in the power spectrum. Using random walk arguments, in conjunction with a cascade equation, we develop a phenomenological theory that predicts the critical exponents for this transition and explains the self-organizing behavior. These predictions are consistent with all of our numerical results. Comment: TeX-file only. Postscript version including figures available from http://studguppy.tsasa.lanl.gov/research_team/
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.
Based on experimental investigations of traffic on highways it is shown that traffic jams can move stable through a highway keeping their structure and characteristic parameters for a long time (at least for about 50 min, when the jams moved through the longest, 13.1 km, section of the investigated highways). The experimental features of an almost stationary moving jam have been found. An occurrence of complex space-time structures of traffic inside a wide traffic jam has been observed. \textcopyright{} 1996 The American Physical Society.
Introduction to the Theory of Traffic Flow ͑Springer-Verlag
- ͓4͔ B S Kerner
- H Rehborn
- ͑1996͒ ͓5͔
- W Leutzbach
- B S Kerner
- H Rehborn
͓4͔ B. S. Kerner and H. Rehborn, Phys. Rev. E 53, 1297 ͑1996͒. ͓5͔ W. Leutzbach, Introduction to the Theory of Traffic Flow ͑Springer-Verlag, Berlin, 1988͒. ͓6͔ B. S. Kerner and P. Konhä, Phys. Rev. E 48, 2335 ͑1993͒; 50, 54 ͑1994͒. ͓7͔ M. Schreckenberg, A. Schadschneider, K. Nagel, and N. Ito, Phys. Rev. E 51, 2939 ͑1995͒; K. Nagel and M. Paczuski, ibid. 51, 2909 ͑1995͒; M. Bando, K. Hasebe, A. Nakayama, A. Shi-bata, and Y. Sugiyama, ibid. 51, 1035 ͑1995͒. R4278 53 B. S. KERNER AND H. REHBORN