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and flow rate (d, f) at two different locations within traffic congestion shown in (a, b); the data in (c, d) and (e, f) are measured respectively at location 17.1 km (c, d) (just downstream of on-ramp lane of an on-ramp bottleneck labelled "On-ramp bottleneck" in (a, b)) and at location 16.2 km (e, f) (upstream of the bottleneck). At location 17.1 the flow rate (d) in free and synchronized flows is greater in comparison with that at location 16.2 (f) due to on-ramp inflow at the bottleneck.
975:
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:
1988:
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61:
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Fig.2. Empirical spatiotemporal common features of traffic congestion and the associated traffic phase definitions in Kerner's theory: (a) Measured data of average vehicle speed in time and space. (b) Representation of speed data in (a) on the time-space plane. (c-f) Time-dependences of speed (c, e)
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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
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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
1991:
Fig. 4: Measured traffic data that illustrates the characteristic jam feature : (a, b) Average speed denoted by v km/h (a) and flow rate denoted by q (b) in space and time. (c, d) Time-dependences of flow rate and speed within traffic congestion in (a, b) at two different road locations shown for
1983:
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
681:
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
2181:
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
689:
Fig. 3. Explanation of ASDA/FOTO models. Superscripts "jam 1", "jam 2" are related to two different wide moving jams. Superscripts "syn" are associated with synchronized flows. Subscripts "up" and "down" are related respectively to the upstream and downstream fronts of synchronized flow and wide
121:
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
619:
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 this pattern of congested traffic belongs to the "wide
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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
179:
Kerner's jam feature 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
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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
64:
Fig. 1. Empirical examples of traffic congestion reconstructed by the ASDA/FOTO models using raw data measured by road detectors on different highways in the United
Kingdom, Germany, and the USA. Representation of traffic congestion in space-time plane through regions associated with two
682:
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)).
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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 this pattern of congested traffic belongs to the "synchronized flow" traffic phase (Fig. 2 (a) and (b)).
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Fig. 5: Congested traffic pattern reconstructed by FOTO and ASDA models: space-time diagram with vehicle trajectories 1-4 and related travel delay times. Road detector data as input for ASDA/FOTO models is measured on freeway A5-North in Hessen, Germany, 14 June,
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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).
2454:
Kerner B. S., Rehborn H., Aleksić M., Haug A., Lange R. (2000) Verfolgung und
Vorhersage von Verkehrsstörungen auf Autobahnen mit "ASDA" und "FOTO" im online-Betrieb in der Verkehrsrechnerzentrale Rüsselsheim, Straßenverkehrstechnik, No. 10, pp
1471:
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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
1979:
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.
444:
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Boris S. Kerner, Rehborn H, Klenov S L, Palmer J, Prinn M (2009) Verfahren zur
Verkehrszustandsbestimmung in einem Fahrzeug, (Method for traffic state detection in a vehicle), German Patent publication DE 10 2008 003 039
2473:
Palmer J., Rehborn H. (2009) Reconstruction of congested traffic patterns using traffic state detection in autonomous vehicles based on Kerner's three-phase traffic theory, In: Proceedings of. 16th World
Congress on ITS,
1975:
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Boris S. Kerner; Method for monitoring the condition of traffic for a traffic network comprising effective narrow points, Deutsche
Patentoffenlegung DE19944075A1; USA patent: US 6813555B1; Japan: JP 2002117481 (Filed:
2189:. 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.
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is the characteristic velocity of the downstream jam front associated with Kerner's jam feature discussed above. This means that after the downstream front of a wide moving jam has been identified at a time instant
950:(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.
2461:
Kerner B. S., Rehborn H., Aleksić M., Haug A., Lange R. (2001) Online
Automatic tracing and forecasting of traffic patterns with models "ASDA" and "FOTO", Traffic Engineering and Control, 11/2001, pp 345–350
20:
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,
148:
A wide moving jam is a moving traffic jam, which exhibits the characteristic jam feature to propagate through any bottlenecks while maintaining the mean velocity of the downstream jam front denoted by
585:. 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.
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Boris S. Kerner, Kirschfink H, Rehborn H; Method for the automatic monitoring of traffic including the analysis of back-up dynamics, Deutsches Patent DE19647127C2, USA patent: US 5861820 (Filed: 1996)
1788:
90:
Kerner's definitions and , respectively, for the synchronized flow and wide moving jam phases in congested traffic are examples of common spatiotemporal empirical features of traffic congestion.
607:
Thus Kerner's definitions and 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.
980:
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2185:, 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
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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
2458:
Kerner B. S., Rehborn H., Aleksić M., Haug A. (2001) Methods for
Tracing and Forecasting of Congested Traffic Patterns on Highways, Traffic Engineering and Control, 09/2001, pp 282–287
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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
274:
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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.
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Palmer J., Rehborn H., Mbekeani L. (2008) Traffic
Congestion Interpretation Based on Kerner's Three-Phase Traffic Theory in USA, In: Proceedings 15th World Congress on ITS, New York
604:
Synchronized flow is defined as congested traffic that does not exhibit the jam feature ; in particular, the downstream front of synchronized flow is often fixed at the bottleneck.
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Boris S. Kerner, Rehborn H., Traffic surveillance method and vehicle flow control in a road network, Deutsche
Patentoffenlegung DE19835979A1, USA patent: US 6587779B1 (Filed: 1998)
503:
234:
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Rehborn H, Klenov S.L. (2009) Traffic
Prediction of Congested Patterns, In: R. Meyers (Ed.): Encyclopedia of Complexity and Systems Science, Springer New York, 2009, pp 9500–9536
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Kerner B. S., Rehborn H., Aleksić M., Haug A. (2004): Recognition and Tracing of Spatial-Temporal Congested Traffic Patterns on Freeways, Transportation Research C, 12, pp 369–400
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Boris S. Kerner Deutsches Patent DE10036789A1; Method for determining the traffic state in a traffic network with effective bottlenecks, USA patent: US 6522970B2 (Filed: 2000)
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Kerner B. S., Rehborn H. (1998) Messungen des Verkehrsflusses: Charakteristische Eigenschaften von Staus auf Autobahnen, Internationales Verkehrswesen, 5/1998, pp 196–203
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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
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Common spatiotemporal empirical features of traffic congestion are those spatiotemporal features of traffic congestion, which are qualitatively the same for different
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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
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can depend considerably on traffic parameters like the percentage of long vehicles in traffic, weather, driver characteristics, etc. As a result, the mean velocity
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Palmer J., Rehborn H. (2007) ASDA/FOTO based on Kerner's Three-Phase Traffic Theory in North-Rhine Westfalia (in German), Straßenverkehrstechnik, No. 8, pp 463–470
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In contrast with the jam feature , the mean velocity of the downstream front of synchronized flow is not self-maintained during the front propagation. This is the
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B.S. Kerner, H. Rehborn, J. Palmer, S.L. Klenov, Using probe vehicle to generate jam warning messages, Traffic Engineering and Control Vol 52, No 3 141-148 (2011)
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qualitatively different traffic phases in congested traffic: 1. Wide moving jam (red regions). 2. Synchronized flow (yellow regions). White regions – free flow.
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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
53:
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
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applications without calibration of model parameters under different environment conditions, road infrastructure, percentage of long vehicles, etc.
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spatiotemporal empirical feature of traffic congestion. The jam feature defines the wide moving jam traffic phase in congested traffic as follows.
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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
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J. Palmer, H. Rehborn, B.S. Kerner, ASDA and FOTO Models based on Probe Vehicle Data, Traffic Engineering and Control Vol 52 No 4, 183-191 (2011)
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Boris S. Kerner, M. Aleksić, U. Denneler; Verfahren und Vorrichtung zur Verkehrszustandsüberwachung, Deutsches Patent DE19944077C1 (Filed: 1999)
83:
in different countries measured during years of traffic observations. In particular, common features of traffic congestion are independent on
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Vehicle speeds measured with road detectors (1 min averaged data) illustrate Kerner's definitions and (Fig. 2 (a, b)). There are two
38:
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Kerner B. S., Kirschfink H., Rehborn H. (1997) Automatische Stauverfolgung auf Autobahnen, Straßenverkehrstechnik, No. 9, pp 430–438
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If measured data are not available for the tracking of the downstream jam front with the Stokes-shock-wave formula (3), the formula
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Boris S. Kerner, "Congested Traffic Flow: Observations and Theory", Transportation Research Record, Vol. 1678, pp. 160-167 (1999)
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nalyse: Automatic Tracking of Moving Jams) model reconstructs and tracks wide moving jams. The ASDA/FOTO models are devoted to
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565:(1) is the characteristic parameter that does not depend on the flow rates and densities upstream and downstream of the jam.
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Kerner B. S., Rehborn H. (1996). Experimental features and characteristics of traffic jams. Physical Review E, Vol. 53, 1297
2403:
2358:
Boris S. Kerner, "Experimental Features of Self-Organization in Traffic Flow", Physical Review Letters, 81, 3797-3400 (1998)
1153:{\displaystyle x_{up}^{(syn)}(t)=\mu {\frac {1}{n}}\int _{t_{0}}^{t}(q_{S}(t)-q_{F}(t))dt,\ \ t\geq t_{0}\qquad \qquad (2)}
2529:
2445:
Kerner B. S., Rehborn H. (1996). Experimental properties of complexity in traffic flow. Physical Review E, Vol. 53, R4257
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Kerner B. S., Konhäuser P. (1994). Structure and parameters of clusters in traffic flow, Physical Review E, Vol. 50, 54
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When traffic parameters (percentage of long vehicles, weather, driver characteristics, etc.) do not change over time,
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in an initially free flow at the bottleneck. A highway bottleneck can result from on- and off-ramps, road curves and
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of a front of a wide moving jam is calculated though the use of the shock-wave formula derived by Stokes in 1848:
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of the downstream jam front is independent of the flow rates and densities upstream and downstream of the jam,
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is time (Fig. 3). The ASDA model tracks the downstream and upstream fronts of wide moving jams denoted by
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George G. Stokes, "On a difficulty in the theory of sound", Philosophical Magazine, 33, pp 349-356 (1848)
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236:. Because the average distance between vehicles within the jam, including average vehicle length, equals
87:, road conditions and road infrastructure, vehicular technology, driver characteristics, day time, etc.
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1466:{\displaystyle v^{(jam)}(t)={\frac {q_{2}(t)-q_{1}(t)}{\rho _{2}(t)-\rho _{1}(t)}}\qquad \qquad (3)}
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Introduction to Modern Traffic Flow Theory and Control: The Long Road to Three-Phase Traffic Theory
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found in different data measured over years of observations varies approximately within the range
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bjects) model reconstructs and tracks regions of synchronized flow in space and time. The ASDA (
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is the average vehicle density within the jam), the mean velocity of the downstream jam front
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A wide moving jam is a moving jam that exhibits the characteristic jam feature , which is a
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Boris S. Kerner, "The physics of traffic", Physics World Magazine 12, 25-30 (August 1999)
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There are two main approaches for the tracking of wide moving jams with the ASDA model:
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are respectively the flow rates upstream and downstream of the synchronized flow front,
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are constant in time. This explains why the mean velocity of the downstream jam front
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439:{\displaystyle v_{g}=-{\frac {1}{\rho _{max}\tau _{del,jam}^{(a)}}}\qquad \qquad (1)}
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the flow rate and density upstream of the jam front that velocity should be found;
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feature of synchronized flow that is one of the two phases of traffic congestion.
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spatiotemporal features of traffic congestion observed in measured traffic data.
1853:, the location of the downstream front of the jam can be estimated with formula
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1970:{\displaystyle x(t)-x(t_{1})=v_{g}(t-t_{1}),\ \ t>t_{1}\qquad \qquad (5)}
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Catch effect: pinning of downstream front of synchronized flow at bottleneck
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In empirical observations, traffic congestion occurs usually at a highway
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any vehicle trajectory (see examples of trajectories 1–4 in Fig. 5).
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On-line applications of ASDA/FOTO models in traffic control centres
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are the flow rate and density downstream of this jam front. In (3)
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Common spatiotemporal empirical features of traffic congestion
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Propagation of wide moving jams through highway bottlenecks
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Empirical example of wide moving jam and synchronized flow
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The use of a characteristic velocity of wide moving jams.
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In many data measured on German highways has been found
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The use of a characteristic velocity of wide moving jams
1783:{\displaystyle v_{down}^{(jam)}=v_{g}\qquad \qquad (4)}
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found from measured data independent of each other.
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2165:{\displaystyle -12>v_{g}>-20{\mbox{km/h}}}
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269:{\displaystyle {\frac {1}{\rho _{max}}}}
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2039:. However, although the mean velocity
498:{\displaystyle \tau _{del,jam}^{(a)}}
229:{\displaystyle \tau _{del,jam}^{(a)}}
7:
1984:velocity of the upstream jam front.
887:{\displaystyle x_{down}^{(jam)}(t)}
749:{\displaystyle x_{down}^{(syn)}(t)}
39:intelligent transportation systems
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2505:, Springer, Berlin, New York 2004
2496:, Springer, Berlin, New York 2009
2241:Intelligent transportation system
970:Cumulative flow approach for FOTO
943:{\displaystyle x_{up}^{(jam)}(t)}
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589:Definition for synchronized flow
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1992:each of the three road lanes.
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531:{\displaystyle \rho _{max}}
302:{\displaystyle \rho _{max}}
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2525:Transportation engineering
2281:Transportation forecasting
2256:Three phase traffic theory
51:three-phase traffic theory
2226:Active Traffic Management
1696:{\displaystyle \rho _{2}}
1669:{\displaystyle \rho _{1}}
1577:{\displaystyle \rho _{2}}
1523:{\displaystyle \rho _{1}}
1312:{\displaystyle v^{(jam)}}
137:for wide moving jam": -->
41:, the reconstruction of
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1846:{\displaystyle t=t_{1}}
617:spatiotemporal patterns
2503:The Physics of Traffic
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1229:{\displaystyle \mu }
1220:
1193:
1166:
981:
898:
836:
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760:
698:
633:ASDA and FOTO models
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184:
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2391:9 December 2012 at
2236:Fundamental diagram
1755:
1593:fundamental diagram
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494:
421:
225:
2276:Traffic congestion
2261:Traffic bottleneck
2199:
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2056:
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1994:
1967:
1843:
1809:
1780:
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1693:
1666:
1639:
1612:
1574:
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630:
555:
528:
495:
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383:
326:
299:
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226:
187:
166:
67:
43:traffic congestion
27:probe vehicle data
2231:Floating car data
2159:
2026:
1939:
1936:
1792:is used in which
1450:
1249:{\displaystyle n}
1122:
1119:
1037:
825:{\displaystyle t}
423:
264:
104:traffic breakdown
33:). For efficient
2542:
2428:
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2417:
2412:
2406:
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2383:
2374:
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2355:
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2065:
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2057:
2055:
2054:
2038:
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2024:
2012:
2011:
1976:
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1968:
1955:
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1934:
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1159:
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1120:
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1073:
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1038:
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1012:
995:
949:
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941:
929:
912:
893:
891:
890:
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873:
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831:
829:
828:
823:
811:
809:
808:
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791:
774:
755:
753:
752:
747:
735:
718:
677:General features
601:
600:
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562:
561:
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504:
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437:
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382:
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354:
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327:
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308:
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275:
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175:
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145:
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140:
2550:
2549:
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2544:
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2541:
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2539:
2510:
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2488:
2486:Further reading
2436:
2431:
2424:
2420:
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2409:
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2377:
2370:
2363:
2356:
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2222:
2213:
2204:
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2136:
2122:
2121:
2100:
2095:
2094:
2073:
2068:
2067:
2046:
2041:
2040:
2003:
1998:
1997:
1946:
1918:
1899:
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1856:
1833:
1822:
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814:
813:
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757:
696:
695:
679:
635:
613:
602:
598:
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571:
545:
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539:
512:
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451:
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367:
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316:
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283:
278:
277:
248:
238:
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182:
181:
156:
151:
150:
146:
142:
138:
136:
135:
102:as a result of
96:
77:
72:
35:traffic control
12:
11:
5:
2548:
2546:
2538:
2537:
2532:
2527:
2522:
2520:Road transport
2512:
2511:
2508:
2507:
2498:
2487:
2484:
2483:
2482:
2478:
2475:
2471:
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2177:
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2154:
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2148:
2143:
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2129:
2107:
2103:
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2076:
2053:
2049:
2021:
2018:
2015:
2010:
2006:
1966:
1963:
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1953:
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1945:
1942:
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1930:
1925:
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1911:
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1245:
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1199:
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1028:
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1022:
1019:
1016:
1011:
1008:
1005:
1002:
999:
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987:
971:
968:
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939:
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908:
904:
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842:
821:
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795:
790:
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773:
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766:
745:
742:
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731:
728:
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717:
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678:
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634:
631:
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492:
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13:
10:
9:
6:
4:
3:
2:
2547:
2536:
2533:
2531:
2528:
2526:
2523:
2521:
2518:
2517:
2515:
2506:
2504:
2501:B.S. Kerner,
2499:
2497:
2495:
2492:B.S. Kerner,
2490:
2489:
2485:
2479:
2476:
2472:
2469:
2466:
2463:
2460:
2457:
2453:
2450:
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2441:
2438:
2437:
2433:
2427:
2422:
2419:
2416:
2411:
2408:
2405:
2400:
2397:
2394:
2393:archive.today
2390:
2387:
2382:
2380:
2376:
2373:
2368:
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2362:
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2348:
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2237:
2234:
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2175:
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2141:
2137:
2133:
2130:
2127:
2105:
2101:
2078:
2074:
2051:
2047:
2019:
2016:
2013:
2008:
2004:
1989:
1985:
1981:
1977:
1961:
1951:
1947:
1943:
1940:
1931:
1923:
1919:
1915:
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1111:
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1049:
1045:
1040:
1034:
1031:
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1023:
1017:
1006:
1003:
1000:
992:
989:
985:
976:
969:
964:
962:
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956:
951:
934:
923:
920:
917:
909:
906:
902:
878:
867:
864:
861:
853:
850:
847:
844:
840:
819:
796:
785:
782:
779:
771:
768:
764:
740:
729:
726:
723:
715:
712:
709:
706:
702:
687:
683:
676:
674:
672:
668:
664:
660:
656:
652:
648:
644:
640:
632:
625:
621:
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605:
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586:
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578:
576:
568:
566:
550:
546:
523:
520:
517:
513:
487:
479:
476:
473:
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467:
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461:
457:
447:
430:
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384:
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375:
372:
368:
363:
358:
355:
350:
346:
337:
321:
317:
294:
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288:
284:
259:
256:
253:
249:
245:
218:
210:
207:
204:
201:
198:
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192:
188:
177:
161:
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141:
132:
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128:
123:
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115:
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109:
105:
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93:
91:
88:
86:
82:
74:
69:
62:
58:
56:
52:
48:
44:
40:
36:
32:
28:
24:
23:video cameras
19:
2502:
2493:
2434:Bibliography
2421:
2410:
2399:
2339:
2327:
2316:
2305:
2294:
2271:Traffic wave
2266:Traffic flow
2214:
2205:
2179:
1995:
1982:
1978:
1855:
1791:
1713:
1710:
1589:
1585:
1475:
1321:
1279:
1263:
1161:
977:
973:
954:
952:
693:
690:moving jams.
680:
670:
666:
662:
658:
657:utomatische
654:
650:
646:
642:
638:
636:
614:
606:
603:
583:catch effect
582:
579:
574:
572:
448:
338:
178:
147:
126:
124:
116:
97:
89:
78:
54:
47:Boris Kerner
15:
641:orecasting
2514:Categories
637:The FOTO (
119:moving jam
112:road works
100:bottleneck
75:Definition
37:and other
31:phone data
16:Vehicular
2474:Stockholm
2150:−
2128:−
2017:−
2014:≈
1916:−
1875:−
1685:ρ
1658:ρ
1566:ρ
1512:ρ
1432:ρ
1428:−
1410:ρ
1385:−
1224:μ
1127:≥
1084:−
1041:∫
1027:μ
514:ρ
458:τ
385:τ
369:ρ
359:−
285:ρ
250:ρ
189:τ
108:gradients
2389:Archived
2220:See also
812:, where
81:highways
2455:521–527
959:merging
671:on-line
649:raffic
276:(where
114:, etc.
85:weather
18:traffic
1938:
1935:
1586:no any
1476:where
1162:where
1121:
1118:
665:ynamik
575:common
127:common
55:common
2333:1999)
2287:Notes
29:, or
2197:2006
2158:km/h
2147:>
2134:>
2025:km/h
1944:>
1557:and
1503:and
1189:and
595:edit
505:and
139:edit
2481:A1.
2187:RDS
2183:WDR
661:tau
446:.
336:is
176:.
49:’s
2516::
2378:^
2364:^
2350:^
2172:.
2153:20
2131:12
2020:15
1676:,
1622:,
1590:no
1473:,
955:no
894:,
756:,
645:f
110:,
25:,
2142:g
2138:v
2106:g
2102:v
2079:g
2075:v
2052:g
2048:v
2009:g
2005:v
1965:)
1962:5
1959:(
1952:1
1948:t
1941:t
1932:,
1929:)
1924:1
1920:t
1913:t
1910:(
1905:g
1901:v
1897:=
1894:)
1889:1
1885:t
1881:(
1878:x
1872:)
1869:t
1866:(
1863:x
1839:1
1835:t
1831:=
1828:t
1805:g
1801:v
1778:)
1775:4
1772:(
1765:g
1761:v
1757:=
1752:)
1749:m
1746:a
1743:j
1740:(
1735:n
1732:w
1729:o
1726:d
1722:v
1689:2
1662:1
1635:2
1631:q
1608:1
1604:q
1570:2
1543:2
1539:q
1516:1
1489:1
1485:q
1461:)
1458:3
1455:(
1447:)
1444:t
1441:(
1436:1
1425:)
1422:t
1419:(
1414:2
1404:)
1401:t
1398:(
1393:1
1389:q
1382:)
1379:t
1376:(
1371:2
1367:q
1360:=
1357:)
1354:t
1351:(
1346:)
1343:m
1340:a
1337:j
1334:(
1330:v
1305:)
1302:m
1299:a
1296:j
1293:(
1289:v
1244:n
1202:S
1198:q
1175:F
1171:q
1148:)
1145:2
1142:(
1135:0
1131:t
1124:t
1115:,
1112:t
1109:d
1106:)
1103:)
1100:t
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1092:F
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1070:S
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1057:t
1050:0
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1032:1
1024:=
1021:)
1018:t
1015:(
1010:)
1007:n
1004:y
1001:s
998:(
993:p
990:u
986:x
938:)
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932:(
927:)
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915:(
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876:(
871:)
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800:)
797:t
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789:)
786:n
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780:s
777:(
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765:x
744:)
741:t
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733:)
730:n
727:y
724:s
721:(
716:n
713:w
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707:d
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667:a
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659:S
655:A
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639:F
599:]
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547:v
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488:a
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356:=
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322:g
318:v
295:x
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260:x
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219:a
216:(
211:m
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202:,
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196:e
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162:g
158:v
143:]
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