Automatic Tracing and Forecasting of Moving Traffic Jams Using Predictable Features of Congested Traffic Flow

Copyright @ IFAC Control in Transportation Systems, Braunschweig, Germany, 2000

AUTOMATIC TRACING AND FORECASTING OF MOVING TRAFFIC JAMS USING PREDICTABLE FEATURES OF CONGESTED TRAFFIC FLOW

B. S. Kerner, M. Aleksic, H. Rehborn

DaimlerChrysler AG, HPC: £224, D-70546 Stuttgart, Tel.: +49-711-17-21718, +49-711-34897, Fax: +49-711-17-51642 e-mail: [email protected] Abstract: The results of investigations of a recent model (Kerner, et aI., 1997) for the automatic tracing of moving traffic jams and of the prediction of the jam propagation and time-dependent vehicle trip times are presented. It is found that the model which perfonns without any validation of the parameters of a model under different infrastructures of a highway, weather, etc. and which is based on the previous fmdings that moving traffic jams possess some characteristic parameters (i.e., the parameters of moving jams are unique, reproducible and predictable) can be applied for a reliable traffic forecasting on a highway. Copyright © 2000 IFAC Keywords: traffic control, parameters, prediction methods, algorithm, data processing.

1.1 Characteristic Parameters afTraffic Jams

1. INTRODUCTION Traffic forecasting based on applications of different dynamic traffic flow models whose parameters should be validated corresponding to real traffic conditions is a well-known approach (e.g. Cremer (1979); Ben-Akiva, et al. (1994); Kronjliger and Konhliuser (1997». However, due to very complex dynamics of real traffic flow strongly depending on the highway infrastructure, weather, etc. it is impossible to choose a set of model parameters in a way that the model shows results compatible with real traffic flow at totally different traffic conditions. A theory of moving traffic jams by Kerner and Konhliuser (1994) has predicted that jams should possess some characteristic parameters. Indeed, the characteristic parameters of jams have recently been found out experimentally (Kerner and Rehborn, 1996a). "Characteristic" means that the parameters do not depend on initial conditions, they are the same for different moving jams and do not depend on time: the characteristic parameters are unique, coherent and predictable. These properties of moving jams have been used for a development of models of traffic forecasting which can perform without any validation of model parameters (Kerner, et al., 1997). The model based on available data allows a prediction of the propagation of moving traffic jams on a highway and therefore a forecasting of time-dependent vehicle trip times without any validating of model parameters under different infrastructures and environmental conditions. In this paper, the results of experimental investigations of the model for the tracing and short-time prediction of traffic jams are presented. However, first properties of congested traffic flow discovered recently will be considered briefly (see also a recent review by Kerner (1999a».

The characteristic (i.e. reproducible and predictable) parameters of moving traffic jams are (Kerner and Rehborn, 1996a): (i) velocity of the downstream front of the moving jam; (ii) vehicle flow rate quut and other parameters of the flow in the outflow of the moving jam, (iii) vehicle density inside the moving jam. It is important that the velocity of the downstream front of the jam is always a characteristic parameter independent of the traffic parameters downstream from the moving jam.

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An illustration of characteristic parameters of traffic jams can be seen on Figs. 1-3 (Kemer and Rehbom 1996a). It can be observed that two traffic jams following one another propagate through a section 13 km long of the highway AS-North (near Frankfurt) without changing the average velocity of the downstream fronts of both moving jams. This stationary movement of the downstream fronts of the jams can be represented on the flow-density-plane by a line which has its slope equal to the velocity of this front. This line is the characteristic line for the jam's downstream front, called the line J (Fig. 3).

flow out from the jam is free flow, this traffic flow can be on an average represented on the flow-density-plane as one average point with the co-ordinates (qoub Pmin), where Pmin = qoutlv max . Thus, we have this co-ordinate and the slope of the line J, which allow us to estimate the average vehicle density inside the jam as the intersection point of the line J and the axis of the density (x-axis).

1.2 Three Phases a/Traffic Recently, it has been found out (Kemer and Rehborn, 1996b) that in congested traffic flow two different phases have to be distinguished: wide moving traffic jams and synchronized traffic flow. Therefore, together with free traffic flow there are three phases of traffic: (i) free traffic flow, (ii) synchronized traffic flow and (ii) moving jams. All three phases of traffic flow are realized in the example in Fig. 1. In contrast to free traffic flow where vehicles are able to overtake one another freely the probability of overtaking in synchronized traffic flow is very low (Kemer, 1999a, b). Therefore, there is a tendency to synchronization of the vehicle speeds on the different lanes of a highway running in the same direction in such a traffic flow. Strictly speaking, this tendency leads to the synchronization of the vehicle speeds usually only outside on- and off-ramps and other bottlenecks if there is only one route for the traffic flow. However, because each traffic flow which has this tendency of synchronization shows the same features, these traffic flows belong to the same traffic phase "synchronized traffic flow". In contrast to free flow, synchronized flow shows a very complex dynamic behavior. In particular, even the multitude of homogeneous states of synchronized flow (i.e., states which are homogeneous spatially and stationary in time; often such states are called •steady speed' states) cover a two-dimensional region in the flow-density plane: a given vehicle speed (a steady speed) in a homogeneous and stationary state of synchronized flow may be related to an infmity multitude of vehicle densities, and a given density may be related to an infmity multitude of different steady speeds. In other words, there are no fundamental diagrams which may describe the whole multitude even of homogeneous (steady) states of synchronized traffic flow. One can distinguish between three different types of synchronized traffic flow (Kemer and Rehbom, 1996b): (i) Nearly stationary and homogeneous states. (ii) States where only the average speed is stationary. (iii) Essentially non-stationary and non-homogeneous states of synchronized traffic flow. Complex spatial-temporal structures of synchronized traffic flow which consists of spatial-temporal combinations of these three types of synchronized traffic flow are usually observed in real traffic flow. Experimental investigations have shown that moving traffic jams propagating through synchronized traffic flow maintain the average velocity of the

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Fig. 3: Flow-density-p1ane with line J for the average traffic data (a) and for each lane on the threelane-road (b). The velocity of the downstream front of the moving jam can be measured easily by the 16 sets of double-loop detection sites along the highway section (Fig. 1 (a)). When the jams pass one of the detectors, the flow rate and the speed time series show a similar picture like in Fig. 2 for D9. Because the distances between the detectors are known, it is easy to calculate the velocities of the downstream fronts of the moving traffic jams within the accuracy of the one-minute-measurements: the reth sult is that on October 9 , 1992, the downstream fronts of both jams propagate on an average with the same velocity of -15 kmIh. Besides, the velocities of the downstream fronts of moving jams, the flow rate and the average vehicle speed downstream of the moving jam V max are measured. If the 478

downstream front that is characteristic for moving jams propagating through free flow (Kemer, 1998). This property ofjams allows the proposal of models for the prediction of the jam propagation on the highway independently of a traffic state in which the traffic is. One model which allows a short-time prediction of the propagation of traffic congestion and a forecasting of time-dependent vehicle trip times based on available traffic data without a validation of model parameters (Kemer, et al., 1997) is considered next.

at detectors Qn below some given value, Vbegin, has been chosen (Fig. 5). The value to can also be determined via other well-known incident detection methods. The same is true for the time t l which determines the appearance of the downstream jam front at the detector. In the case under consideration t l is determined by the time when the vehicle speed increases above some given value Vend' On q Vo

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2. MODEL FOR THE AUTOMATIC TRACING OF TRAFFIC JAMS AND THE PREDICTION OF VEHICLE TRIP TIMES

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Because the downstream front of a moving jam propagates with nearly constant velocity independent of traffic parameters on different days, one can first find this velocity from available data (measured through stationary detection sites or floating car data or other alternative measurement techniques) and further use this velocity for the prognosis of the propagation of a traffic jam after the jam is detected on a highway section. This basic idea has been used in the model presented below (Kemer, et al., 1997) where also some other important properties of traffic flow have been taken into account. Next, we will briefly discuss the model restricting the consideration of traffic data on stationary detection sites on highways. However, the same model can be used when floating car data or other types of measurements are available. To get an overview on the model, let us consider Fig. 4 where in a schematic illustration the dynamic movement of a moving traffic jam is shown on a highway section for different times. The development of the model for tracing and prediction of moving traffic jams uses essentially that the propagation of the moving jam's fronts can be calculated with the available measured traffic data. The model is automatically able to handle lane changings, on- and off-ramps and other kinds of possible influences of the infrastructure. The schematic illustration for the jam tracing model in Fig. 4 shows as a measurement infrastructure two detection sites (Qo, Qn) on a road section. After the registration of a moving traffic jam in the cyclic measured data at Qn at time to the model starts to calculate continuously the positions of the downstream (xr
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Fig. 5: Schematic illustration of a vehicle speed time series with registration times of the upstream (at time to) and downstream (at time t l ) fronts of the traffic jam, respectively. The aim of the model is to trace and to predict a moving traffic jam at all times between detection sites even when the jam can not be measured. In an application of the model the following useful results were achieved: (i) The movement of the jam can be traced and predicted at any time - even if the moving jam is between detection sites on a road section. (ii) The prediction of vehicle trip times can be done according to the position and length of the moving traffic jam. (iii) Using the dynamics of the jam, the usefulness of traffic control methods can be evaluated. Tracing both upstream and downstream fronts of the moving traffic jam within each time step, the position and the length of the jam are known. This leads to a calculation of the vehicle loss time on the jammed road section. It is possible to predict first the positions of the upstream and downstream front of the jam and then automatically determine the individual vehicle trip times. Many useful applications of the model are possible: the output information of the model can be used for driver information systems or for traffic control systems. It is possible to conclude a prediction of the traffic jam dissolution: if the flow rate data upstream of a moving jam is below the flow rates downstream, the mo-

479

ving traffic jam will decrease in time and the dissolution time can be calculated.

surements. Note that when a sequence of jams occurs, the velocity Vgr between the jams is set to the automatically measured characteristic value, if no measurements of flow rate and speeds bewtween jams are possible. In formula (1), (2) the measured flow rate qmin within the time interval to < t < t 1 can be used. In the time t > t, this qmin has to be approximated. The parameter qmin can be determined either through the formula (5a) or (5b):

2.2 Detailed Formulation ofthe Model In this section we consider a detailed formulation of the model for tracing and predicting moving traffic jams on the basis of measurements from installed detection sites measuring cyclic vehicle flow rates and vehicle speeds (Kemer, et al., 1997). The movement and the tracing of a moving traffic jam can be determined as follows: (a) equation for the position of the upstream front of the moving traffic jam (see Fig. 4):

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Altogether the proposed model for the tracing of moving jams and for the prediction of vehicle trip times consists of the formulas (1 )-(5), where in this application traffic data measured by local detection sites (double loop detectors) and an incident detection algorithm to determine to and t( is used. The parameters LpKW and LLKW are not dependent on the local situation. Therefore, they can be chosen as constants. Consequently, the model has no parameters to be validated under different environmental conditions.

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2.3 Short-time Prediction of Vehicle Trip Times

(c) equation for the time-dependent length of the moving traffic jam:

The model allows a short-time prediction of the traffic jam dynamics and a short-time vehicle trip time prediction. The vehicle trip time prediction can be determined at the time t > t\. For this purpose in model (1)-(5) instead of actually measured parameters of traffic some predicted parameters upstream (qo(t), wo(t) and the vehicle speed downstream of the jam (wo(t) should be used. The predicted values (qo(t), wo(t), wo(t» can be determined via a historical time series prediction. Because v gr is a characteristic parameter, the actual measured value of vgr is used for the prediction of the movement of the downstream front of the jam through equation (2). Let us illustrate the latter general approach of a short-time prediction of vehicle trip times by a simplification using constant values for the flow rates and vehicle speeds. The predicted positions of the upstream (X)(t» and downstream (xr
In this formulas to is the time when the moving jam is detected at the downstream detectors Qn (Fig. 4, Fig. 5); tl determines the appearance of the downstream jam front at the detectors Qn (Fig. 4, Fig. 5); vgr and vgl are the velocities of the downstream and upstream fronts of the jam, respectively; qo(t) is the measured traffic flow rate into the road section (Fig. 4, x=O); wo(t) is the measured averaged vehicle speed at the downstream border of the section;

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with LpKW as an average length of individual vehicles including a (small) average distance between vehicles inside the jam (e.g., LpKW = 7m), LLKW as an average length of long vehicles including a (small) average distance between vehicles inside the jam (e.g., L pKW = 17m); ApKW as the percentage of individual vehicles and (l-ApKW) as the percentage of long vehicles. The corresponding percentages can be determined with the local detection site mea-

with: tzu is the time when the driver meets the jam;

tab is the time when the driver leaves the jam (Fig. 6), Wst the vehicle speed of the drivers inside the traffic jam. In many cases the vehicle speed Wst is

480

very low, so that the tenn Wst(tab-lzu) in (6a) could be neglected. Then tR is as follows: t = L+ wnt ab -wotzu R

In situations when qmiD is noticeably above zero, however, this is not the case, i.e. Pmax is considerably lower than the value calculated in (4) because many vehicles do move and keep larger distances than stopped vehicles. This explains why the use of qmiD as calculated in (5a) together with Pmax calculated in (4) for the tracing of jams does not give good results. The fact that the combination qmin set to zero (5b) and Pmax as calculated by (4) does give good results, i.e. Vgr is calculated correctly, suggests that the real traffic state inside a jam performs slides along the line J since Vgr as calculated in (2) has the same (characteristic) value for all values of (qmiD, Pmax) on the line J.

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Table 1: Input and output of the jam tracing model Input • Pennanent measurements of traffic speeds and traffic volumes with detection sites or other sensors (floating car data, infra-red sensors, cameras, etc.) • Percentages of trucks andHGV • Information about the infrastructure (on-, offramps, lane reductions, intersections,lanes, etc.) • For the prediction: time series of traffic measurements

Fig. 7: Infrastructure of the highway A5-South after 1995.

Output of the model • position of the upstream and downstream front and the jam length • speeds of the upstream and downstream front of the jam and short-time prediction of the jam position • prediction of vehicle trip time on a section • loss-time on a section • result for the appropriateness of the current traffic control • prediction of the time ofjam disappearance

Figs. 8 and 9 visualize the application of the model for the automatic tracing of traffic jams on real traffic data. While the x-axis in both graphs denotes the time, the y-axis denotes the location, measured in kilometers from the beginning of the highway stretch under consideration (Fig. 7). Solid black circles represent those measurement intervals (x-coordinate of the circle) during which the incident detection method reports an incident, i.e. a jam, at the detection site located at the location denoted by the y-coordinate of the circle. Solid lines represent the upstream and downstream fronts of the traffic jams traced by the model. Note that these fronts can be anywhere within the considered stretch of the highway while circles can only be at the exact locations of the detection sites. Solid lines starting at the xaxis represent the trajectories of one particular vehicle moving along the highway. These trajectories have been calculated with the vehicle speed inside a traffic jam set to a constant 15 kmIh. To show the accurracy of the model using a small number of detection sites, two scenarios are compared (Fig. 8 and Fig. 9): both experimental examples show the propagation of the same moving traffic jam on the highway A5-South on 17th March, 1997. In one case (Fig. 8) all available detection sites of the road section have been used; in the other case (Fig. 9) the results of the model using a reduced number of detection sites are illustrated. Fig. 8 shows the results of the model using all available data: the propagation of a wide moving jam on a 15-km-stretch between 8:49-9:43. The jam grows approximately during the time interval 8:498:58, remains nearly constant during 8:59-9:31 and shrinks afterwards until its extinction at approximately 9:43. This is because the vehicle flow rate into the jam changes over time. The positions of the

3. DISCUSSION OF RESULTS The model has been tested on a lot of experimental data and it shows very good results. Below we discuss some of them which are related to data from the highway A5 in Gennany whose infrastructure is schematically shown in Fig. 7. In these example for a determination of the times to and tl in the model very simple criteria are used: traffic at a detection site is considered to be in the phase "jam" if the flow rate is below 1000 vehlh and the average speed is below 30 kmIh during a one-minute measurement interval. Both calculating the value of qmin by (5a) and setting qmin to zero (5b) has been tested. Results show that setting qmin to zero actually gives better results than using the "exact" value calculated in (5a). The problem is that fonnula (4) for the calculation of Pmax is only applicable if nearly all vehicles inside the jam are at a full stop and do not keep large distances to the vehicle in front of them. 481

jam's fronts can be calculated very exactly here because of the great number of detection sites on a short highway stretch. Fig. 9 shows the model results using only 4 out of the 18 detection sites: the propagation of the moving jam and its extinction at approximately 9:43 is very similar to Fig. 8. In the comparison, the calculated positions of the jam's fronts and the predicted vehicle trip time trajectory (start time here 9:10) in Fig. 9 are in good agreement with the positions in Fig. 8: for a useful application of the model the number of necessary measurements can be reduced according to table 2. Taking only 4 instead of 18 detection sites into account, the model is able to predict the jam's fronts within the accuracy of the one-minute-interval.

reaches the jam. Similarly, the measurements made at B often do not represent the outflow from a jam because traffic in the outflow of the jam is influenced by ramps before it gets to detection site B. If traffic at the ramps is fully detected, the congestion tracing model can compensate these effects and still produce good results even for large distances of A and B. On the contrary, if there is no detection at the ramps, the model can only produce reasonable results if A and B are not more than 3 km apart. Table 2 summarizes these results. Table 2: Suitability of the infrastructure Suitability of the infrastructure for the model

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REFERENCES

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Cremer, M. (1979). Der Verkehrsfluj3 auf Schnellstraj3en, Springer-Verlag, Berlin. Ben-Akiva, M., Koutsopoulos, H. and Mukundan, A. (1994). A dynamic traffic model system for ATMSIATIS operations. IVHS Journal 2( 1). Kronjager, W. and Konhauser, P. (1997). Applied Traffic Flow Simulation. In: Transportation Systems, (Papageorgiou, M. and Pouliezos, A. (Ed.», 805-808, IFAC, Kreta (Greece). Kemer, B. S. and Konhauser, P. (1994). Structure and parameters of clusters in traffic flow. Physical Review E, 50, 54. Kemer, B. S. and Rehbom, H. (1996a). Experimental features and characteristics of traffic jams. Physical Review E, 53, 1297. Kemer, B. S., Kirschfmk, H. and Rehbom, H. (1997). German Patent DE 196 47 127 (published on May 28 th , 1998). United States Patent US 5861820 (published on January 19th , 1999), Automatische Stauverfolgung auf Autobahnen. Straj3enverkehrstechnik 9/97, 430-438. Kemer, B. S. (1999a). The Physics of Traffic. Physics World, 25-30, No. 8. Kemer, B. S. and Rehbom, H. (1996b). Experimental properties of complexity in traffic flow. Physical Review E, 53, R4257. Kemer, B. S. (l999b). Congested traffic flow: Observations and theory. Transportation Research Record 1678, 160-167. Kemer, B. S. (1998). Traffic flow: Experiment and theory. In: Traffic and Granular Flow '97, (Schreckenberg, M. and Wolf, D. E. (Eds.», 239-267, Springer, Singapore.

Fig. 8: Propagation of a moving traffic jam on highway A5 south, on March 17th , 1997 using all available input data. 20 I - - . . . . . . : : - - - - - - - - - - j - - D 18 t-----.~-o;;::_---~<-- D

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4. VERIFICATION OF THE CONGESTION TRACING MODEL An application of the congestion tracing model on

different days and infrastructures has shown that accurate results can be achieved with distances between detection sites of up to 6 km on highway stretches without intersections. Even when there are somewhat larger distances between detection sites the accuracy of the results of the model are still acceptable as long as there are no on- and off-ramps between the detection sites. When there are on- and off-ramps between two detection sites A and B (A is upstream of the ramps, B is downstream), however, the measurements made at A often do not represent the inflow into a jam because traffic at A is influenced by ramps before it 482