Traffic congestion: Reconstruction with Kerner’s three-phase theory
Encyclopedia
Vehicular traffic
can be either free or congested. Traffic occurs in time and space, i.e., it is a spatiotemporal process. However, usually traffic can be measured only at some road locations (for example, via road detectors, video-cameras
, probe vehicle data
, or phone data
). For efficient traffic control
and other intelligent transportation systems, the reconstruction of traffic congestion
is necessary at all other road locations at which traffic measurements are not available. Traffic congestion can be reconstructed in space and time (Fig. 1) based on Boris Kerner
’s three-phase traffic theory
with the use of the ASDA and FOTO models introduced by Kerner. Kerner’s three-phase traffic theory and, respectively, the ASDA/FOTO models are based on some common spatiotemporal features of traffic congestion observed in measured traffic data.
, road conditions and road infrastructure, vehicular technology, driver characteristics, day time, etc.
Kerner’s definitions [S] and [J], respectively, for the synchronized flow and wide moving jam phases in congested traffic are examples of common spatiotemporal empirical features of traffic congestion.
as a result of traffic breakdown
in an initially free flow at the bottleneck. A highway bottleneck can result from on- and off-ramps, road curves and gradients, road works, etc.
In congested traffic (this is a synonym term to traffic congestion), a phenomenon of the propagation of a moving traffic jam (moving jam for short) is often observed. A moving jam
is a local region of low speed and great density that propagates upstream as a whole localized structure. The jam is limited spatially by two jam fronts. At the downstream jam front, vehicles accelerate to a higher speed downstream of the jam. At the upstream jam front, vehicles decelerate while approaching the jam.
A wide moving jam is a moving jam that exhibits the characteristic jam feature [J], which is a common spatiotemporal empirical feature of traffic congestion. The jam feature [J] defines the wide moving jam traffic phase in congested traffic as follows.
.
Kerner’s jam feature [J] can be explained as follows. The motion of the downstream jam front results from acceleration of drivers from a standstill within the jam to traffic flow downstream of the jam. After a vehicle has begun to accelerate escaping from the jam, to satisfy safety driving, the following vehicle begins to accelerate with a time delay. We denote the mean value of this time delay in vehicle acceleration at the downstream jam front by
. Because the average distance between vehicles within the jam, including average vehicle length, equals to 
(where 
is the average vehicle density within the jam), the mean velocity of the downstream jam front 
is
.
When traffic parameters (percentage of long vehicles, weather, driver characteristics, etc.) do not change over time,
and 
are constant in time. This explains why the mean velocity of the downstream jam front 
(1) is the characteristic parameter that does not depend of the flow rates and densities upstream and downstream of the jam.
A particular case of this common feature of synchronized flow is that the downstream synchronized flow front is usually caught at a highway bottleneck. This pinning of the downstream front of synchronized flow at the bottleneck is called the catch effect. Note that at this downstream front of synchronized flow, vehicles accelerate from a lower speed within synchronized flow upstream of the front to a higher speed in free flow downstream of the front.
Thus Kerner’s definitions [J] and [S] for the wide moving jam and synchronized flow phases of his three-phase traffic theory are indeed associated with common empirical features of traffic congestion.
One of the empirical features the synchronized flow and wide moving jam phases used in the ASDA/FOTO models for traffic phase identification is as follows: Within a wide moving jam, both the speed and flow rate are very small (Fig. 2 (c-f)). In contrast, whereas the speed with the synchronized flow phase is considerably lower than in free flow (Fig. 2 (c, e)), the flow rate in synchronized flow can be as great as in free flow (Fig. 2 (d, f)).
Secondly, based on the abovementioned common features of wide moving jams and synchronized flow, the FOTO model tracks the downstream and upstream fronts of synchronized flow denoted by
, 
, where 
is time (Fig. 3). The ADSA model tracks the downstream and upstream fronts of wide moving jams denoted by 
, 
(Fig. 3). This tracking is carried out between road locations at which the traffic phases have initially been identified in measured data, i.e., when synchronized flow and wide moving jams cannot be measured.
In other words, the tracking of synchronized flow by the FOTO model and wide moving jams by the ASDA model is performed at road locations at which no traffic measurements are available, i.e., the ASDA/FOTO models make the forecasting of the front locations of the traffic phases in time. The ASDA/FOTO models enable us to predict the merging and/or the dissolution
of one or more initially different synchronized flow regions and of one or more initially different wide moving jams that occur between measurement locations.
where
and 
[vehicles/h] are respectively the flow rates upstream and downstream of the synchronized flow front, 
is a model parameter [m/vehicles], and 
is the number of road lanes.
The current velocity
of a front of a wide moving jam is calculated though the use of the shock-wave formula derived by Stokes in 1848:
,
where
and 
the flow rate and density upstream of the jam front that velocity should be found; 
and 
are the flow rate and density downstream of this jam front. In (3) no any relationship
, in particular, no fundamental diagram is used between the flow rates
, 
and vehicle densities 
, 
found from measured data independent of each other.
If measured data are not available for the tracking of the downstream jam front with the Stokes-shock-wave formula (3), the formula
is used in which
is the characteristic velocity of the downstream jam front associated with Kerner’s jam feature [J] discussed above. This means that after the downstream front of a wide moving jam has been identified at a time instant 
, the location of the downstream front of the jam can be estimated with formula
The characteristic jam velocity is illustrated in Fig. 4. Two wide moving jams propagate upstream while maintaining the mean velocity of their downstream fronts. There are two jams following each other in this empirical example.
However, in contrast with the mean velocity of the downstream jam front, the mean velocity of the upstream jam front depends on the flow rate and density in traffic flow upstream of the jam. Therefore, in a general case the use of formula (5) can lead to a great error by the estimation of the mean velocity of the upstream jam front.
In many data measured on German highways has been found
. However, although the mean velocity 
of the downstream jam front is independent of the flow rates and densities upstream and downstream of the jam, 
can depend considerably on traffic parameters like the percentage of long vehicles in traffic, weather, driver characteristics, etc. As a result, the mean velocity 
found in different data measured over years of observations varies approximately within the range 
.
. The application covers a part of the whole freeway network with 1900 km of freeway and more than 1000 double loop detectors. In addition, since 2009 ASDA/FOTO models are online in the northern part of Bavaria.
Traffic
Traffic on roads may consist of pedestrians, ridden or herded animals, vehicles, streetcars and other conveyances, either singly or together, while using the public way for purposes of travel...
can be either free or congested. Traffic occurs in time and space, i.e., it is a spatiotemporal process. However, usually traffic can be measured only at some road locations (for example, via road detectors, video-cameras
Video camera
A video camera is a camera used for electronic motion picture acquisition, initially developed by the television industry but now common in other applications as well. The earliest video cameras were those of John Logie Baird, based on the electromechanical Nipkow disk and used by the BBC in...
, probe vehicle data
Floating Car Data
Floating car data , also known as floating cellular data, is a method to determine the traffic speed on the road network. It is based on the collection of localisation data, speed, direction of travel and time information from mobile phones in vehicles that are being driven...
, or phone data
Floating Car Data
Floating car data , also known as floating cellular data, is a method to determine the traffic speed on the road network. It is based on the collection of localisation data, speed, direction of travel and time information from mobile phones in vehicles that are being driven...
). For efficient traffic control
Traffic control
Road traffic control involves directing vehicular and pedestrian traffic around a construction zone, accident or other road disruption, thus ensuring the safety of emergency response teams, construction workers and the general public....
and other intelligent transportation systems, the reconstruction of traffic congestion
Traffic congestion
Traffic congestion is a condition on road networks that occurs as use increases, and is characterized by slower speeds, longer trip times, and increased vehicular queueing. The most common example is the physical use of roads by vehicles. When traffic demand is great enough that the interaction...
is necessary at all other road locations at which traffic measurements are not available. Traffic congestion can be reconstructed in space and time (Fig. 1) based on Boris Kerner
Boris Kerner
Boris S. Kerner is the pioneer of the much-discussed three-phase traffic theory.- Life and work :Boris S. Kerner is a leading expert in intelligent transportation systems and in the theory of pattern formation in dissipative physical, chemical, biological systems. He was born in Moscow, Soviet...
’s three-phase traffic theory
Three phase traffic theory
Three-phase traffic theory is an alternative theory of traffic flow developed by Boris Kerner between 1996 and 2002. It focuses mainly on the explanation of the physics of traffic breakdown and resulting congested traffic on highways...
with the use of the ASDA and FOTO models introduced by Kerner. Kerner’s three-phase traffic theory and, respectively, the ASDA/FOTO models are based on some common spatiotemporal features of traffic congestion observed in measured traffic data.
Definition
Common spatiotemporal empirical features of traffic congestion are those spatiotemporal features of traffic congestion, which are qualitatively the same for different highways in different countries measured during years of traffic observations. In particular, common features of traffic congestion are independent on weatherWeather
Weather is the state of the atmosphere, to the degree that it is hot or cold, wet or dry, calm or stormy, clear or cloudy. Most weather phenomena occur in the troposphere, just below the stratosphere. Weather refers, generally, to day-to-day temperature and precipitation activity, whereas climate...
, road conditions and road infrastructure, vehicular technology, driver characteristics, day time, etc.
Kerner’s definitions [S] and [J], respectively, for the synchronized flow and wide moving jam phases in congested traffic are examples of common spatiotemporal empirical features of traffic congestion.
Propagation of wide moving jams through highway bottlenecks
In empirical observations, traffic congestion occurs usually at a highway bottleneckBottleneck
A bottleneck is a phenomenon where the performance or capacity of an entire system is limited by a single or limited number of components or resources. The term bottleneck is taken from the 'assets are water' metaphor. As water is poured out of a bottle, the rate of outflow is limited by the width...
as a result of traffic breakdown
Three phase traffic theory
Three-phase traffic theory is an alternative theory of traffic flow developed by Boris Kerner between 1996 and 2002. It focuses mainly on the explanation of the physics of traffic breakdown and resulting congested traffic on highways...
in an initially free flow at the bottleneck. A highway bottleneck can result from on- and off-ramps, road curves and gradients, road works, etc.
In congested traffic (this is a synonym term to traffic congestion), a phenomenon of the propagation of a moving traffic jam (moving jam for short) is often observed. A moving jam
Three phase traffic theory
Three-phase traffic theory is an alternative theory of traffic flow developed by Boris Kerner between 1996 and 2002. It focuses mainly on the explanation of the physics of traffic breakdown and resulting congested traffic on highways...
is a local region of low speed and great density that propagates upstream as a whole localized structure. The jam is limited spatially by two jam fronts. At the downstream jam front, vehicles accelerate to a higher speed downstream of the jam. At the upstream jam front, vehicles decelerate while approaching the jam.
A wide moving jam is a moving jam that exhibits the characteristic jam feature [J], which is a common spatiotemporal empirical feature of traffic congestion. The jam feature [J] defines the wide moving jam traffic phase in congested traffic as follows.
Definition [J] for wide moving jam
A wide moving jam is a moving traffic jam, which exhibits the characteristic jam feature [J] to propagate through any bottlenecks while maintaining the mean velocity of the downstream jam front denoted by.Kerner’s jam feature [J] can be explained as follows. The motion of the downstream jam front results from acceleration of drivers from a standstill within the jam to traffic flow downstream of the jam. After a vehicle has begun to accelerate escaping from the jam, to satisfy safety driving, the following vehicle begins to accelerate with a time delay. We denote the mean value of this time delay in vehicle acceleration at the downstream jam front by
. Because the average distance between vehicles within the jam, including average vehicle length, equals to (where is the average vehicle density within the jam), the mean velocity of the downstream jam front is.When traffic parameters (percentage of long vehicles, weather, driver characteristics, etc.) do not change over time,
and are constant in time. This explains why the mean velocity of the downstream jam front (1) is the characteristic parameter that does not depend of the flow rates and densities upstream and downstream of the jam.Catch effect: pinning of downstream front of synchronized flow at bottleneck
In contrast with the jam feature [J], the mean velocity of the downstream front of synchronized flow is not self-maintained during the front propagation. This is the common feature of synchronized flow that is one of the two phases of traffic congestion.A particular case of this common feature of synchronized flow is that the downstream synchronized flow front is usually caught at a highway bottleneck. This pinning of the downstream front of synchronized flow at the bottleneck is called the catch effect. Note that at this downstream front of synchronized flow, vehicles accelerate from a lower speed within synchronized flow upstream of the front to a higher speed in free flow downstream of the front.
Definition [S] for synchronized flow
Synchronized flow is defined as congested traffic that does not exhibit the jam feature [J]; in particular, the downstream front of synchronized flow is often fixed at the bottleneck.Thus Kerner’s definitions [J] and [S] for the wide moving jam and synchronized flow phases of his three-phase traffic theory are indeed associated with common empirical features of traffic congestion.
Empirical example of wide moving jam and synchronized flow
Vehicle speeds measured with road detectors (1 min averaged data) illustrate Kerner’s definitions [J] and [S] (Fig. 2 (a, b)). There are two spatiotemporal patterns of congested traffic with low vehicle speeds in Fig. 2 (a). One pattern of congested traffic propagates upstream with almost constant mean velocity of the downstream pattern front through the freeway bottleneck. According to the definition [J] this pattern of congested traffic belongs to the "wide moving jam" traffic phase. In contrast, the downstream front of the other pattern of the congested traffic is fixed at the bottleneck. According to the definition [S] this pattern of congested traffic belongs to the "synchronized flow" traffic phase (Fig. 2 (a) and (b)).ASDA and FOTO models
The FOTO (Forecasting of traffic objects) model reconstructs and tracks regions of synchronized flow in space and time. The ASDA (Automatische Staudynamikanalyse: Automatic Tracking of Moving Jams) model reconstructs and tracks wide moving jams. The ASDA/FOTO models are devoted to on-line applications without calibration of model parameters under different environment conditions, road infrastructure, percentage of long vehicles, etc.General features
Firstly, the ASDA/FOTO models identify the synchronized flow and wide moving jam phases in measured data of congested traffic.One of the empirical features the synchronized flow and wide moving jam phases used in the ASDA/FOTO models for traffic phase identification is as follows: Within a wide moving jam, both the speed and flow rate are very small (Fig. 2 (c-f)). In contrast, whereas the speed with the synchronized flow phase is considerably lower than in free flow (Fig. 2 (c, e)), the flow rate in synchronized flow can be as great as in free flow (Fig. 2 (d, f)).
Secondly, based on the abovementioned common features of wide moving jams and synchronized flow, the FOTO model tracks the downstream and upstream fronts of synchronized flow denoted by
, , where is time (Fig. 3). The ADSA model tracks the downstream and upstream fronts of wide moving jams denoted by , (Fig. 3). This tracking is carried out between road locations at which the traffic phases have initially been identified in measured data, i.e., when synchronized flow and wide moving jams cannot be measured.In other words, the tracking of synchronized flow by the FOTO model and wide moving jams by the ASDA model is performed at road locations at which no traffic measurements are available, i.e., the ASDA/FOTO models make the forecasting of the front locations of the traffic phases in time. The ASDA/FOTO models enable us to predict the merging and/or the dissolution
Dissolution
Dissolution or dissolve may refer to:* Dissolution , in law, means to end a legal entity or agreement such as a marriage, adoption, or corporation...
of one or more initially different synchronized flow regions and of one or more initially different wide moving jams that occur between measurement locations.
Cumulative flow approach for FOTO
While the downstream front of synchronized flow at which vehicles accelerate to free flow is usually fixed at the bottleneck (see Fig. 2 (a, b)), the upstream front of synchronized flow at which vehicles moving initially in free flow must decelerate approaching synchronized flow can propagate upstream. In empirical (i.e., measured) traffic data, the velocity of the upstream front of synchronized flow depends usually considerably both on traffic variables within synchronized flow downstream of the front and within free flow just upstream of this front. A good correspondence with empirical data is achieved, if a time-dependence of the location of the synchronized flow front is calculated by the FOTO model with the use of a so-called cumulative flow approach:where
and [vehicles/h] are respectively the flow rates upstream and downstream of the synchronized flow front, is a model parameter [m/vehicles], and is the number of road lanes.Two approaches for jam tracking with ASDA
There are two main approaches for the tracking of wide moving jams with the ASDA model:- The use of the Stokes-shock-wave formula.
- The use of a characteristic velocity of wide moving jams.
The use of the Stokes-shock-wave formula in ASDA
The current velocity
of a front of a wide moving jam is calculated though the use of the shock-wave formula derived by Stokes in 1848:,where
and the flow rate and density upstream of the jam front that velocity should be found; and are the flow rate and density downstream of this jam front. In (3) no any relationshipRelationship
Relationship or relationships may refer to:* Interpersonal relationship* Intimate relationship* In mathematics and statistics:** Binary relation** Causal relationship** Correlation and dependence** Direct relationship** Inverse relationship...
, in particular, no fundamental diagram is used between the flow rates
, and vehicle densities , found from measured data independent of each other.The use of a characteristic velocity of wide moving jams
If measured data are not available for the tracking of the downstream jam front with the Stokes-shock-wave formula (3), the formula
is used in which
is the characteristic velocity of the downstream jam front associated with Kerner’s jam feature [J] discussed above. This means that after the downstream front of a wide moving jam has been identified at a time instant , the location of the downstream front of the jam can be estimated with formulaThe characteristic jam velocity is illustrated in Fig. 4. Two wide moving jams propagate upstream while maintaining the mean velocity of their downstream fronts. There are two jams following each other in this empirical example.
However, in contrast with the mean velocity of the downstream jam front, the mean velocity of the upstream jam front depends on the flow rate and density in traffic flow upstream of the jam. Therefore, in a general case the use of formula (5) can lead to a great error by the estimation of the mean velocity of the upstream jam front.
In many data measured on German highways has been found
. However, although the mean velocity of the downstream jam front is independent of the flow rates and densities upstream and downstream of the jam, can depend considerably on traffic parameters like the percentage of long vehicles in traffic, weather, driver characteristics, etc. As a result, the mean velocity found in different data measured over years of observations varies approximately within the range .On-line applications of ASDA/FOTO models in traffic control centres
Reconstruction and tracking of spatiotemporal congested patterns with the ASDA/FOTO models is done today online permanently in the traffic control centre of the federal state Hessen (Germany) for 1200 km of freeway network. Since April 2004 measured data of nearly 2500 detectors are automatically analyzed by ASDA/FOTO. The resulting spatiotemporal traffic patterns are illustrated in a space-time diagram showing congested pattern features like Fig. 5. The online system has also been installed in 2007 for North-Rhine Westphalia freeways. The raw traffic data are transferred to WDR, the major public radio broadcasting station from North-Rhine Westphalia in Cologne, who offers traffic messages to the end customer (e. g., radio listener or driver) via broadcast channel RDSRadio Data System
Radio Data System, or RDS, is a communications protocol standard for embedding small amounts of digital information in conventional FM radio broadcasts. RDS standardises several types of information transmitted, including time, station identification and programme information.Radio Broadcast Data...
. The application covers a part of the whole freeway network with 1900 km of freeway and more than 1000 double loop detectors. In addition, since 2009 ASDA/FOTO models are online in the northern part of Bavaria.
Average traffic flow characteristics and travel time
In addition to spatiotemporal reconstruction of traffic congestion (Figs. 1 and 5), the ASDA/FOTO models can provide average traffic flow characteristics within synchronized flow and wide moving jams. In turn, this permits the estimation of either travel time on a road section or travel time along any vehicle trajectory (see examples of trajectories 1-4 in Fig. 5).ASDA/FOTO models for data measured by probe vehicles
Firstly, the ASDA and FOTO models identify transition points for phase transitions along the trajectory of a probe vehicle. Each of the transition points is associated to the front separating spatially two of the three different traffic phases each other (free flow (F), synchronized flow (S), wide moving jam (J)). After the transition points have been found, the ASDA/FOTO models reconstruct regions of synchronized flow and wide moving jams in space and time with the use of empirical features of these traffic phases discussed above (see Figs. 2 and 4).Publications
- B.S. Kerner, Introduction to Modern Traffic Flow Theory and Control: The Long Road to Three-Phase Traffic Theory, Springer, Berlin, New York 2009
- B.S. Kerner, The Physics of Traffic, Springer, Berlin, New York 2004
See also
- Active Traffic ManagementActive Traffic ManagementActive traffic management , also known as managed lanes or smart lanes, is a scheme for improving traffic flow and reducing congestion on motorways. It has been implemented in several countries, including Germany, the United Kingdom, and the United States...
- Fundamental diagram
- Intelligent transportation systemIntelligent transportation systemThe term intelligent transportation systems refers to information and communication technology that improve transport outcomes such as transport safety, transport productivity, travel reliability, informed travel choices, social equity, environmental performance and network operation...
- Microscopic traffic flow modelMicroscopic traffic flow modelMicroscopic traffic flow models are a class of scientific models of vehicular traffic dynamics.In contrast to macroscopic models, microscopic traffic flow models simulate single vehicle-driver units, thus the dynamic variables of the models represent microscopic properties like the position and...
- TrafficTrafficTraffic on roads may consist of pedestrians, ridden or herded animals, vehicles, streetcars and other conveyances, either singly or together, while using the public way for purposes of travel...
- Traffic bottleneckTraffic bottleneckA traffic bottleneck is a localized disruption of vehicular traffic on a street, road or highway. As opposed to a traffic jam, a bottleneck is a result of a specific, often temporary, physical condition.- Causes :...
- Traffic flowTraffic flowTraffic flow, in mathematics and civil engineering, is the study of interactions between vehicles, drivers, and infrastructure , with the aim of understanding and developing an optimal road network with efficient movement of traffic and minimal traffic congestion problems.-History:Attempts to...
- Traffic waveTraffic waveTraffic waves, also called stop waves or traffic shocks, are travelling disturbances in the distribution of cars on a highway. Traffic waves usually travel backwards in relation to the motion of the cars themselves, or "upstream". The waves can also travel downstream, however, more commonly become...
- Traffic congestionTraffic congestionTraffic congestion is a condition on road networks that occurs as use increases, and is characterized by slower speeds, longer trip times, and increased vehicular queueing. The most common example is the physical use of roads by vehicles. When traffic demand is great enough that the interaction...
- Three phase traffic theoryThree phase traffic theoryThree-phase traffic theory is an alternative theory of traffic flow developed by Boris Kerner between 1996 and 2002. It focuses mainly on the explanation of the physics of traffic breakdown and resulting congested traffic on highways...
- Transportation forecastingTransportation forecastingTransportation forecasting is the process of estimating the number of vehicles or people that will use a specific transportation facility in the future. For instance, a forecast may estimate the number of vehicles on a planned road or bridge, the ridership on a railway line, the number of...