Boris Kerner

In Kerner's three phase traffic theory, in addition to the free flow traffic phase (F), there are two traffic phases in congested traffic: the synchronized flow traffic phase (S) and the wide moving jam phase (J). One of the main results of Kerner's theory is that traffic breakdown at a highway bottleneck is a random (probabilistic) phase transition from free flow to synchronized flow (F → S transition) that occurs in a metastable state of free flow at a highway bottleneck. This means that traffic breakdown (F → S transition) exhibits the nucleation nature. The main reason for the Kerner’s three-phase theory is the explanation of the empirical nucleation nature of traffic breakdown (F → S transition) at highway bottlenecks observed in real field traffic data. The prediction of the Kerner’s three-phase theory is that this metastability of free flow with respect to the F → S phase transition is governed by the nucleation nature of an instability of synchronized flow with respect to the growth of a large enough local increase in speed in synchronized flow (called a S → F instability). The S → F instability is a growing speed wave of a local increase in speed in synchronized flow at the bottleneck. The development of Kerner's S → F instability leads to a local phase transition from synchronized flow to free flow at the bottleneck (S → F transition).

At the end of 1990's Kerner introduced a new traffic phase, called synchronized flow whose basic feature leads to the nucleation nature of the F → S transition at a highway bottleneck. Therefore, Kerner's synchronized flow traffic phase can be used synonymously with the term three-phase traffic theory.

In 2015 Kerner found that before traffic breakdown occurs at a highway bottleneck, there can be a random sequence of F → S → F transitions at the bottleneck: The development of a F → S transition is interrupted by a S → F instability that leads to synchronized flow dissolution resulting in a S → F transition at the bottleneck. The effect of Kerner's F → S → F transitions is as follows: The F → S → F transitions determine a random time delay of traffic breakdown at the bottleneck.

The basic result of Kerner's three-phase traffic theory about the nucleation nature of traffic breakdown (F → S transition) at a bottleneck shows the incommensurability of three-phase traffic theory with all earlier (standard) traffic flow theories. The term "incommensurability" has been introduced by Kuhn in his classical book[7] to explain a paradigm shift in a scientific field. The paradigm shift in traffic and transportation science is the fundamental change in the meaning of stochastic highway capacity because the meaning of highway capacity is the basis for the development of any method for traffic control, management, and organization of a traffic network as well as applications of intelligent transportation systems. The paradigm of standard traffic and transportation theories is that at any time instant there is a value of stochastic highway capacity. When the flow rate at a bottleneck exceeds the capacity value at this time instant, traffic breakdown must occur at the bottleneck. The new paradigm of traffic and transportation science following from the empirical nucleation nature of traffic breakdown (F → S transition) and Kerner's three-phase traffic theory changes fundamentally the meaning of stochastic highway capacity as follows. At any time instant there is a range of highway capacity values between a minimum and a maximum highway capacity, which are themselves stochastic values. When the flow rate at a bottleneck is inside this capacity range related to this time instant, traffic breakdown can occur at the bottleneck only with some probability, i.e., in some cases traffic breakdown occurs, in other cases it does not occur.

Rather than a mathematical model of traffic flow, Kerner’s three-phase traffic theory is a qualitative traffic flow theory that consists of several hypotheses. The first mathematical model of traffic flow in the framework of Kerner’s three-phase traffic theory that mathematical simulations can show and explain traffic breakdown by an F → S phase transition in the metastable free flow at the bottleneck was the Kerner-Klenov stochastic microscopic traffic flow model introduced in 2002. Some months later, Kerner, Klenov, and Wolf developed a cellular automaton (CA) traffic flow model in the framework of Kerner’s three-phase traffic theory. The Kerner-Klenov stochastic traffic flow model in the framework of Kerner’s theory has further been developed for different applications, in particular to simulate on-ramp metering, speed limit control, dynamic traffic assignment in traffic and transportation networks, traffic at heavy bottlenecks and on moving bottlenecks, features of heterogeneous traffic flow consisting of different vehicles and drivers, jam warning methods, vehicle-to-vehicle (V2V) communication for cooperative driving, the performance of self-driving vehicles in mixture traffic flow, traffic breakdown at traffic signals in city traffic, over-saturated city traffic, vehicle fuel consumption in traffic networks.

Kerner's three phase traffic theory is a theoretical basis for applications in transportation engineering. One of the first applications of the three-phase traffic theory is ASDA/FOTO methods that are used in on-line applications for spatiotemporal reconstruction of congested traffic patterns in highway networks.

In 2004 Kerner introduced congested pattern control approach. Contrarily to standard traffic control at a network bottleneck in which a controller (for example, through the use of on-ramp metering, speed limit, or other traffic control strategies) tries to maintain free flow conditions at the maximum possible flow rate at the bottleneck, in congested pattern control approach no control of traffic flow at the bottleneck is realized as long as free flow is realized at the bottleneck. Only when an F → S transition (traffic breakdown) has occurred at the bottleneck, the controller starts to work trying to return free flow at the bottleneck. Congested pattern control approach is consistent with the empirical nucleation nature of traffic breakdown. Due to the congested pattern control approach, either free flow recovers at the bottleneck or traffic congestion is localized at the bottleneck.

In 2004 Kerner introduced a concept of an autonomous driving vehicle in the framework of the three-phase traffic theory. The autonomous driving vehicle in the framework of the three-phase traffic theory is a self-driving vehicle for which there is no fixed time headway to the preceding vehicle. This means the existence of an indifference zone in car-following for the autonomous driving vehicle. Kerner's indifference zone in car-following results from Kerner's two-dimensional (2D) region of steady states of synchronized flow hypothesized in the three-phase traffic theory.

In 2011–2014, Boris Kerner has expanded three phase traffic theory, which he developed initially for highway traffic, for the description of city traffic. It turns out that like traffic breakdown at highway bottlenecks, traffic breakdown (transition from under- to over-saturated traffic) at traffic signals is also a random phase transition that occurs in metastable under-saturated city traffic. This theory of traffic breakdown at traffic signals can explain the physics of traffic gridlock in city traffic as well as the breakdown of green wave that is often observed in real city traffic. Moreover, like empirical studies of highway traffic, recent empirical studies of over-saturated city traffic prove the existence of empirical synchronized flow in city traffic.

In 2011 Kerner introduced the breakdown minimization principle that is devoted to control and optimization of traffic and transportation networks while keeping the minimum of the probability of the occurrence of traffic congestion in a network.

In 2016 Kerner developed an application of the breakdown minimization principle called network throughput maximization approach. Kerner's network throughput maximization approach is devoted to the maximization of the network throughput while keeping free flow conditions in the whole network.

In 2016 Kerner introduced a measure (or "metric") of a traffic or transportation network called network capacity. Kerner's network capacity determines the maximum total network inflow rate that is still possible to assign in the network while keeping free flow conditions in the whole network. Network capacity allows us to formulate a general condition for the maximization of the network throughput at which free flow does persist in the whole network: Under application of a network throughput maximization approach, as long as the total network inflow rate is smaller than the network capacity traffic breakdown with resulting traffic congestion cannot occur in the network, i.e., free flow remains in the whole network.

• B.S. Kerner, V.V. Osipov, Autosolitons: A New Approach to Problems of Self-Organization and Turbulence (Fundamental Theories of Physics), Kluwer, Dordrecht, 1994
• Boris S. Kerner, The Physics of Traffic: Empirical Freeway Pattern Features, Engineering Applications, and Theory, Springer, Berlin, Heidelberg, New York 2004
• Boris S. Kerner, Introduction to Modern Traffic Flow Theory and Control: The Long Road to Three-Phase Traffic Theory, Springer, Heidelberg, Dordrecht, London, New York, 2009
• Boris S. Kerner, Breakdown in Traffic Networks: Fundamentals of Transportation Science, Springer, Berlin, 2017

• Boris S. Kerner, "Failure of classical traffic flow theories: Stochastic highway capacity and automatic driving", Physica A: Statistical Mechanics and its Applications 450, 700–747 (2016). doi.org/10.1016/j.physa.2016.01.034
• Boris S. Kerner, "Breakdown minimization principle versus Wardrop's equilibria for dynamic traffic assignment and control in traffic and transportation networks: A critical mini-review", Physica A: Statistical Mechanics and its Applications 466, 626-662 (2017)
• Boris S. Kerner, "Criticism of generally accepted fundamentals and methodologies of traffic and transportation theory: A brief review", Physica A: Statistical Mechanics and its Applications 392, 5261–5282 (2013). doi: 10.1016/j.physa.2013.06.004
• Boris S. Kerner, "Failure of classical traffic flow theories: a critical review", Elektrotech. Inftech. 132, 417-433 (2015). doi: 10.1007/s00502-015-0340-3
• Boris S. Kerner, "Complex Dynamics of Management: Introduction", Springer Science+Business Media LLC, R.A. Meyers (ed.), Encyclopedia of Complexity and Systems Science, Springer, Berlin (2019). doi: 10.1007/978-3-642-27737-5_78-3
• Boris S. Kerner (Ed.), Complex Dynamics of Traffic Management, Encyclopedia of Complexity and Systems Science Series, Springer, New York, 2019

• Boris S. Kerner, Peter Konhäuser, "Cluster effect in initially homogeneous traffic flow" Phys. Rev. E 48, 2335-2338 (1993). doi: 10.1103/PhysRevE.48.R2335
• Boris S. Kerner, Peter Konhäuser, "Structure and parameters of clusters in traffic flow" Phys. Rev. E 50, 54-83 (1994). doi: 10.1103/PhysRevE.50.54
• Boris S. Kerner, Peter Konhäuser, Martin Schilke, "Deterministic spontaneous appearance of traffic jams in slightly inhomogeneous traffic flow" Phys. Rev. E 51, 6243-6246 (1995). doi: 10.1103/PhysRevE.51.6243
• Boris S. Kerner, Hubert Rehborn, "Experimental features and characteristics of traffic jams" Phys. Rev. E 53, R1297-R1300 (1996). doi: 10.1103/PhysRevE.53.R1297
• Boris S. Kerner, Sergey L. Klenov, Peter Konhäuser, "Asymptotic theory of traffic jams" Phys. Rev. E 56, 4200-4216 (1997). doi: 10.1103/PhysRevE.56.4200

• Boris S. Kerner, "Experimental Properties of Self-Organization in Traffic Flow" Physical Review Letters 81, 3797-3800 (1998). doi: 10.1103/PhysRevLett.81.3797
• Boris S. Kerner, "Congested Traffic Flow: Observations and Theory" Transportation Research Record, 1678, 160-167 (1999). doi: 10.3141/1678-20
• Boris S. Kerner, "The Physics of Traffic" Physics World 12, No. 8, 25-30 (August 1999). doi: 10.1088/2058-7058/12/8/30
• Boris S. Kerner, "Experimental features of the emergence of moving jams in free traffic flow" J. Physics A: Math. Gen. 33, L221-L228 (2000). doi: 10.1088/0305-4470/33/26/101
• Boris S. Kerner, "Theory of Breakdown Phenomenon at Highway Bottlenecks" Transportation Research Record, 1710, 136-144 (2000). doi: 10.3141/1710-16
• Boris S. Kerner, "Complexity of Synchronized Flow and Related Problems for Basic Assumptions of Traffic Flow Theories" Networks and Spatial Economics. 1, 35-76 (2001). doi: 10.1023/A:1011577010852
• Boris S. Kerner, "Synchronized Flow as a New Traffic Phase and related Problems for Traffic Flow Modelling" Mathematical and Computer Modelling. 35, 481-508 (2002). doi: 10.1016/S0895-7177(02)80017-6
• Boris S. Kerner, "Empirical Features of Congested Patterns at Highway Bottlenecks" Transportation Research Record, 1802, 145-154 (2002). doi: 10.3141/1802-17
• Boris S. Kerner, "Empirical macroscopic features of spatial-temporal traffic patterns at highway bottlenecks" Phys. Rev. E. 65, 046138 (2002). doi: 10.1103/PhysRevE.65.046138
• Boris S. Kerner, "Three-phase traffic theory and highway capacity" Physica A, 333, 379-440 (2004). doi: 10.1016/j.physa.2003.10.017

• Boris S. Kerner, Hubert Rehborn, "Experimental properties of complexity in traffic flow" Phys. Rev. E 53, R4275-R4278 (1996). doi: 10.1103/PhysRevE.53.R4275
• Boris S. Kerner, Hubert Rehborn, "Experimental Properties of Phase Transitions in Traffic Flow" Physical Review Letters 79, 4030-4033 (1997). doi: 10.1103/PhysRevLett.79.4030
• Boris S. Kerner, Micha Koller, Sergey L. Klenov, Hubert Rehborn, Michael Leibel, "The physics of empirical nuclei for spontaneous traffic breakdown in free flow at highway bottlenecks" Physica A 438 365–397 (2015). doi: 10.1016/j.physa.2015.05.102
• Boris S. Kerner, Peter Hemmerle, Micha Koller, Gerhard Hermanns, Sergey L. Klenov, Hubert Rehborn, and Michael Schreckenberg, "Empirical synchronized flow in oversaturated city traffic" Phys. Rev. E 90, 032810 (2014). doi: 10.1103/PhysRevE.90.032810

• Boris S. Kerner, Sergey L. Klenov, Andreas Hiller, "Criterion for traffic phases in single vehicle data and empirical test of a microscopic three-phase traffic theory" J. Phys. A: Math. Gen. 39, 2001-2020 (2006). doi: 10.1088/0305-4470/39/9/002
• Boris S. Kerner, Sergey L. Klenov, Hubert Rehborn, and Andreas Hiller, "Microscopic features of moving traffic jams" Phys. Rev. E 73, 046107 (2006). doi: 10.1103/PhysRevE.73.046107
• Boris S. Kerner, Sergey L. Klenov, Andreas Hiller, "Empirical test of a microscopic three-phase traffic theory" Nonlinear Dynamics, 49, 525-553 (2007). doi: 10.1007/s11071-006-9113-1

• Boris S. Kerner, Sergey L. Klenov, "A microscopic model for phase transitions in traffic flow" J. Phys. A: Math. Gen. 35, L31-L43 (2002). doi: 10.1088/0305-4470/35/3/102
• Boris S. Kerner, Sergey L. Klenov, Dietrich E Wolf, "Cellular automata approach to three-phase traffic theory" J. Phys. A: Math. Gen. 35, 9971–10013 (2002). doi: 10.1088/0305-4470/35/47/303
• Boris S. Kerner, Sergey L. Klenov, "Microscopic theory of spatio-temporal congested traffic patterns at highway bottlenecks" Phys. Rev. E 68, 036130 (2003). doi: 10.1103/PhysRevE.68.036130
• Boris S. Kerner, Sergey L. Klenov, "Spatiotemporal patterns in heterogeneous traffic flow with a variety of driver behavioural characteristics and parameters" J. Phys. A: Math. Gen. 37, 8753-8788 (2004). doi: 10.1088/0305-4470/37/37/001
• Boris S. Kerner, Sergey L. Klenov, "Deterministic microscopic three-phase traffic flow models" J. Phys. A: Math. Gen. 39, 1775-1809 (2006). doi: 10.1088/0305-4470/39/8/002
• Boris S. Kerner, Sergey L. Klenov, "Phase transitions in traffic flow on multilane roads" Phys. Rev. E 80, 056101 (2009). doi: 10.1103/PhysRevE.80.056101
• Boris S. Kerner, Sergey L. Klenov, "A study of phase transitions on multilane roads in the framework of three-phase traffic theory", Transportation Research Record, 2124, 67-77 (2009). doi: 10.3141/2124-07
• Boris S. Kerner, Sergey L. Klenov, "A Theory of Traffic Congestion at Moving Bottlenecks" J. Phys. A: Math. Gen. 43, 425101 (2010). doi: 10.1088/1751-8113/43/42/425101
• Boris S. Kerner, Sergey L. Klenov, and Michael Schreckenberg, "Simple cellular automaton model for traffic breakdown, highway capacity, and synchronized flow" Phys. Rev. E 84, 046110 (2011). doi: 10.1103/PhysRevE.84.046110
• Boris S. Kerner, Sergey L. Klenov, Gerhard Hermanns, and Michael Schreckenberg, "Effect of driver over-acceleration on traffic breakdown in three-phase cellular automaton traffic flow models" Physica A 392, 4083-4105 (2013). doi: 10.1016/j.physa.2013.04.035
• Boris S. Kerner, Sergey L. Klenov, and Michael Schreckenberg, "Probabilistic physical characteristics of phase transitions at highway bottlenecks: Incommensurability of three-phase and two-phase traffic-flow theories" Phys. Rev. E 89, 052807 (2014). doi: 10.1103/PhysRevE.89.052807

• Boris S. Kerner, "Statistical Physics of Synchronized Traffic Flow: Spatiotemporal Competition between S → F and S → J Instabilities", Phys. Rev. E 100, 012303 (2019). doi: 10.1103/PhysRevE.100.012303

• Boris S. Kerner, "Microscopic theory of traffic-flow instability governing traffic breakdown at highway bottlenecks: Growing wave of increase in speed in synchronized flow", Phys. Rev. E, 92, 062827 (2015)

• Boris S. Kerner, "A theory of traffic congestion at heavy bottlenecks" J. Phys. A: Math. Gen. 41, 215101 (2008). doi: 10.1088/1751-8113/41/21/215101

• Boris S. Kerner, "Complexity of Spatiotemporal Traffic Phenomena in Flow of Identical Drivers: Explanation based on Fundamental Hypothesis of Three-Phase Theory", Phys. Rev. E 85, 036110 (2012). doi:10.1103/PhysRevE.84.045102

• Boris S. Kerner, "Physics of traffic gridlock in a city", Phys. Rev. E 84, 045102(R) (2011). doi:10.1103/PhysRevE.84.045102
• Boris S. Kerner, "The physics of green-wave breakdown in a city " Europhysics Letters 102, 28010 (2013). doi:10.1209/0295-5075/102/28010
• Boris S. Kerner, "Three-phase theory of city traffic: Moving synchronized flow patterns in under-saturated city traffic at signals", Physica A: Statistical Mechanics and its Applications 397, 76–110 (2014). doi:10.1016/j.physa.2013.11.009
• Boris S. Kerner, Sergey L. Klenov, and Michael Schreckenberg, "Traffic breakdown at a signal: classical theory versus the three-phase theory of city traffic" Journal of Statistical Mechanics: Theory and Experiment, P03001 (2014). doi: 10.1088/1742-5468/2014/03/p03001

• Boris S. Kerner, "Physics of automated driving in framework of three-phase traffic theory" Phys. Rev. E, 97, 042303 (2018). doi: 10.1103/PhysRevE.97.042303
• Boris S. Kerner, "Autonomous Driving in the Framework of Three-Phase Traffic Theory". In: "Complex Dynamics of Traffic Management", Encyclopedia of Complexity and Systems Science Series, 2nd ed., edited by Boris S. Kerner (Springer, New York, 2019), pp. 343–385. doi: 10.1007/978-1-4939-8763-4_724
• Boris S. Kerner, Hubert Rehborn, Mario Aleksic, Andreas Haug "Recognition and tracking of spatial-temporal congested traffic patterns on freeways", Transportation Research Part C: Emerging Technologies, 12, 369-400 (2004). doi: 10.1016/j.trc.2004.07.015
• Boris S. Kerner, "Control of spatiotemporal congested traffic patterns at highway bottlenecks", Physica A, 355, 565-601 (2005). doi: 10.1016/j.physa.2005.04.025
• Boris S. Kerner, "Control of Spatiotemporal Congested Traffic Patterns at Highway Bottlenecks", IEEE Transactions on Intelligent Transportation Systems 8, 308-320 (2007). doi: 10.1109/TITS.2007.894192
• Boris S. Kerner, "Study of freeway speed limit control based on three-phase traffic theory", Transportation Research Record, 1999, 30-39 (2007). doi: 10.3141/1999-04
• Boris S. Kerner, "On-Ramp Metering Based on Three-Phase Traffic Theory: Downstream Off-Ramp and Upstream On-Ramp Bottlenecks", Transportation Research Record, 2088, 80-89 (2008). doi: 10.3141/2088-09

• Boris S. Kerner, "Optimum principle for a vehicular traffic network: minimum probability of congestion", J. Phys. A: Math. Theor. 44, 092001 (2011). doi:10.1088/1751-8113/44/9/092001

• Boris S. Kerner, "The maximization of the network throughput ensuring free flow conditions in traffic and transportation networks: Breakdown minimization (BM) principle versus Wardrop’s equilibria", Eur. Phys. B J., 89, 199 (2016). doi: 10.1140/epjb/e2016-70395-8