Three-phase traffic theory

The three-phase traffic theory is an alternative transport theory founded by Boris Kerner in 1996-2002. She explains the traffic breakdown and the resulting congested traffic on highways. Kerner describes three stages of the circulation, whereas the classical theories based on the fundamental diagram of traffic flow includes two phases: the free movement and jammed traffic. The jammed traffic of Kerner in two phases, Synchronized traffic and wide moving jam yourself, divided, from which results in a total of three phases:

A phase is defined as a state in time and space.

• 4.1 Hypothetical homogeneous states of synchronized traffic
• 4.2 infinite number of distances between vehicles at a given speed

• 6.1 Spontaneous and induced F → S phase transitions
• 6.2 Statement of the traffic breakdown

• 7.1 Maximum and minimum road capacity
• 7.2 road capacity and metastability of free movement
• 7.3 Discussion of the definitions of road capacity

• 8.1 Characteristic properties of wide moving jams
• 8.2 Minimum road capacity and congestion outflow

Free circulation (F)

In free traffic, drivers can choose their speed mostly free. Empirical data show a positive correlation between the flow of traffic ( in vehicles per unit time) and the density of traffic ( in vehicles per unit length). This relationship is a maximum point on the movement of a maximum flow with a corresponding critical density limited ( Fig. 1).

Dammed traffic

In congested traffic, the vehicle speed is lower than the minimum possible vehicle speed of free traffic. Thus, the line divides with the slope corresponding to the minimum vehicle speed of free movement (dotted line in Figure 2), all empirical data on the flow - density plane into two areas: data links lying correspond to the free circulation correspond to data righthand the jammed ( English: congested ) traffic.

Definitions of the phases J and S in jammed traffic

The phase definitions [J ] and [ S] in jammed traffic are the result of the general empirical temporal- spatial characteristics of the traffic data.

Generally valid temporal- spatial characteristics of traffic disruptions

Generally valid temporal- spatial characteristics of traffic disruptions are those that have been identified on the basis of long-term measurements on different highways in different countries alike. In particular, these properties are independent on weather, road conditions and road infrastructure conditions, vehicle technology, driver characteristics, time of day etc..

The Kerner definitions [S ] and [ J] for the phases of synchronized traffic ( marked in the other by " S" ) and the wide moving jams ( marked in the other by " J", in English: "wide moving jam" ) are examples of this general temporal- spatial characteristics of traffic incidents.

Locomotion wide moving jams by constrictions of highways

In empirical observations traffic congestion normally occurs at a narrow point of a highway as a result of a traffic collapse in an initially free traffic. Such a bottleneck can be caused by entries and exits, curvy lines, slopes, construction sites, etc..

(: Moving jam less) frequently observed in jammed traffic ( is hereafter used as a synonym for traffic disruption ) is the phenomenon of a locomotive wide jams. Such a moving jam is a spatial area at low speed and high traffic density, which moves against the direction of travel. The storage area is bounded by two jam fronts: speed at the downstream in the direction the vehicles back and delay at the upstream these as they approach the dam area.

A moving widespread congestion is congestion with the characteristic property of the phase Y, is one of the general characteristics of traffic congestion.

Definition [ J ] for the transport phase " wide moving jam "

The Kerner'sche definition [ J] Phase J is as follows: A wide moving jam moves through all the narrow pass. The average speed of the downstream side accumulating front is maintained (indicated ).

This Kerner'sche storage capacity of [J ] is explained as follows: the locomotion of the downstream front of a wide moving jams caused by the acceleration of the driver from a standstill in traffic. Once a vehicle has started with this acceleration, followed by a next vehicle, maintaining a safe distance with a time lag. We denote the mean value of this time delay. Since the average distance between vehicles in traffic jams, including the mean vehicle length is the same ( with the average density of vehicles in a traffic jam ) is obtained for the mean velocity of the downstream jam front

.

If you can not change the parameters of the traffic as proportion of trucks, weather, driver characteristics, etc. over time, the values ​​and time are constant. This explains why the average front velocity is a characteristic value, which does not depend on the traffic flows and traffic densities before and after the jam.

"Catch effect": capturing the downstream front of synchronized traffic at a narrow

In contrast to the characteristics of [ J ] is the mean velocity of the downstream front of the synchronized traffic is not preserved during its movement: this is a general property of the synchronized traffic. A special case of this characteristic property for the synchronized traffic is that, the downstream front is held at a narrow point. This holding the front at a narrow point was designated as catch- effect. At the downstream front accelerate the vehicle from a lower speed to a higher one.

Definition [ S ] for the traffic phase " synchronized traffic "

Definition [ S] for the phase S: Synchronized traffic is configured to have as a jammed traffic without the characteristic property of [J ]; in particular, the downstream front of the synchronized traffic is fixed often fixed at a narrow point.

The Kerner definitions [J ] and [ S] the phases wide moving jam and synchronized traffic within the three -phase traffic theory, the general characteristics of traffic incidents on the road.

Declaration of phase definitions [J ] and [ S] with empirical data

The definitions [J ] and [ S] are illustrated by real data for the average vehicle speed (Fig. 3 ( a)). There are two different spatio-temporal structures of the congested traffic with low vehicle speeds in Figure 3 (a). A structure of the congested traffic propagates upstream at a nearly constant velocity of the downstream front through the constriction on the freeway. According to the definition [J ], this structure of the congested traffic to the traffic belongs phase " wide moving jam ". In contrast, the downstream front of the other structure of the congested traffic at the bottleneck is fixed. According to the definition [ S], this structure of the congested traffic is part of the traffic phase " synchronized traffic " (Figs. 3 (a) and ( b)).

The fundamental hypothesis of Kerner's three-phase traffic theory

Hypothetical homogeneous states of synchronized traffic

The fundamental hypothesis of Kerner's three-phase traffic theory is connected with states of the homogeneous synchronized traffic ( in further referred to as homogeneous synchronized traffic, English: "a steady state of synchronized flow" ). Such a homogeneous synchronized traffic is a hypothetical state of synchronized traffic of the same vehicles and drivers, in which all vehicles with the same time-independent velocity and equal distances (the distance is the net distance between two successive vehicles ) move, which means this synchronized traffic is homogeneous in time and space.

Infinite number of distances between vehicles at a given speed

The fundamental hypothesis is as follows: states of homogeneous synchronized traffic flow cover a two-dimensional surface in the flow - density plane ( 2D region S in Figure 4 (a) ). The set of possible states free movement overlaps while the set of states of the homogeneous synchronized traffic for a given traffic density. The states of the free traffic on a multi-lane road, and the states of the homogeneous synchronized traffic are separated by a gap in the traffic flow, and, consequently, through a gap in the velocity at a given traffic density: at each traffic density is the speed in synchronized homogeneous traffic lower than in free circulation

In accordance with the fundamental hypothesis of Kerner's three-phase traffic theory can make an arbitrary choice of the distance to the vehicle ahead, a driver at a given speed in a homogeneous synchronized traffic. This is within a certain range of distances corresponding to the two-dimensional plane of the states of the uniform synchronized traffic possible (Fig. 4 (b)): a driver accepts at different times and at different distances does not control towards a fixed distance to the preceding vehicle.

The fundamental hypothesis of Kerner's three-phase traffic theory is at odds with previous traffic flow theories about the fundamental diagram of traffic, which knows a one-dimensional relationship between traffic density and traffic flow.

Headways in the three-phase traffic theory

In Kerner three-phase transport theory accelerates a vehicle to the preceding vehicle when the distance g is greater than a synchronization distance, ie (described as a vehicle acceleration in Figure 5) at. The vehicle is decelerating when its distance is smaller than a safety distance, ie (described as the deceleration of the vehicle in Figure 5) at

A smaller distance than the synchronization distance corresponds to a distance between two vehicles, within which a vehicle is the speed of the preceding vehicle adapts without paying attention to the exact distance. This is the case until this distance is not less than a safety distance (described as speed adaptation in Figure 5). In other words, the vehicle follow-up performance in the three-phase Kerner traffic theory, each distance may be in the area.

Traffic breakdown - an F → S phase transition

In measurement data of the jammed traffic usually occurs at a narrow point of the highway, such as a driveway, a departure or a construction site. Such a transition from free to congested traffic is known as traffic breakdown (ie collapse of traffic ). In Kerner three-phase traffic theory, a traffic breakdown is explained by an F → S phase transition. This statement is confirmed by available data, as in measurements of traffic for a traffic breakdown at a narrow point, the downstream edge of the congested traffic is fixed at the bottleneck. Therefore, the resulting in a traffic breakdown jammed traffic meets the definition of [S ] for the traffic phase " synchronized traffic ".

Spontaneous and induced F → S phase transitions

Kerner notes with the use of empirically measured data that synchronized traffic is in free circulation spontaneously ( spontaneous F → S phase transition ) or externally induced ( induced F → S phase transition ) can form. Spontaneous F → S phase transition means that a traffic breakdown occurs when the free movement previously existed of the constriction on both the constriction and downstream and upstream. This means that a spontaneous F → S phase transition occurs by the growth of a separate disorder in free circulation. In contrast, an induced collapse is caused by disturbances in the traffic flow at a different location. This usually is associated with an upstream propagation of an area of synchronized traffic or wide moving jams. An empirical example of induced traffic breakdown at a narrow point, which leads to synchronized traffic is seen on Figure 3, : by the movement of a wide moving jams through the constriction created synchronized traffic.

Declaration of the traffic breakdown

Kerner explains the nature of the F → S phase transition by a temporal- spatial competition of the vehicle acceleration by overtaking a slower front man and the vehicle deceleration to the speed of the slower person in front ( " speed adjustment "). An overtaking the slower front man promotes the preservation of freedom of movement. In contrast, leads the "speed adjustment " to synchronized traffic. Such a speed adjustment is made, if a passing operation is not possible. Kerner assumes that the dependence of the Überholwahrscheinlichkeit a discontinuous density function ( Fig. 6): at a given vehicle density, the Überholwahrscheinlichkeit in free circulation is much larger than that in the synchronized traffic.

Infinite number of road capacity

Maximum and minimum road capacity

The spontaneous traffic breakdown, that is, a spontaneous F → S phase transition, can occur in a wide range of traffic flows in free circulation. Kerner notes with the use of empirically measured data, that because of the possibility of a spontaneous or induced traffic breakdown at the same constriction of a road an infinite number of road capacity exists. This endless road capacities are between a minimum and a maximum road capacity road capacity of free movement ( Fig. 7).

Road capacity and metastability of free movement

Even small disturbances in free circulation at a narrow lead to spontaneous F → S phase transition, if the traffic flow in free circulation approaches the maximum road capacity. By contrast, could lead to a bottleneck for spontaneous F → S phase transition in a traffic flow, which is equal to the minimum road capacity, only very large disturbances in free circulation. The probability of a small perturbation in free circulation is much larger than that of a larger disorder. Why is that the greater the flow of traffic in free circulation at the constriction, the greater is the probability of spontaneous F → S phase transition. If the traffic flow in free circulation is less than the minimum road capacity can no traffic breakdown (F → S phase transition ) take place at the constriction, ie the free circulation is stable.

The infinite number of road capacity can also by the metastability on the movement of the traffic flows in the area

Be clarified. Metastability of free movement means that small faults occur the traffic state can still be stable (free movement remains), but with major disruptions in the free movement becomes unstable and then held an F → S phase transition to synchronized traffic.

Discussion of the definitions of road capacity

The infinite number of street capacities of Kerner's three-phase traffic theory contradicts fundamentally the classical transport theories and methods for traffic management and control, where at any time the existence of a certain road capacity is assumed. In contrast, there is the three-phase transport Kerner theory each time an infinite number of road capacity, located within the aforementioned range between the minimum and the maximum capacity road road capacity. The values ​​that may be considerably different traffic parameters depend (percentage of trucks, weather, properties of the effective bottleneck, etc.).

Slow moving traffic ( J)

A moving jam is "wide" called when the width of the moving jam ( in the direction of the highway ) the width of the jam fronts significantly exceeds. The average speed of vehicles within the wide moving jams is significantly lower than the mean velocity in free circulation. At the downstream jam front the vehicles accelerate again to the possible in free circulation speed. On the upstream front, the vehicles come from free trade and have to reduce their speed. According to the definition [J ] a wide moving jam retains the mean velocity of the downstream jam front, even if the jam progresses through different phases of traffic or bottlenecks. The traffic flow (number of vehicles per unit time) is greatly reduced within a wide moving jams.

Characteristic properties of wide moving jams

Kerner's empirical results show that some characteristics of wide moving jams from the traffic and the properties of a constriction, such as where and when a jam has arisen independently. However, these characteristics of the weather conditions, road conditions, etc. strongly depend. The velocity of the downstream jam front of a wide moving jams ( in upstream direction ) is a typical parameters, just as the traffic flow downstream of the downstream jam front (with free traffic at this point, see Figure 8). This means that several slow moving traffic under similar conditions with similar properties. These parameters can be predicted for these reasons in a certain extent. The movement of the front downstream side accumulating, in the flux density level of a line is called the line J are displayed ( line J in Figure 8). The slope of the line J is equal to the speed of the downstream congestion front, because the coordinate of the line J at the null traffic flow corresponding to the traffic density in the reservoir.

Minimum road capacity and congestion outflow

Kerner stresses that the minimum road capacity and the runoff from a wide moving jam two qualitatively different characteristics of the free movement correspond: the minimum road capacity is a characteristic of the F → S- phase transition at a narrow point (ie, the transport collapse ). In contrast, the outflow characterized from a wide moving jam the conditions of existence and the origin of the congestion, ie the transport phase J. Depending on traffic parameters ( such as weather, percentage of trucks in the traffic flow, etc. ) and characteristics of the throat, where the F is taking place → S- phase transition, the minimum road capacity either smaller than the jam outflow (as in image was shown. 8), or as larger.

Synchronized traffic (S )

Unlike moving jams both the flow of traffic and the speeds of the vehicles within the transport phase of the synchronized traffic can vary considerably. The downstream front of the synchronized traffic is often fixed in place (see definition [ S] ), usually in a narrow part of a certain road position. The traffic flow at this stage may still be comparable for free circulation, although the speeds of the vehicles are greatly reduced.

Since, in contrast to wide moving jams the synchronized traffic does not have the characteristic property of the storage phase [ J] Kerner in three-phase traffic theory, it is assumed that hypothetical homogeneous states of synchronized traffic a two-dimensional surface in the flow - density - level form (dotted areas in Figure 8).

S → J phase transition

Slow moving traffic do not arise spontaneously in free circulation, but they can form spontaneously only in areas of the synchronized traffic. This phase transition is called S → J phase transition.

"Jam out of nothing" - F → S → J phase transitions

Therefore, we observe the emergence of wide moving jams in free traffic ( "traffic jam out of nothing" ) as a sequence of F → S → J phase transitions: first arises synchronized traffic in an area of free movement. As explained above, such a F → S phase transition usually occurs in a narrow part of the road. This is a self- compression of synchronized traffic this place, the traffic density is higher, the rate continues to decrease. This self- compression is called "pinch effect". In these areas, the pinch- synchronized traffic moving form tight jams. When these moving narrow jams grow, they develop into wide moving jams. Kerner states that the frequency of occurrence of wide moving jams is higher, the higher the density of the synchronized traffic. This wide moving jams move upstream and propagate further, even if they move through areas of synchronized traffic or other constrictions.

Physics of the S → J phase transition

To illustrate the S → J phase transition, should you notice that in Kerner three-phase traffic theory, the line J are all homogeneous states of synchronized traffic divided into two areas ( Fig. 8). States of the homogeneous synchronized traffic, which are above the line J are metastable. In contrast, the homogeneous synchronized traffic conditions, which are below the line J stable. Metastable homogeneous synchronized traffic means that for small disturbances occurring the traffic condition is still stable, but with major disruptions in the synchronized traffic is unstable and S can take place → J phase transition to a wide moving jam.

Traffic patterns of S and J

Through R → S and S → J phase transitions are observed in measurements of traffic very complex temporal- spatial traffic patterns.

Classification of traffic patterns from S

A model of the synchronized traffic (Synchronized Flow Pattern ( SP) ), with a fixed downstream and not continuously propagating upstream front, local synchronized traffic is called ( Localised Synchronized Flow ( LSP) ).

However, it is frequently observed that the upstream front of a SP moves upstream. If only the upstream jam front moves upstream, then this SP will be a Broadening pattern of synchronized traffic ( Widening Synchronized Flow Pattern (WSP ) ) called. The downstream front remains at the effective bottleneck and the extent of the SP increases.

It is even possible that move both the upstream and the downstream front upstream. The downstream front is no longer fixed to the effective bottleneck. These patterns are moving pattern of synchronized traffic called (Moving Synchronized Flow Patterns ( MSP) ).

"Capture" the traffic patterns of S at a narrow

The difference between a SP and a wide moving jam, however, can be that if a WSP or MSP reaches an upstream bottleneck, there the so-called " catch- effect" occur. The SP is trapped at the constriction and as a result, a new pattern forms at this bottleneck. A wide moving jam, however, is not captured in a narrow and always moves further upstream through the constriction. In contrast to wide moving jams has synchronized traffic, even if it moves as an MSP, no characteristic parameters. For example, the speed of the downstream front of MSP may vary over a wide range and be different for different MSP. These properties of the SP and wide moving jams are a result of traffic phase definitions [S] and [J].

General stowage patterns - traffic patterns of S and J

A very often festzustellendes pattern includes both phases of congested traffic, both [S ] and [J]. Such a traffic pattern that consists of two phases of traffic [S ] and [ J] of the congested traffic is called General stowage patterns ( general pattern ( GP) ).

On many highways, there are very often more narrow near lying adjacent. The then occurring traffic patterns that can occur on two or more narrow the road is called EP (EP: Expanded Pattern). An EP may also consist of synchronized traffic ( ESP: Expanded Synchronized Flow Pattern), but usually form in the synchronized traffic slow moving traffic. In the latter case, the EP is called EGP: means (EGP Expanded General Pattern). An EGP is then both of synchronized traffic, as well as from wide moving jams ( Figure 9).

Applications of the three-phase theory

One of the implemented in software, widely used applications of Kerner's three-phase traffic theory, the models ASDA / FOTO ( Automatic dynamic jam Analysis and Forecasting Of Traffic Objects). ASDA / FOTO generated in an online traffic system based on traffic measurements the phases of congested traffic, [S] and [J]. For the detection, tracking and forecasting of the respective phases of traffic [S ] and [ J] here are the properties of the Kerner be theory used and implemented in the models ASDA / FOTO in a software tool, the large traffic volumes of data quickly in larger expressway networks and can efficiently process (see examples from three countries, Figure 10).

Other possible applications of the theory are in addition to the development of simulation models for example, a ramp metering ( ancona ), collective traffic control, driver assistance and traffic state identification in the vehicle, which are described in the two books by Kerner.