Boris S. Kerner

THE PHYSICS OF TRAFFIC

Traffic jams are a fact of life for many car drivers. Every morning millions of drivers around the world sit motionless in their vehicles for long periods of time as they try to get to work, and then repeat the experience on their journeys home in the evening. The same thing often happens when they are driving to the coast for the weekend or to the airport to go on their holidays. They blame other drivers, increasing volumes of traffic and, inevitably, roadworks. So what has any of this got to do with physics?

Cellular automata approach to three-phase traffic theory

The cellular automata (CA) approach to traffic modelling is extended to allow for spatially homogeneous steady state solutions that cover a two-dimensional region in the flow–density plane. Hence these models fulfil a basic postulate of a three-phase traffic theory proposed by Kerner. This is achieved by a synchronization distance, within which a vehicle always tries to adjust its speed to that of the vehicle in front. In the CA models presented, the modelling of the free and safe speeds, the slow-to-start rules as well as some contributions to noise are based on the ideas of the Nagel–Schreckenberg-type modelling. It is shown that the proposed CA models can be very transparent and still reproduce the two main types of congested patterns (the general pattern and the synchronized flow pattern) as well as their dependence on the flows near an on-ramp, in qualitative agreement with the recently developed continuum version of the three-phase traffic theory (Kerner B S and Klenov S L 2002 J. Phys. A: Math. Gen. 35 L31 ). These features are qualitatively different from those in previously considered CA traffic models. The probability of the breakdown phenomenon (i.e. of the phase transition from free flow to synchronized flow) as function of the flow rate to the on-ramp and of the flow rate on the road upstream of the on-ramp is investigated. The capacity drops at the on-ramp which occur due to the formation of different congested patterns are calculated.

Traffic state detection with floating car data in road networks

A method for a reporting behavior at optimal costs of single vehicles (FCD: floating car data) in road networks with the aim of a high quality of traffic state recognition is presented. It is shown that based on minimum two FCD messages the substantial information of a typical traffic incident in a traffic center can be recognized. The two relevant periods of such an obstruction of traffic in road networks are the periods, in which either a travel time increase takes place due to congestion emergence or a travel time decrease because of congestion dissolution. A statistic analysis already shows the high quality of the reconstruction of the actual travel times in the net with 1.5% equipped FCD vehicles and a reduction of the FCD message sending of the vehicles by suppression of redundant incident information. Incidents with at least 20 min duration can be recognized with a probability of 65% with an penetration rate of 1.5% FCD vehicles within the whole amount of vehicles, whereby the FCD vehicles send only in each incident case two messages per event.

LOCAL CLUSTER EFFECT IN DIFFERENT TRAFFIC FLOW MODELS

A comparison of diverse effects of self-organization in traffic flow in microscopic and macroscopic traffic flow models is made. It is shown that traffic flow models which are mathematically different, belong to the same universality class of traffic flow models in the sense of their possibility to reproduce properties of real traffic jams, if they show the complete properties of the local cluster effect in traffic flow found out by Kerner and Konhauser in 1994.

CONGESTED TRAFFIC FLOW: OBSERVATIONS AND THEORY

Recent and some new results of observations of traffic flow dynamics in congested conditions are considered. On the basis of these results, hypotheses about properties of congested flow are proposed and discussed. In particular, it is proposed that the complexity of congested flow is linked to (a) the existence of three qualitatively different phases in traffic flow: free flow, synchronized flow, and wide traffic jams; (b) an occurrence of three qualitatively different types of phase transitions between these three phases of traffic flow; (c) the result that all these qualitatively different phase transitions are related to the same class of “first-order local phase transitions;” (d) complex dynamical behavior of synchronized flow; and (e) the existence of two qualitatively different kinds of “nucleation effects” in traffic flow: the nucleation effect responsible for the jam’s formation, which is linked to an avalanche increase in the amplitude of an initial local perturbation of traffic variables (vehicle speed, density, or both), and the one responsible for the phase transition from free flow to synchronized flow, which is linked to an avalanche decrease in the probability of passing in free traffic flow.

Deterministic microscopic three-phase traffic flow models

Two different deterministic microscopic traffic flow models, which are in the context of the Kerner’s there-phase traffic theory, are introduced. In an acceleration time delay model (ATD-model), different time delays in driver acceleration associated with driver behaviour in various local driving situations are explicitly incorporated into the model. Vehicle acceleration depends on local traffic situation, i.e., whether a driver is within the free flow, or synchronized flow, or else wide moving jam traffic phase. In a speed adaptation model (SAmodel), vehicle speed adaptation occurs in synchronized flow depending on driving conditions. It is found that the ATDand SA-models show spatiotemporal congested traffic patterns that are adequate with empirical results. In the ATDand SA-models, the onset of congestion in free flow at a freeway bottleneck is associated with a first-order phase transition from free flow to synchronized flow; moving jams emerge spontaneously in synchronized flow only. Differences between the ATDand SA-models are studied. A comparison of the ATDand SA-models with stochastic models in the context of three phase traffic theory is made. A critical discussion of earlier traffic flow theories and models based on the fundamental diagram approach is presented. Deterministic approach to microscopic three-phase traffic theory 2Two different deterministic microscopic traffic flow models, which are in the context of the Kerners there-phase traffic theory, are introduced. In an acceleration time delay model (ATD model), different time delays in driver acceleration associated with driver behaviour in various local driving situations are explicitly incorporated into the model. Vehicle acceleration depends on local traffic situation, i.e., whether a driver is within the free flow or synchronized flow or else wide moving jam traffic phase. In a speed adaptation model (SA model), vehicle speed adaptation occurs in synchronized flow depending on driving conditions. It is found that the ATD and SA models show spatiotemporal congested traffic patterns that are adequate with empirical results. In the ATD and SA models, the onset of congestion in free flow at a freeway bottleneck is associated with a first-order phase transition from free flow to synchronized flow; moving jams emerge spontaneously in synchronized flow only. Differences between the ATD and SA models are studied. A comparison of the ATD and SA models with stochastic models in the context of three-phase traffic theory is made. A critical discussion of earlier traffic flow theories and models based on the fundamental diagram approach is presented.

COMPLEXITY OF SYNCHRONIZED FLOW AND RELATED PROBLEMS FOR BASIC ASSUMPTIONS OF TRAFFIC FLOW THEORIES

A review of an experimental study of traffic phases and phase transitions in traffic flow is presented. A critical comparison of model results with real features of traffic phases is given. A qualitative theory of congested traffic which has recently been developed is discussed.

THEORY OF BREAKDOWN PHENOMENON AT HIGHWAY BOTTLENECKS

On the basis of an empirical study of congestion occurring at a freeway bottleneck, it is shown that the congested regime can exist under a large variation of the discharge flow rate downstream of the bottleneck. This variation can be from about 1,600 to 1,700 vehicles/h to 2,600 to 2,700 vehicles/h per lane. A criticism of the application of queuing theories for the description of traffic pattern features is given. An explanation is given of the features of a congested regime on the basis of the recently discovered properties of synchronized flow as a new traffic phase.

Phase Transitions in Traffic Flow

A review of an experimental study of phase transitions in traffic flow is presented. A critical comparison of real features of phase transitions with recent numerical results is given. A qualitative theory of congested traffic flow recently developed is discussed.

Spatial–temporal patterns in heterogeneous traffic flow with a variety of driver behavioural characteristics and vehicle parameters

A microscopic theory of spatial–temporal congested traffic patterns in heterogeneous traffic flow with a variety of driver behavioural characteristics and vehicle parameters is presented. A microscopic model for heterogeneous traffic flow is developed based on three-phase traffic theory. Diverse congested pattern features at a freeway bottleneck due to an on-ramp in heterogeneous traffic flow on a two-lane freeway are found. A numerical study of these specific pattern features and their comparison with empirical results are performed. A comparison of congested patterns in heterogeneous traffic flow with congested patterns in traffic flow with identical vehicles is made.