Classifications

• • G—PHYSICS
  • G08—SIGNALLING
  • G08G—TRAFFIC CONTROL SYSTEMS
  • G08G1/00—Traffic control systems for road vehicles
  • G08G1/07—Controlling traffic signals
  • G08G1/08—Controlling traffic signals according to detected number or speed of vehicles
• • G—PHYSICS
  • G08—SIGNALLING
  • G08G—TRAFFIC CONTROL SYSTEMS
  • G08G1/00—Traffic control systems for road vehicles
  • G08G1/01—Detecting movement of traffic to be counted or controlled
  • G08G1/0104—Measuring and analyzing of parameters relative to traffic conditions

Definitions

• the present invention relates to a method for determining the state of vehicle traffic along traffic routes and road networks.
• the method can also be applied to predict traffic states with the aid of the latest measuring data obtained and earlier measured values. Prediction is important, since it creates conditions which enable appropriate measures and procedures to be adopted and the traffic to be controlled in a manner to avoid immanent traffic problems. Prediction is also important from the aspect of vehicle or transport control, in which route planning and the selection of the best roads at a particular time is effected preferably with respect to futuristic traffic situations when the vehicles concerned are located on respective road sections.
• Incidents and events that occur can also have a great influence on prevailing traffic, and a prediction of a change in traffic flow will provide a basis on which to make a decision as to which control measures should be taken, for instance by broadcasting information over the radio or through the medium of changeable road signs.
• OD-matrix based methods have long been used to calculate traffic flows under different circumstances and in a long-term future perspective. These methods are used, for instance, in city-planning projects, road planning, etc., and the futuristic perspective can apply for several years.
• OD stands for Origin Destination and an OD-matrix which describes how many vehicles are driven from an origin o to a destination D per unit of time and the routes used by these vehicles can be generated by using the knowl edge of domestic areas, work places, travel habits, etc., and by measuring the traffic flows.
• the information basic to OD-matrices is difficult to obtain.
• the method is used to produce the average values over a period of one year, and the accuracy can be improved successively by calibrating the assigned values with regard to the values actually measured.
• Those predictions with which the present invention is concerned are predictions which cover much shorter time periods, for instance time periods of from 1-3 minutes up to the nearest hour, and with successively less precision for the nearest day.
• typical traffic curves which are modified with regard to known obstructions, interference, road works, etc. are used in the case of time periods longer than one calendar day.
• the nature of traffic is such that the best way of predicting traffic over a longer time perspective is to say that the traffic will be as usual at the time of the day, on that week day, at that time of year, and so on. To this end, it is essential to take many measurements and to store significant average values for traffic on the road network links for different time periods.
• Such a data base can also be used conveniently together with the present invention.
• OD-matrices have also been discussed for short time perspectives, such as those applicable to the present invention. This is encumbered with a number of problems. A great deal of work is involved in defining different OD-matrices for each short time period of the day. At present, there is no reasonable assaying or measuring method which assays the origins of the vehicles, the destinations of the vehicles and the routes travelled by the vehicles. Methods of enabling the journeys of individual vehicles from O to D to be identified and followed have been discussed. A traffic control system in which all vehicles report to a central their start and destination and also their successive respective positions during their journeys has also been proposed.
• Present-day measuring sensors can be used when practicing the present invention.
• Another fundamental principle of the invention is one in which the parameter values used are constantly adapted to the current measurement values, so that the system will automatically endeavour to improve its accuracy and adapt itself successively to changes in travel patterns, traffic rhythms, road networks, and so on.
• noise is noise
• the parameter values used to characterize noise include, for instance, the average values and variances that can be calculated from the noise distribution function.
• qualified methods such as the Kalman filtration method for instance, which can also be applied in the present invention. It is essential that the methods are used for the right type of problem and with an adapted model of reality.
• Vehicle traffic simulating programs have also been developed. These programs are often used when dimensioning street crossings, slip-ways to and from highways, motorways, etc.
• the stochastic nature of the traffic is expressed here by using random number generation to randomly select the positions and start times of individual vehicles, driver behaviour factors, etc.
• the result obtained is one example of the possible state of the traffic, depending on the model and the randomly selected parameters applied. It is possible to obtain some idea of how the traffic tends to flow in a road crossing or road intersection, for instance, with a larger number of simulations, and therewith modify the road crossing or road intersection already at the planning stage.
• this type of simulation will exemplify the possible futuristic state of the traffic. This shall be compared with a prediction which is required to provide a solution that lies within the most probable result area, including an understanding of relevant variancies.
• the invention is characterized by the features set forth in the following Claims.
• Figure la illustrates a simple model of a control centre having only one operator site
• Figure 1b illustrates an example of a control unit included in the traffic model unit
• FIG. 2 illustrates data flow and functions for prediction and updating purposes
• Figure 3 illustrates sensor information delivered to the control centre
• Figure 4 illustrates prediction by a link in a first stage
• Figure 5 illustrates prediction of several links in a subsequent stage
• Figure 6 illustrates updating of historical values X H in a database
• Figure 7 illustrates how the traffic parameters can be processed to produce function values included in obtaining the correlation coefficient and the prediction factor
• Figure 8 is a simplified example of a road network which includes approach roads or entrances to a city centre.
• the traffic situation in and close to large towns and cities represents one example of the area in which the invention can be used.
• the road network is divided into different parts or sections having different properties or qualities and of different significance from a traffic technical aspect.
• the traffic is preferably measured with regard to two of the following parameters:
• One interesting task is to predict the traffic on a link A on a traffic route on the basis of measurements obtained by sensors on a link B upstream of the traffic route.
• the basic concept is that the vehicle traffic in B will reach A after a time lapse of t 1 and that it is therefore possible to anticipate the traffic in A while using the time allowance of t 1 .
• the measuring time is five minutes, this will mean that the first vehicles included in the measurement will already have arrived at A before the measuring process is terminated. If this five-minute prediction is required in order to gain time in which to control the traffic, it is apparent that in the illustrated example a measuring sensor must be placed at a travel distance of 10 minutes from A. This implies a distance of 1.2 metric miles from A, and there are often many factors which influence the traffic during a travel distance of such length, which means that a "one to one" relation between the traffic in B and the traffic in A cannot be expected.
• the measuring sensor is placed close to A so as to obtain good correlation with the measurement values in B, no prediction time is obtained since this prediction time is consumed by the measuring time. If the sensor is placed far away from A, so as to obtain prediction time, the correlation level is lost.
• I 1 is an average value of the time interval T 1 superimposed on I 0 ;
• I 0 is an average value of the time interval T 0 .
• T 2 30 s
• I 0 can be calculated successively as the approximation
• I 2 (t+T 2 ) I(t+T 2 ) - I 0 (t+T 2 ) - I 1 (t+T 2 )
• the density values P 0 , P 1 and P 2 are calculated in a corresponding manner.
• the advantage afforded by dividing the flow into three different time components has strong affinity with the object of the invention.
• Traffic management information that is of interest is the expected travel time per link, and when traffic flows with a good margin to the traffic capacity of the link, the link time t L - L/v L , where L is the length of the link and v L is the basic link speed, which corresponds approximately to the link speed limit.
• the link time t L will apply in most cases over a twenty-four hour period.
• the link time can therefore be easily predicted. It is not until traffic becomes denser and approaches the capacity of the link that more comprehensive analyses are required. (Some exceptions in this regard will be presented later.)
• I 0 and I 1 are small, the risk of large traffic congestions or traffic jams is also small and there is therefore no need for a more accurate analysis.
• the traffic flow is also characterized by the fact that vehicle density tends to increase and vehicle speed to drop as the traffic flow reaches the capacity of the link concerned.
• I 1 indicates a long period of high traffic flow. If P 1 is high and v is low, there is a long vehicle tail-back which affects link times and can cause traffic congestions at the approach roads to the traffic route, for instance.
• Good correlation is expected between different approach roads or entry routes of mutually the same type with regard to traffic developments during the morning hours. Good correlation is also expected between traffic as it is, for instance, on a Tuesday on one traffic route with how the traffic usually behaves on Tuesdays on the same route.
• Historical measurement data on one route is used to define historical mean value curves for respective calendar days. These curves may, for instance, be comprised of I 0 , P 0 curves.
• the historical I OH , P OH curves are used to determine the correlation between the links of diffrent "sister routes" with regard to the size ( ⁇ ) of the correlation and the time shift ( ⁇ ).
• the following example illustrates traffic prediction on a link B.
• a limited number of sensors are available.
• One sensor is located on an upstream link C. Between C and B there are several traffic flow connections towards C and also traffic flow exits from the route.
• L 1 up to and including h 4 are the sister routes of the route concerned (L 3 ).
• ⁇ (L 3 , L 1 ) and the ⁇ (L 3 , L 1 ) , etc., are known for the links of the sister routes.
• ⁇ (C, B) and ⁇ (C, B), i.e. corresponding relationship between the values in C and B along the same traffic route are also known.
• a prediction in B can be obtained from the measurement values obtained in C through the medium of a transfer factor W. Assistance can also be obtained from the sister routes (L 1 -L 4 ) and from the historical and relevant measurement values in B, i.e. in total three different sources of information.
• the correlation coefficient ⁇ ( ⁇ ) has a maximum value of magnitude 1 when X and Y are fully correlated.
• ⁇ c ( ⁇ ) - ⁇ ( ⁇ ) ⁇ also includes a set scale factor
• the correlation coefficient ⁇ ( ⁇ ) calculated in accordance with the above may be small despite x and y being strongly correlated. This is because ⁇ ( ⁇ ) is calculated around X H (t) and Y H (t), which take-up the strong correlation, and ⁇ ( ⁇ ) therewith indicates that the traffic variations around X H (t) and Y H (t) may partly be random variations which do not depend on factors that are common to x and y.
• Corresponding correlation coefficients for X H (t) and Y H (t+ ⁇ ) are calculated by forming the mean value of X H (t) and Y H (t+ ⁇ ) and calculating ⁇ H ( ⁇ ) around these mean values for selected correlation periods.
• Y H can also be related to X H by forming
• ⁇ 2 is an expression which denotes how large a part of the variance in Y can be related to the dependency on
• ⁇ 2 is normally proportional to the mean value and the measurement time concerned. In view of this, it is possible to distribute noise in a stereotype fashion between X and Y, from
• the correlation coffecient ⁇ can thus be expressed as a function of the signal/noise ratio on respective links corresponding to the values X and Y.
• the correlation can be improved by improving the signal-noise ratios.
• the measurement values will not preferably be added straight ahead, but that those values which have a better signal/noise ratio will preferably be weighted higher than the others.
• This weighting method also enables contributions to be obtained from weakly-correlated system links.
• the mean values of the variations X 2 and Y 2 can be estimated from the traffic distribution function.
• ⁇ X is small, i.e. smaller than or roughly equal to the mean value X 2
• it is not worthwhile in practice to predict ⁇ Y to anything other than ⁇ Y 0, knowing that the mean variation is roughly Y 2 .
• Lower limit values are obtained when selecting more sister routes. Nevertheless, it is important that ⁇ Y can be predicted quickly when the measured value of ⁇ X is large. A large value of ⁇ X need not mean that ⁇ Y becomes large. When several sister routes simultaneously give large ⁇ X-values, this indicates that a probability of a common change in the traffic is greater.
• the prediction of traffic flow on one link is not an isolated process, but requires continued analysis of the traffic flow both upstream and downstream of the link, in order to identify the risk of traffic building-up and therewith altering the first "primary" prediction.
• a transfer or propagation function W(X,t) describes how vehicle density (flow and speed) changes as a function of distance and time along a road section, for instance a change in the flows I 1 and I 2 from one measuring occasion at (X 1 ,t 1 ) to a measuring occasion downstream at (X 2 ,t 2 ).
• ⁇ (t) and ⁇ (t) which describe changes at approach roads and exit roads.
• W(X,t) can describe disturbance growth and the increased probability of the formation of tail-backs and traffic congestions when traffic flows are close to the capacity of the route. These growth functions can be measured and plotted to predict traffic conditions downstream of a link equipped with a measuring sensor.
• W may be used more freely to describe a transformation of traffic from one place to another place at a time (t 2 -t 1 ) later on.
• I 2 (Z,t) W(Z,t) ⁇ I 2 (0,0).
• W(Z,t) can be given a linear growth function where W(Z,t) - (1+ ⁇ 1 t) ⁇ f(Z-vt).
• the term W can then be comprised of a function I 2 (Z, t) which describes "disturbance" I 2 in movement along the route and a function f 2 (I 0 , t) which describes growth of the disturbance.
• the function W(Z,t) which describes how "traffic disturbances" I 2 grow, can be defined by measuring I 2 along routes for different I o /C. Corresponding functions for the I.-term can be obtained in a similar fashion. Measurements can also identify those levels on I 0 , I 1 and I 2 at which traffic congestions will normally occur, and consequently the function W is of interest in predicting traffic along traffic routes, particularly when there are not many sensors along the route. In this way, measurements carried out on a highly trafficated route can be used to predict risk locations along the route at which traffic congestions are likely to occur.
• ⁇ (t) and ⁇ (t) measurements are made for defining ⁇ (t) and ⁇ (t). It is assumed in this regard that ⁇ (t) will give a percentile thinning of the traffic, whereas the approach problems, and therewith the function ⁇ (t) become more complicated. ⁇ (t) will in some cases generate congestions, particularly at high I 0 -values on the route, and to some extent will also equalize existing I 2 -variations, by adapting traffic to some extent at the approaches. ⁇ (t) can be determined more easily and will provide a smoother flow on the route, when "ramp-metering" is applied at the approach. It is of particular interest to identify by measurement those flow values on the route where there is a danger that the approach flow will result in traffic congestions.
• Figure la illustrates a simple model of a traffic control centre.
• the traffic control centre will include a large number of operator sites and the control centres will be similar to those control centres used in National Defense systems, such as air defense control or marine control systems.
• National Defense systems such as air defense control or marine control systems.
• These control systems are constructed to satisfy high demands on real-time performances and modern-day systems are comprised of distributed data processing architectures.
• Figure la illustrates some essential building blocks of the control centre.
• "Sensor communication” (4) receives sensor inforamtion from the road network and "Control means communication” (5) transmits resultant procedure information from the control centre.
• the "Operator” (2) fulfils an important function in the operation of the control centre. He/she inserts information concerning incidents and events reported to the control centre, so that the "Traffic model” (3) is able to take into account corresponding changes in the capacity of the roads, highways, etc., when calculating and predicting traffic flows. Relevant and predicted traffic situations may also be presented to the operator, who then makes a decision concerning the procedures or measures that should be taken. Much of the historical information relating to the traffic on the different links of the road network at different times is stored in the "database" (1).
• the traffic model unit Since many calculations are required to predict traffic situations on a large road network, it is necessary that these calculations and predictions can be made very quickly. The predictions shall be updated successively and constantly kept current. The real-time requirement will be apparent in the application concerned, and the traffic model unit is constructed so as to provide quick access to local data areas, utilizing powerful computer capacity and a real-time operative system. Examples of building blocks in present-day technology are IBM's RS6000 and the AIX operative system, or SUN's corresponding Unix-package with Sparc-computer and Solaris.
• Figure 1b illustrates an approximate structure of the processing unit, in which a control processor (6) communicates with the unit (7) through an address bus (10) and a data bus (11), wherein the unit (7) stores data used in the arithmetical unit (8) and wherein an In/Out unit (9) communicates with other units, for instance through the medium of a LAN.
• a control processor (6) communicates with the unit (7) through an address bus (10) and a data bus (11), wherein the unit (7) stores data used in the arithmetical unit (8) and wherein an In/Out unit (9) communicates with other units, for instance through the medium of a LAN.
• Figure 2 illustrates the information flow when Predicting and Updating between different functions blocks. These blocks relate to Sensor Information (12), shown in Figure 3, Prediction (14), shown in Figure 4, Updating (15) shown in Figure 6, Database (13), in which large amounts of data system information are stored, and a block (16) which relates to continued procedures, such as Control or traffic related information. New measurement values obtained from the sensors are compared with earlier historical values which have been taken from the database to the local data area of the traffic model and new predicted traffic parameters are generated on which control decisions can be taken.
• Sensor Information shown in Figure 3, Prediction (14), shown in Figure 4, Updating (15) shown in Figure 6, Database (13), in which large amounts of data system information are stored
• a block (16) which relates to continued procedures, such as Control or traffic related information. New measurement values obtained from the sensors are compared with earlier historical values which have been taken from the database to the local data area of the traffic model and new predicted traffic parameters are generated on which control decisions can be taken.
• the new measurement values are also used to calculate new updated historical values and these values are stored in the data area concerned for immediate use, or alternatively are stored in the database for later use.
• sensor information obtained from the road network sensors (17) are transmitted to the control centre and subsequent to being received (18) are either filtered (19) or the mean values of differently time-varying parameters are formed. These sensor information may consist of traffic flow, traffic density and/or traffic speed.
• the traffic parameters concerned are transmitted to the prediction function (14).
• Figure 4 illustrates a first stage of the prediction.
• Data is sent to Analysis I (21) from the Data area (20).
• this data consists of historical data, X H , capacity C, standard deviations, ⁇ and status symbol, S.
• Processed measurement data is obtained from sensor information. Measurement data is compared with historical data in Analysis I and a decision is made as to whether or not the measurement values shall be further processed for prediction purposes.
• the traffic density of the majority of road links is so low as to enable link times, mean speeds, etc., to be added to the basic values of respective links. Consequently, it is important to sort out quickly those values which do not need to be further processed for prediction purposes.
• X c a limit value
• X ⁇ X c denotes prediction according to a basic value.
• ⁇ the variance
• ⁇ a chosen factor, for instance 1.7.
• a value which lies outside this interval may indicate an occurrence which requires separate analysis. If X lies beneath the interval, this may be due to traffic obstruction upstream of the link, and the status variable S is encoded for upstream links. The operator can be informed with a warning symbol and the link can be registered on a monitoring list.
• the value predicted for the link concerned Y 1 ( t p ) is obtained from the measured values from the same route Y(t- ⁇ 0 ) and the sister route (X 1 (t- ⁇ 1 ), X 2 (t- ⁇ 2 ), and so on.
• the values of respective routes are multiplied by the factor ⁇ i /k i and are added to give the result Y i (t p ).
• the factor k i is the weighting factor which relates the contribution of each route to its signal/noise ratio or to some corresponding correlation coefficient.
• Figure 6 shows that the preceding historical value X H (0) is updated by forming ⁇ X from the difference between the current measurement value and the historical value, whereafter the new historical value is formed by adding ⁇ X/k to the old value.
• the factor k determines the time constant for the length of time taken before a change in the measurement values results in a corresponding change in X H .
• the historical value X H is not a mean value where a plurality of the measurement values have the same weight when forming a mean value, but that the factor k gives a greater weight to the present input values than the earlier values.
• the updating method is simple, since it is not necessary to save more than the current value.
• Figure 7 illustrates how the correlation coefficient and the prediction factor can be obtained from the signals X and Y.
• the top of the Figure shows the values of Y and X being inserted into a respective register.
• Corresponding values X i and Y i are multiplied together and new pairs for multiplication are obtained by shifting X i and Y i relative to one another. By successively shifting, multiplying and summating these values, there is obtained a series of values which have a maximum at displacement ⁇ between the Y and the X values. It has been assumed in the illustration that the changes in ⁇ x och ⁇ y are small during the operation of the relative shifts of Y and X. In another case, the whole of the correlation coefficient ⁇ can be calculated for each shift and the maximum ⁇ -value is sought to determine the ⁇ -value.
• Figure 7 also shows how statistical basic parameters are obtained for the parameters X and Y.
• the expression for correlation coefficient and correlation factor is repeated at the bottom of Figure 7, to facilitate an understanding of the relationships between the parameters illustrated.
• One reason for predicting traffic situations is to be warned of the risk of overloading or traffic congestion in good time, so that measures can be taken to avoid the predicted traffic congestions.
• Certain traffic congestions cannot be predicted and occur without warning. For instance, there may be a road accident, the engine of a vehicle may stall or a truck may lose its load and block the road. It is necessary to be able to detect this type of problem as soon as possible, and to be able to predict the new traffic situation that occurs and which may be influenced by procedures from traffic operators, police, and so on.
• Detection of a new situation and the localization of the source of the disturbance are effected with information obtained from measuring sensors and by comparison with historical values.
• traffic upstream of the disturbance will become more dense while traffic downstream of the disturbance will become more sparse, and traffic located upstream exit roads to alternative roads will become more dense.
• An alternative information source consists in external messages, such as telephone calls from drivers of vehicles, police, etc., informing that an accident has occurred and passability on the route concerned is restricted to about X%.
• a prediction of the new traffic situation can be made immediately, by initiating a number of activities with the aim of obtaining quickly a rough prediction which can be later refined as new measurement data successively enables better predictions to be made.
• the new traffic situation tends to stabilize after an initial dynamic happening or occurrence, and the prediction, process then becomes simpler.
• Many disturbances resulting from minor traffic accidents, stalled engines, etc. block the route for less than 5- 15 minutes, and the duration of the disturbance will depend on the traffic intensity at that time and the tail-backs that are formed and the time taken for these tail-backs to disappear. It is seldom that such disturbances will attain a stable phase, but should be treated entirely as belonging to the first dynamic period.
• the following examples illustrate how the arrangement or system operates to give predictions in current or prevailing situations.
• the difference between the 1-3 best routes and remaining routes will normally be so great as to enable the remaining routes to be ignored in a first stage in which the traffic attempt to circumnavigate the incident on the alternative routes judged to be the best, which tends to result in an overload on the best alternative and successively increased traffic on the next best alternative, and so on.
• the traffic is divided in the calculating unit of the arrangement in accordance with the above, so that when the best alternative route is loaded with so much extra traffic that its cost value increases, traffic is distributed to the next best route, and so on.
• the traffic to be redirected is very considerable and the alternative route is already heavily trafficated, the first redistribution will predict the occurrence of tail-backs and traffic congestions, wherewith the traffic control operator is warned to this effect and may be given suggestions as to which measures or procedures should be taken, for instance measures which will inform motorists at an early stage, upstream of the blockage, through the medium of information, variable message signs, etc., redirecting the traffic to other routes.
• the traffic flows should be kept at a safe margin from maximum capacity, to avoid traffic congestions. As before mentioned, it is very important to maintain traffic flows beneath traffic congestion limits. The road network will then be used to a maximum. Passability is considerably impaired when traffic congestions occur, and the capacity of the road network is reduced when it is best needed. If traffic redistribution does not suffice, the next best alternative is to slow down the traffic flows at suitable places upstream of the disturbance source. For instance, it is better for traffic to queue on an entry road in a suburban area than to allow traffic to approach the city or town centre, where queues would increase blocking of other important traffic routes where a high capacity is still more essential.
• the new traffic situation that arises is determined by existing sensors, and those sensors which are located at the beginning of the alternative routes provide information as to how the traffic flows are actually distributed.
• the measured values are used to correct the allocated traffic distribution and to predict the traffic on the alternative routes downstream of the sensors.
• High frequency components of the type I 2 , P 2 and I 1 , P 1 are used to obtain the traffic distribution measurement values quickly. These parameters constitute characteristic traffic patterns and can be recognized along a route and also correlated with corresponding components of the primary route. The measurements are also able to show from this how much of the traffic on the primary route has elected to take respective alternative routes.
• the control measures taken by the operator are coupled to the prediction unit of the system as supplementary information concerning an anticipated control effect or redistribution of traffic, and hence a new prediction is made with respect to these values.
• measurement values are obtained which disclose the actual traffic redistribution situation, whereafter a new prediction is made, and so on. Particular attention is paid to the sensors located around the incident location, so as to be quickly aware of when the traffic begins to move on the earlier blocked link, whereafter traffic prediction returns to normal.
• the dynamic change in traffic can often be considered as local, i.e. the main change in traffic flow occurs within an adjacent restricted area around the incident.
• This area is comprised of a few links upstream of the incident and including exit roads for the best alternative routes, via the alternative routes to and including entry routes to the blocked route downstream of the incident.
• traffic can then be considered to flow roughly as normal.
• the traffic readapts downstream of the blocked link Firstly, part of the traffic upstream of the blockage or incident have a destination on the actual route concerned, so that the best route selection is to return to the same route downstream of the incident. The other reason is because the alternative routes are heavily laden with traffic, causing traffic to endeavour to return to the blocked route, downstream of the blockage or incident and therewith utilize the better passability of this route.
• Predictions can also be made more precise by assuming that the disturbances are, in the main, local and to construct databases for local traffic flow distribution.
• Components of the type I 2 and I 1 can be used in this regard, as previously mentioned.
• the measurement values on the link concerned can be correlated with the measurement values on different alternative routes downstream of the link, so as to obtain an assessment of the percentage of traffic flow on the link concerned divides onto respective alternative routes downstream of said link.
• the "cost calculation" for alternative routes may take into account knowledge of downstream traffic distribution and therewith sometimes provide a better prediction of the traffic distribution on the alternative routes.

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• 1992
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