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Kerner BS. Physics of automated-driving vehicular traffic. Phys Rev E 2023; 108:014302. [PMID: 37583140 DOI: 10.1103/physreve.108.014302] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2023] [Accepted: 06/07/2023] [Indexed: 08/17/2023]
Abstract
We have found that phase transitions occurring between three traffic phases [free flow (F), synchronized flow (S), and wide moving jam (J)] determine the spatiotemporal dynamics of traffic consisting of 100% automated-driving vehicles moving on a two-lane road with an on-ramp bottleneck. This means that three-phase traffic theory is a common framework for the description of traffic states independent of whether human-driving or automated-driving vehicles move in vehicular traffic. To prove this, we have studied automated-driving vehicular traffic with the use of classical Helly's model [Proceedings of the Symposium on Theory of Traffic Flow (Elsevier, Amsterdam, 1959), pp. 207-238] widely applied for automated vehicle motion. Although dynamic rules of the motion of automated-driving vehicles in a road lane are qualitatively different from those of human-driving vehicles, we have revealed that traffic breakdown (F→S transition) at the bottleneck exhibits the nucleation nature, which was observed in empirical field data measured in traffic consisting of 100% human-driving vehicles. The physics of the nucleation nature of the F→S transition in automated-driving traffic is associated with a discontinuity in the rate of lane-changing that causes the discontinuity in the rate of over-acceleration. This discontinuous character of over-acceleration leads to both the existence and self-maintaining of synchronized flow at the bottleneck in automated-driving vehicular traffic as well as to the existence at any time instant of a range of highway capacities between some minimum and maximum capacities. Within the capacity range, an F→S transition can be induced; however, when the maximum capacity is exceeded, then after some time-delay a spontaneous F→S transition occurs at the bottleneck. The phases F, S, and J can coexist each other in space and time.
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Affiliation(s)
- Boris S Kerner
- Physics of Transport and Traffic, University of Duisburg-Essen, 47048 Duisburg, Germany
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Wiering V, Klenov SL, Kerner BS, Schreckenberg M. Statistical physics of the development of Kerner's synchronized-to-free-flow instability at a moving bottleneck in vehicular traffic. Phys Rev E 2022; 106:054306. [PMID: 36559348 DOI: 10.1103/physreve.106.054306] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/08/2022] [Accepted: 09/14/2022] [Indexed: 06/17/2023]
Abstract
With the use of simulations of a stochastic microscopic traffic model in the framework of the three-phase traffic theory, we have revealed the statistical physics of a traffic flow instability with respect to a transition from synchronized flow (S) to free flow (F) (Kerner's S→F instability) at a moving bottleneck (MB) occurring through a slow-moving vehicle in vehicular traffic. We have found that the S→F instability can occur at the MB more frequently than at an on-ramp bottleneck. From a comparison of the occurrence of the S→F instability at the MB and on-ramp bottleneck at the same probability of traffic breakdown and the same flow rate it has been found that, whereas the frequency of the S→F instability at the on-ramp bottleneck barely changes, the larger the velocity of the MB, the more frequently the S→F instability occurs at the MB. Contrarily, when the MB velocity decreases considerably, then rather than the S→F instability, in synchronized flow at the MB the classical traffic flow instability leading to the emergence of wide-moving jams (S→J instability) occurs. It has been found that the physics of the intensification of the S→F instability at the MB with the increase in the MB velocity is associated with the increase in the mean space gap (mean time headway) between vehicles in synchronized flow. For this reason, when the MB velocity increases, there is an MB velocity at which the S→F instability dominates the S→J instability: The MB velocity influences considerably on the competition between the S→F and classical traffic flow instabilities in synchronized flow.
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Affiliation(s)
- Vincent Wiering
- Physik von Transport und Verkehr, Universität Duisburg-Essen, 47048 Duisburg, Germany
| | - Sergey L Klenov
- Moscow Institute of Physics and Technology, Department of Physics, 141700 Dolgoprudny, Moscow Region, Russia
| | - Boris S Kerner
- Physik von Transport und Verkehr, Universität Duisburg-Essen, 47048 Duisburg, Germany
| | - Michael Schreckenberg
- Physik von Transport und Verkehr, Universität Duisburg-Essen, 47048 Duisburg, Germany
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Shahal S, Wurzberg A, Sibony I, Duadi H, Shniderman E, Weymouth D, Davidson N, Fridman M. Synchronization of complex human networks. Nat Commun 2020; 11:3854. [PMID: 32782263 PMCID: PMC7419301 DOI: 10.1038/s41467-020-17540-7] [Citation(s) in RCA: 26] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2020] [Accepted: 07/02/2020] [Indexed: 11/09/2022] Open
Abstract
The synchronization of human networks is essential for our civilization and understanding its dynamics is important to many aspects of our lives. Human ensembles were investigated, but in noisy environments and with limited control over the network parameters which govern the network dynamics. Specifically, research has focused predominantly on all-to-all coupling, whereas current social networks and human interactions are often based on complex coupling configurations. Here, we study the synchronization between violin players in complex networks with full and accurate control over the network connectivity, coupling strength, and delay. We show that the players can tune their playing period and delete connections by ignoring frustrating signals, to find a stable solution. These additional degrees of freedom enable new strategies and yield better solutions than are possible within current models such as the Kuramoto model. Our results may influence numerous fields, including traffic management, epidemic control, and stock market dynamics.
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Affiliation(s)
- Shir Shahal
- Faculty of Engineering and the Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, 5290002, Ramat Gan, Israel
| | - Ateret Wurzberg
- Faculty of Engineering and the Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, 5290002, Ramat Gan, Israel
| | - Inbar Sibony
- Faculty of Engineering and the Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, 5290002, Ramat Gan, Israel
| | - Hamootal Duadi
- Faculty of Engineering and the Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, 5290002, Ramat Gan, Israel
| | - Elad Shniderman
- Department of Music, Stony Brook University, Stony Brook, NY, 11794, USA
| | - Daniel Weymouth
- Department of Music, Stony Brook University, Stony Brook, NY, 11794, USA
| | - Nir Davidson
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot, Israel
| | - Moti Fridman
- Faculty of Engineering and the Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, 5290002, Ramat Gan, Israel.
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Kerner BS. Statistical physics of synchronized traffic flow: Spatiotemporal competition between S→F and S→J instabilities. Phys Rev E 2019; 100:012303. [PMID: 31499898 DOI: 10.1103/physreve.100.012303] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2019] [Indexed: 06/10/2023]
Abstract
We have revealed statistical physics of synchronized traffic flow that is governed by a spatiotemporal competition between S→F and S→J instabilities (where F, S, and J denote, respectively, the free flow, synchronized flow, and wide moving jam traffic phases). A probabilistic analysis of synchronized flow based on simulations of a cellular automaton model in the framework of three-phase traffic theory is made. This probabilistic analysis shows that there is a finite range of the initial space gap between vehicles in synchronized flow within which during a chosen time for traffic observation either synchronized flow persists with probability P_{S}, or an S→F transition occurs with probability P_{SF}, or else an S→J transition occurs with probability P_{SJ}. Space-gap dependencies of the probabilities P_{S}, P_{SF}, and P_{SJ} have been found. It has been also found that (i) an initial S→F instability can lead to sequences of S→F→S→J transitions; (ii) an initial S→J instability can lead to sequences of S→J→S→F transitions. Each of the phase transitions in the sequences S→F→S→J transitions and S→J→S→F transitions exhibits the nucleation nature; these sequences of phase transitions determine spatiotemporal features of traffic patterns resulting from the competition between S→F and S→J instabilities. The statistical features of synchronized flow found for a homogeneous road remain qualitatively for a road with a bottleneck. However, rather than nuclei for S→F and S→J instabilities occurring at random road locations of the homogeneous road, due to a permanent nonhomogeneity introduced by the bottleneck, nuclei for initial S→F and S→J instabilities appear mostly at the bottleneck.
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Affiliation(s)
- Boris S Kerner
- Physics of Transport and Traffic, University Duisburg-Essen, 47048 Duisburg, Germany
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Kerner BS. Physics of automated driving in framework of three-phase traffic theory. Phys Rev E 2018; 97:042303. [PMID: 29758629 DOI: 10.1103/physreve.97.042303] [Citation(s) in RCA: 31] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/27/2017] [Indexed: 11/07/2022]
Abstract
We have revealed physical features of automated driving in the framework of the three-phase traffic theory for which there is no fixed time headway to the preceding vehicle. A comparison with the classical model approach to automated driving for which an automated driving vehicle tries to reach a fixed (desired or "optimal") time headway to the preceding vehicle has been made. It turns out that automated driving in the framework of the three-phase traffic theory can exhibit the following advantages in comparison with the classical model of automated driving: (i) The absence of string instability. (ii) Considerably smaller speed disturbances at road bottlenecks. (iii) Automated driving vehicles based on the three-phase theory can decrease the probability of traffic breakdown at the bottleneck in mixed traffic flow consisting of human driving and automated driving vehicles; on the contrary, even a single automated driving vehicle based on the classical approach can provoke traffic breakdown at the bottleneck in mixed traffic flow.
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Affiliation(s)
- Boris S Kerner
- Physics of Transport and Traffic, University Duisburg-Essen, 47048 Duisburg, Germany
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Kerner BS. Microscopic theory of traffic-flow instability governing traffic breakdown at highway bottlenecks: Growing wave of increase in speed in synchronized flow. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:062827. [PMID: 26764764 DOI: 10.1103/physreve.92.062827] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/31/2015] [Indexed: 06/05/2023]
Abstract
We have revealed a growing local speed wave of increase in speed that can randomly occur in synchronized flow (S) at a highway bottleneck. The development of such a traffic flow instability leads to free flow (F) at the bottleneck; therefore, we call this instability an S→F instability. Whereas the S→F instability leads to a local increase in speed (growing acceleration wave), in contrast, the classical traffic flow instability introduced in the 1950s-1960s and incorporated later in a huge number of traffic flow models leads to a growing wave of a local decrease in speed (growing deceleration wave). We have found that the S→F instability can occur only if there is a finite time delay in driver overacceleration. The initial speed disturbance of increase in speed (called "speed peak") that initiates the S→F instability occurs usually at the downstream front of synchronized flow at the bottleneck. There can be many speed peaks with random amplitudes that occur randomly over time. It has been found that the S→F instability exhibits a nucleation nature: Only when a speed peak amplitude is large enough can the S→F instability occur; in contrast, speed peaks of smaller amplitudes cause dissolving speed waves of a local increase in speed (dissolving acceleration waves) in synchronized flow. We have found that the S→F instability governs traffic breakdown-a phase transition from free flow to synchronized flow (F→S transition) at the bottleneck: The nucleation nature of the S→F instability explains the metastability of free flow with respect to an F→S transition at the bottleneck.
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Affiliation(s)
- Boris S Kerner
- Physics of Transport and Traffic, University Duisburg-Essen, 47048 Duisburg, Germany
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Kerner BS, Klenov SL, Schreckenberg M. Probabilistic physical characteristics of phase transitions at highway bottlenecks: incommensurability of three-phase and two-phase traffic-flow theories. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:052807. [PMID: 25353844 DOI: 10.1103/physreve.89.052807] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/17/2014] [Indexed: 06/04/2023]
Abstract
Physical features of induced phase transitions in a metastable free flow at an on-ramp bottleneck in three-phase and two-phase cellular automaton (CA) traffic-flow models have been revealed. It turns out that at given flow rates at the bottleneck, to induce a moving jam (F → J transition) in the metastable free flow through the application of a time-limited on-ramp inflow impulse, in both two-phase and three-phase CA models the same critical amplitude of the impulse is required. If a smaller impulse than this critical one is applied, neither F → J transition nor other phase transitions can occur in the two-phase CA model. We have found that in contrast with the two-phase CA model, in the three-phase CA model, if the same smaller impulse is applied, then a phase transition from free flow to synchronized flow (F → S transition) can be induced at the bottleneck. This explains why rather than the F → J transition, in the three-phase theory traffic breakdown at a highway bottleneck is governed by an F → S transition, as observed in real measured traffic data. None of two-phase traffic-flow theories incorporates an F → S transition in a metastable free flow at the bottleneck that is the main feature of the three-phase theory. On the one hand, this shows the incommensurability of three-phase and two-phase traffic-flow theories. On the other hand, this clarifies why none of the two-phase traffic-flow theories can explain the set of fundamental empirical features of traffic breakdown at highway bottlenecks.
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Affiliation(s)
- Boris S Kerner
- Physik von Transport und Verkehr, Universität Duisburg-Essen, 47048 Duisburg, Germany
| | - Sergey L Klenov
- Moscow Institute of Physics and Technology, Department of Physics, 141700 Dolgoprudny, Moscow Region, Russia
| | - Michael Schreckenberg
- Physik von Transport und Verkehr, Universität Duisburg-Essen, 47048 Duisburg, Germany
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Kerner BS. Complexity of spatiotemporal traffic phenomena in flow of identical drivers: explanation based on fundamental hypothesis of three-phase theory. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:036110. [PMID: 22587152 DOI: 10.1103/physreve.85.036110] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2012] [Indexed: 05/31/2023]
Abstract
Based on numerical simulations of a stochastic three-phase traffic flow model, we reveal the physics of the fundamental hypothesis of three-phase theory that, in contrast with a fundamental diagram of classical traffic flow theories, postulates the existence of a two-dimensional (2D) region of steady states of synchronized flow where a driver makes an arbitrary choice of a space gap (time headway) to the preceding vehicle. We find that macroscopic and microscopic spatiotemporal effects of the entire complexity of traffic congestion observed up to now in real measured traffic data can be explained by simulations of traffic flow consisting of identical drivers and vehicles, if a microscopic model used in these simulations incorporates the fundamental hypothesis of three-phase theory. It is shown that the driver's choice of space gaps within the 2D region of synchronized flow associated with the fundamental hypothesis of three-phase theory can qualitatively change types of congested patterns that can emerge at a highway bottleneck. In particular, if drivers choose long enough spaces gaps associated with the fundamental hypothesis, then general patterns, which consist of synchronized flow and wide moving jams, do not emerge independent of the flow rates and bottleneck characteristics: Even at a heavy bottleneck leading to a very low speed within congested patterns, only synchronized flow patterns occur in which no wide moving jams emerge spontaneously.
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Affiliation(s)
- Boris S Kerner
- Daimler AG, GR/PTF, HPC: G021, 71059 Sindelfingen, Germany
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Kerner BS, Klenov SL, Schreckenberg M. Simple cellular automaton model for traffic breakdown, highway capacity, and synchronized flow. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:046110. [PMID: 22181230 DOI: 10.1103/physreve.84.046110] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/22/2011] [Revised: 08/29/2011] [Indexed: 05/31/2023]
Abstract
We present a simple cellular automaton (CA) model for two-lane roads explaining the physics of traffic breakdown, highway capacity, and synchronized flow. The model consists of the rules "acceleration," "deceleration," "randomization," and "motion" of the Nagel-Schreckenberg CA model as well as "overacceleration through lane changing to the faster lane," "comparison of vehicle gap with the synchronization gap," and "speed adaptation within the synchronization gap" of Kerner's three-phase traffic theory. We show that these few rules of the CA model can appropriately simulate fundamental empirical features of traffic breakdown and highway capacity found in traffic data measured over years in different countries, like characteristics of synchronized flow, the existence of the spontaneous and induced breakdowns at the same bottleneck, and associated probabilistic features of traffic breakdown and highway capacity. Single-vehicle data derived in model simulations show that synchronized flow first occurs and then self-maintains due to a spatiotemporal competition between speed adaptation to a slower speed of the preceding vehicle and passing of this slower vehicle. We find that the application of simple dependences of randomization probability and synchronization gap on driving situation allows us to explain the physics of moving synchronized flow patterns and the pinch effect in synchronized flow as observed in real traffic data.
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Affiliation(s)
- Boris S Kerner
- Daimler AG, GR/PTF, HPC: G021, D-71059 Sindelfingen, Germany
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Kerner BS, Klenov SL. Phase transitions in traffic flow on multilane roads. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:056101. [PMID: 20365037 DOI: 10.1103/physreve.80.056101] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/27/2009] [Revised: 08/03/2009] [Indexed: 05/29/2023]
Abstract
Based on empirical and numerical analyses of vehicular traffic, the physics of spatiotemporal phase transitions in traffic flow on multilane roads is revealed. The complex dynamics of moving jams observed in single vehicle data measured by video cameras on American highways is explained by the nucleation-interruption effect in synchronized flow, i.e., the spontaneous nucleation of a narrow moving jam with the subsequent jam dissolution. We find that (i) lane changing, vehicle merging from on-ramps, and vehicle leaving to off-ramps result in different traffic phases-free flow, synchronized flow, and wide moving jams-occurring and coexisting in different road lanes as well as in diverse phase transitions between the traffic phases; (ii) in synchronized flow, the phase transitions are responsible for a non-regular moving jam dynamics that explains measured single vehicle data: moving jams emerge and dissolve randomly at various road locations in different lanes; (iii) the phase transitions result also in diverse expanded general congested patterns occurring at closely located bottlenecks.
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Affiliation(s)
- Boris S Kerner
- GR/PTF, HPC, G021, Daimler AG, 71059 Sindelfingen, Germany.
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Gao Z, Jin N. Flow-pattern identification and nonlinear dynamics of gas-liquid two-phase flow in complex networks. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:066303. [PMID: 19658590 DOI: 10.1103/physreve.79.066303] [Citation(s) in RCA: 46] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/22/2008] [Revised: 05/11/2009] [Indexed: 05/28/2023]
Abstract
The identification of flow pattern is a basic and important issue in multiphase systems. Because of the complexity of phase interaction in gas-liquid two-phase flow, it is difficult to discern its flow pattern objectively. In this paper, we make a systematic study on the vertical upward gas-liquid two-phase flow using complex network. Three unique network construction methods are proposed to build three types of networks, i.e., flow pattern complex network (FPCN), fluid dynamic complex network (FDCN), and fluid structure complex network (FSCN). Through detecting the community structure of FPCN by the community-detection algorithm based on K -mean clustering, useful and interesting results are found which can be used for identifying five vertical upward gas-liquid two-phase flow patterns. To investigate the dynamic characteristics of gas-liquid two-phase flow, we construct 50 FDCNs under different flow conditions, and find that the power-law exponent and the network information entropy, which are sensitive to the flow pattern transition, can both characterize the nonlinear dynamics of gas-liquid two-phase flow. Furthermore, we construct FSCN and demonstrate how network statistic can be used to reveal the fluid structure of gas-liquid two-phase flow. In this paper, from a different perspective, we not only introduce complex network theory to the study of gas-liquid two-phase flow but also indicate that complex network may be a powerful tool for exploring nonlinear time series in practice.
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Affiliation(s)
- Zhongke Gao
- School of Electrical Engineering and Automation, Tianjin University, Tianjin 300072, People's Republic of China
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