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SHORT-TERM PREDICTION OF HIGHWAY TRAVEL. TIME USING MLP-NEURAL ... and leads to a loss of resources. These problems increase the need for ...
8th World Congress on Intelligent Transportation Systems Sydney, Australia, 30 Sept. – 4 Oct. 2001

SHORT-TERM PREDICTION OF HIGHWAY TRAVEL TIME USING MLP-NEURAL NETWORKS M.Sc. (Tech.) Satu Innamaa Research Scientist Helsinki University of Technology, Transportation Engineering P.O. Box 2100, 02015 HUT, Finland Tel. +35894513807 - Fax. +35894515019 - Email [email protected]

ABSTRACT The purpose was to study the predictability of travel time on a 28-km long highway section based on on-line travel time measurements with video. The prediction models were made as MLP-neural networks. The goodness of the models was studied both statistically and from the road users’ point of view. The best model predicted correct travel times over 90 percent of the time in congested conditions. Another topic of interest was the structure of the measurement system. An additional camera station within the link or near the starting point of the link improved the results more than a station outside the link or near the end of the link.

PURPOSE OF STUDY Increasing traffic congestion on major highways causes safety and environmental problems and leads to a loss of resources. These problems increase the need for comprehensive traffic system management (i.e. traffic control, information and demand management), which can provide a relief against congestion and its negative impacts. Traditionally traffic flow has been monitored by point measurements. As the traffic control systems develop from point control towards area control, the extent of the monitored area increases and the implementation of the monitoring by point measurements turns costly. A large network can be covered easily with link-based quantities and for example the average travel time of a link gives a good picture of the fluency in the area (1). The travel time is one of the most important pieces of information that the road keeper can offer to road users. However, road users usually expect the information to be up-to-date. The travel time information, which is based on measurements only, is always outdated and the longer the link is the more outdated it is because the vehicles used for measuring the travel time are different from the vehicles that see the information on the road (Figure 1). That is why it is important to make short-term prediction (2). The purpose of the research described in this paper was to study the predictability of the travel time. In this study the forecasts are based on information about travel times on different sublinks and about traffic volumes and point speeds at certain locations. The output of a prediction model is the average travel time of the vehicles entering a particular link in the near future.

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8th World Congress on Intelligent Transportation Systems Sydney, Australia, 30 Sept. – 4 Oct. 2001

Heinola

The travel time of a link is determined as the difference between the passing times of two camera stations.

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Travel time for links AD, BD and CD

Travel time for links AC and BC

B Travel Time 25-30 min

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Figure 1. The vehicle that sees the travel time information on VMS and the vehicles on whose travel time the information is based on. There are four camera stations (A – D) on the study section on main road 4. Inductive loop detectors are located in C and south of Lahti. The objective was to study how different inputs correlate with the travel time to be predicted and what kind of input leads to the best model. The purpose was also to find out whether the forecasts would be accurate enough for an implementation of the model in the field. In this research a model was regarded as acceptable if 90 percent of the forecasts were within the tenpercent error marginal. Another purpose was to study how the structure of the measurement system affects the forecasts. The effect of the length of the link and the location of different additional measurement stations were investigated.

STUDY SECTION The research was carried out on main road 4 between Lahti and Heinola in Southern Finland. The average daily summertime traffic on this 28-kilometer section is about 15,100 vehicles per day. The traffic volumes are high during summer weekends. The section is equipped with an automatic travel time monitoring system. The system is based on an artificial vision and neural network application, which automatically reads license plates at several locations in both directions (3). The study section is divided into three sub-sections with camera stations (Figure 1). The camera stations are approximately equally distributed over link length. The section is a threelane road with alternating passing lanes. The travel time measurement system covers one lane per direction. In addition to the camera stations there are inductive loop detector stations in C and south of the city of Lahti gathering information on traffic volumes, and point speeds. The camera station in C got broken three weeks after the installation and after that the travel time information was gathered only from links that do not start or end at the station C.

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8th World Congress on Intelligent Transportation Systems Sydney, Australia, 30 Sept. – 4 Oct. 2001

A variable message sign (VMS) gives information about the travel time at the beginning of the road section in both Heinola and Lahti. At the moment the value of the travel time displayed on the VMS is based on the last measurements on each sub-link – or on a combination of sub-links if there are one or two camera stations down along the section. The information is normally updated every 20 minutes (the normal travel time on the 28-kilometer section is around 20 minutes) but as the traffic control center notices that congestion is building up, the update can be done every ten or five minutes. However, although the update frequency can be made higher the problem is that the information is always outdated (Figure 1). Thus the objective is to develop a model that would improve the situation.

MODEL AND DATA The prediction models were made as feedforward multilayer perceptron (MLP) neural networks (Figure 2) because of the encouraging results in previous studies (4) and because they have proven to be good in predicting other measures that describe the traffic situation (5 – 8). A separate neural network was trained to predict the travel time of each sub-link. Hidden layer Input Input layer parameters x1

Output parameters y1 y2

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y3 ... ...

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ym Activation function

Figure 2. Multilayer perceptron neural network. As output the models gave the average travel time for vehicles entering the link within the following minute and as input the models got traffic information that was based on the last measurements. The input parameters are described in more detail in the following chapter. The number of input neurons was equal to the number of input parameters and the number of output neurons was one according to the number of output parameters. Neural networks were chosen to have one hidden layer. The number of the hidden neurons was chosen so that the number of training samples was ten times the number of parameters to be estimated. However, the number of the hidden neurons was limited to be at most 20 in order to keep the training process fast. The activation function of the hidden layer was chosen to be a hyperbolic tangent and of the output layer a linear function as in a previous study (8) where this combination gave good results.

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8th World Congress on Intelligent Transportation Systems Sydney, Australia, 30 Sept. – 4 Oct. 2001

The travel time measurement system has been installed only for one lane per direction. As one of the directions always has two lanes on this section, this means that the travel time of the vehicles driving on the unmonitored lane in either end of the link could not be measured. Furthermore the measurement system does not detect all the vehicles driving on the monitored lanes. All this leads to small sample sizes (only a few observations per minute per sub-link) and to the fact that the number of travel time observations is not equal to the flow. The individual vehicle travel time data were filtered by using moving average in order to drop outlier observations. With these outlier observations we mean observations of vehicles that have stopped along the link (too long travel times) or mismatches (too short travel times). After the filtering the data was aggregated into one-minute observations, which were scaled to vary between –1 and 1. The neural networks were trained with Fletcher-Reeves update (9), which is one of the conjugate gradient algorithms. In the conjugate gradient algorithms a search is performed along conjugate directions. This way the search produces generally faster convergence than steepest descent directions, which is a common method in basic backpropagation algorithms. If the neural network learns the training data too well, it memorizes the data and cannot generalize. This can be avoided by making sure that the training set is large enough and by setting some stopping criteria for the training process (9). In this study several stopping conditions were given. These criteria were the maximum number of training epochs, the minimum value of the gradient and of the mean squared error and the situation when the mean squared error of the validation data stops decreasing. For this last mentioned validation data criterion the original training data set was divided into three sub-sets: training, validation, and test set. In practice, the training was most of the time stopped because of the last criterion.

SELECTION OF INPUTS FOR MODELS In this study the output of the prediction model of a certain link was the one-minute average travel time of the vehicles entering this particular link during the following minute. The forecast was based on the latest information about travel times on different sub-links and about traffic volumes and point speeds at locations C and south of the city of Lahti (Figure 1). The reason why different sub-links were used was that by using them the delay caused by the data collection could be kept smaller and the information of the development of the traffic situation was more detailed. The inputs of the models were selected according to their correlation with the travel time to be predicted and to the mutual correlation of the input parameters. The input parameters of a prediction model need to correlate highly with the travel time to be predicted in order to be able to provide sufficient information for the model. However, it may be that different input parameters have high mutual correlation and for this reason the additional information that they give as input may be very small. For this reason it may be better not to use all the highly correlating parameters as inputs. The correlations between different parameters and the travel time to be predicted were studied as well as how these input parameter candidates correlate mutually. The input parameter candidates were time series of one-minute average and median travel times, and median travel 4

8th World Congress on Intelligent Transportation Systems Sydney, Australia, 30 Sept. – 4 Oct. 2001

time and the standard deviation of the observations from the latest five minutes or of the latest 10 or 20 vehicles. The time series of flow, the mean point speed and the standard deviation of the point speed at the inductive loop detector stations were also candidates for the input. The time series of the average travel times were chosen to form the basis for the input of prediction models. Thus all the time series of one-minute average travel time that had a correlation coefficient of at least 0.20 with the travel time to be predicted were selected to the input data. The criterion for the correlation coefficient between the parameter and the travel time to be predicted was the same for other parameters too. However, if two input parameter candidates had a high mutual correlation (the coefficient at least 0.95), the parameter with higher correlation with the travel time to be predicted was chosen and the other parameter was dropped. The correlation coefficients could not give an answer to the question of how long an optimal time series of each input parameter should be. Thus several lengths (5, 4 and 3 minutes) were used in the study. The data sets that contained the C-links were based on observations gathered during a 2–3-week period. Other data sets were based on an 8-week data gathering period. If it was more profitable to use larger data set and leave the C-links (the links starting from and ending to C) off or to use smaller but more detailed data set was left out to be studied. Although the input sets of different models were similar there were slight differences between the sets. The number of input parameters varied between 18 and 54 for different models, the model for the last sub-link having the smallest number of inputs on both directions. As an example, the contents of the input data set for the models of the longest sections AD and DA are presented here: AD (total 36 – 54 inputs): • 3-5-minute time series of one-minute average travel times from all the links • the median travel time from latest 10 or 20 vehicles from links AD, BD, and CD • the standard deviation of the travel time from latest five minutes from links AC, AD, BC, and BD, and the standard deviation from latest 20 vehicles from links AB and CD • 3-5 minutes time series of one-minute average flows in C and in south of Lahti, and similar time series of one-minute average point speeds in C DA (total 30 – 44 inputs): • 3-5-minute time series of one-minute average travel times from all the links • the median travel time from latest 10 or 20 vehicles from links BA, CA, CB, DA, and DB • the standard deviation of the travel time from latest five minutes from the link DB, and the standard deviation from latest 10 or 20 vehicles from links CB, DA, and DC • 3-5 minutes time series of one-minute average flows in C The raw data did not include observations for each sub-link for every minute. The input data set was made according to the principle that the value of an input parameter was assumed to be invariant until a new observation was obtained. However, the maximum time between updates was set to be 30 minutes, i.e. if the information on some of the input information links was older than 30 minutes, the sample was dropped from the training set. For the output samples of the training set this updating rule was not applied, i.e. all the samples without a measurement for the output parameter were excluded from the set.

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RESULTS FROM THE MODELS The goodness of the models was studied both statistically and from the road users’ point of view. The statistical examination was done with different error terms. The mean error and the mean relative error measure whether the model tends to underestimate or overestimate the travel time. The mean squared error, mean absolute value of error, and the mean absolute value of the relative error measure how the errors are distributed around the correct value. The mean relative error was little above zero for all the models and the mean absolute value of relative error was around six percent (Table 1). This means that on the average the models tended to overestimate the forecasts more often than underestimate them, but that the majority of the forecasts were rather close to the measured values. This can also be seen in the graphs of Figure 3. Link AD AC AB BD BC CD DA DB DC CA CB BA

C-links with with with with with with with without with with with with

Time series 4 min 5 min 5 min 5 min 3 min 5 min 5 min 4 min 3 min 3 min 3 min 3 min

MSE 2.5 1.2 0.4 1.0 0.3 0.2 2.1 1.2 0.7 0.5 0.2 0.2

ME 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

M|E| 1.2 0.8 0.4 0.7 0.4 0.4 1.1 0.8 0.6 0.5 0.3 0.3

MRE 0.7 % 0.7 % 0.8 % 0.5 % 0.5 % 0.5 % 0.6 % 0.7 % 0.8 % 0.4 % 0.3 % 0.4 %

M|RE| 6.4 % 6.3 % 6.9 % 6.0 % 6.2 % 5.7 % 6.0 % 6.4 % 7.0 % 4.9 % 5.8 % 5.6 %

Table 1. Mean squared error (MSE), mean error (ME), mean absolute value of error (M|E|), mean relative error (MRE), and mean absolute value of relative error (M|RE|) for the prediction models on different links and sub-links. AD

DA

Best Linear Fit: A = (0.889) T + (2)

Best Linear Fit: A = (0.841) T + (2.93)

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Data Points A=T Best Linear Fit

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R = 0.918 15

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Figure 3. Predicted (vertical axis) and measured travel times (horizontal axis). Let us assume that the VMS tells the road users that the travel time is going to be the predicted travel time plus minus ten percent (i.e. to vary between 0.90 * predicted travel time and 1.10 * predicted travel time). However, the absolute minimum travel times shown on VMS would be those based on the speed limits. Thus it is not considered to be erroneous 6

8th World Congress on Intelligent Transportation Systems Sydney, Australia, 30 Sept. – 4 Oct. 2001

information if the vehicle travels faster than the travel time shown on VMS if the VMS shows the minimum travel times allowed. Thus the travel time information may be correct in two ways: the measured travel time can be between the upper and lower limit shown on VMS or it can be shorter if the VMS shows the minimum limits. The erroneous information can be divided into two categories: the travel time information can be too pessimistic (too long travel times, i.e. road users arriving to their destinations earlier than expected) or too optimistic (too short travel times, i.e. road users arriving to their destinations later than expected). The too optimistic travel time information is worse for the road user than the too pessimistic travel time information. However, the information should be as exact as possible in order to maintain the road users’ trust in the system. First the correctness of the forecasts was investigated for the whole data set. The results of all the models with the biggest proportion of correct forecasts are presented in Table 2. All the models except the model for the DC link would have given correct travel time information over 97 percent of the time during the summer 2000. It is good that the models were rather too pessimistic than optimistic. Link AD AC AB BD BC CD DA DB DC CA CB BA

Length 28.1 km 17.8 km 9.1 km 19.0 km 8.7 km 10.3 km 28.1 km 19.0 km 10.3 km 17.8 km 8.7 km 9.1 km

C-links with with with with with with without without with with with with

Time series 4 min 3 min 4 min 3 min 3 min 3-5 min 3 min 4 min 3 min 3-5 min 4-5 min 3-5 min

Correct 98.4 % 98.0 % 98.0 % 99.1 % 98.2 % 100.0 % 98.3 % 97.1 % 93.0 % 99.8 % 99.8 % 100.0 %

Too Long 1.1 % 1.4 % 1.0 % 0.5 % 1.0 % 0.0 % 1.2 % 1.7 % 3.7 % 0.2 % 0.2 % 0.0 %

Too Short 0.5 % 0.6 % 0.9 % 0.4 % 0.7 % 0.0 % 0.5 % 1.2 % 3.2 % 0.0 % 0.0 % 0.0 %

Table 2. The goodness of models from the road users’ point of view. The numbers are based on the whole data set from the summer 2000. In an uncongested flow the travel time does not vary much and therefore it is easy to predict. Besides, in those conditions the relevance of travel time information is less important than in congested conditions. Thus the same proportions as in Table 2 were defined also for samples when the measured travel time had been longer than the upper limit of the minimum travel times shown on VMS. These proportions could not be defined for all the links because they had had almost no congestion at all during the data collection period. The proportions of the time that the information on VMS was correct were calculated also for the present system. In congested conditions the VMS in direction AD has given correct travel time information 32.9 percent of the time and the VMS in the opposite direction has given correct information 49.7 percent of the time. Thus the prediction models performed clearly better than the current system (Table 3).

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8th World Congress on Intelligent Transportation Systems Sydney, Australia, 30 Sept. – 4 Oct. 2001 Link AD AC AB BD BC DA DB DC

Length 28.1 km 17.8 km 9.1 km 19.0 km 8.7 km 28.1 km 19.0 km 10.3 km

Time series 3 min 3 min 5 min 5 min 3 min 5 min 4 min 3 min

Correct 66.5 % 65.8 % 60.0 % 83.7 % 73.0 % 90.3 % 75.8 % 63.4 %

Too Long 28.2 % 28.3 % 28.2 % 11.7 % 19.5 % 7.7 % 15.1 % 23.3 %

Too Short 5.3 % 6.0 % 11.9 % 4.6 % 7.5 % 2.0 % 9.1 % 13.4 %

Table 3. The goodness of models in congested conditions from the point of view of a road user. Data from C-links have been included in all the training sets. In direction DA the whole link model (DA) was the best model of the direction, and in the opposite direction the best model was the model made for link BD. By comparing the models made for links that start from the same point, it seems that in this case the longer the link was the better the ability of the model to predict travel times was. One might have expected contrary result. However, the results make sense. The standard deviation of the travel time does not increase proportionally to the length of the link but as the length of the link increases the proportion of the deviation decreases. This means that the travel time of a longer link is more stable (easier to predict) than the travel time of a shorter link. It seemed that even the longer delays of getting the information about the changes in the situation could not override this benefit. However, no matter how well the model has been optimised even the best models are always a little late in predicting the congestion. The reason for that is that the model cannot foresee an incident to happen and thus it can not react until the first signs of the problem can be measured. It can be seen from the example in Figure 4 that the model comes a little late all the time. 60

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Figure 4. An example of measured (dots) and predicted travel times (upper and lower limits) during congestion in the AD link on Friday 30th June 2000.

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8th World Congress on Intelligent Transportation Systems Sydney, Australia, 30 Sept. – 4 Oct. 2001

STRUCTURE OF MEASUREMENT SYSTEM Another topic of interest was the structure of the measurement system and how it affects the results of the models. The structure was studied by assuming that only some part of the measurement equipment would be available. The basic arrangement was to have one camera station at both ends of the link. This equipment was supplemented with additional camera stations inside or outside of the link in question or with loop detectors. Because the data on which the study was based on were from a real application, the structure of the system could be studied only in a limited way. First the use of additional camera stations was investigated and then the possibility to use point-based measurements as input for the models. Input parameters of the models were chosen according to the rules explained earlier. The goodness of the model was measured as the proportion of correct travel time forecasts in congestion conditions.

Proportion of Correct Forecasts during Congestion

First it was assumed that the travel time information system was based on two camera stations only. For both links starting from D and B, the results improved as the length of the link increased (Figure 5). However, for links starting from A, the model for the shortest link gave the best results. This may be due to different location of the congestion. 60 % 50 % 40 % A* B* D*

30 % 20 % 10 % 0% 0

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Figure 5. The proportion of the correct travel time forecasts during congestion on different links when the forecast is based on two camera stations. A* means links that start from the camera station A. In this figure all the links starting from B are in direction AD. The second task was to study how additional camera stations affect the forecast and how these additional stations should be located. In most cases the information from the additional camera stations improved the results, and the more additional camera stations there were the better the result were (Table 4). It seemed that an additional camera station within the link improved the results more than a station outside the link. It also seemed that an additional camera point near the starting point of the link improved the results more than an additional station near the end point of the link.

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8th World Congress on Intelligent Transportation Systems Sydney, Australia, 30 Sept. – 4 Oct. 2001 Link AD AC AB BD BC DA DB DC

Length 28.1 km 17.8 km 9.1 km 19.0 km 8.7 km 28.1 km 19.0 km 10.3 km

2 Camera S. 37 % 30 % 41 % 48 % 45 % 56 % 55 % 55 %

2+1 Camera Stations 56 % (B, within) 50 % (C, within) 57 % (B, within) 51 % (D, after) 40 % (C, after) 43 % (D, after) 57 % (A, before) 61 % (C, within) 57 % (A, before) 48 % (D, after) 83 % (C, within) 65 % (B, within) 69 % (C, within) 57 % (A, after) 55 % (B, after) 63 % (A, after)

2+2 Camera S. 66 % 60 % 53 % 76 % 66 % 85 % 69 % 59 %

Table 4. The proportion of correct travel time forecasts in congested conditions for models based on 2 – 4 camera stations on different links. The location of additional camera stations and the information if they are before, within or after the link has been given in parentheses. How does the information from inductive loop detectors affect the results? The information from the loop detectors did not improve the results as much as the information from additional camera stations (Tables 4 and 5). However, this point-based information did also improve the results in the AD-direction (Table 5). It depended strongly on the link whether it was better to place the loop detector before the link or within the link. In most cases, either the information from the inductive loop detector station in C or the information from both stations gave the best results. Link AD AC AB BD BC DA DB DC

Length 28.1 km 17.8 km 9.1 km 19.0 km 8.7 km 28.1 km 19.0 km 10.3 km

No loops 37 % 30 % 41 % 48 % 45 % 56 % 55 % 55 %

Loops in C 41 % 49 % 42 % 56 % 51 % 54 % 53 % 59 %

Loops before A 42 % 32 % 41 % 50 % 49 % -

Loops in C and before A 45 % 43 % 41 % 60 % 47 % -

Table 5. The proportion of correct travel time forecasts during congestion for models based on 2 camera stations and 1 or 2 loop detectors on different links. The loop detector in C is within or at one end point of the link for all other links except AB for which it is after the link.

DISCUSSION AND CONCLUSIONS The order of superiority of the models depends highly on the parameter with which the goodness is measured. If the purpose was to select the statistically best model, the model with smallest error terms or the best goodness of fit would be chosen. However, from the road users’ point of view the statistically most accurate model may not be the best. Road users want a model that is close enough to the real answer as often as possible. It does not matter if the model makes slight mistakes. If the road has an alternative route, the proportion of vehicles taking that route as a function of the information shown on VMS has to be considered. However, on the section studied in this research, there is no real route alternative. Thus this consideration could be left out of the study.

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8th World Congress on Intelligent Transportation Systems Sydney, Australia, 30 Sept. – 4 Oct. 2001

A simple study was done on the structure of the measurement system and how it affects the forecasts. It was shown that the results improved if the link was divided into sub-links with additional camera stations. This result also explains why the forecasts were better for long links than for short links. The long links were divided into sub-links and it was possible to get more detailed information than from short links that were not divided. The aggregated travel time inputs were based on a few observations only. This may have caused larger variation in average travel times than what it actually has. Longer aggregation periods would make variables more stable, although some variation is lost. If bigger portion of travel times had been measured, the flow could have been estimated from the number of observations and this flow information could have improved the forecasts. The models were trained with a relatively small training set (3 or 8 weeks) and the number of congested days was small during the data collection period. More data will be collected during the summer 2001 and hopefully the models can be improved by having more observations of the overdemand situations. For the advanced travel time prediction models of Park et al. (10) the mean absolute value of relative error varied between 6.2 and 9.0 percent for the first ten-minute prediction period. That is close to the results obtained in this study (4.9 – 7.0 percent). However, different models made for different locations should not be compared directly. The length of the links, the type and extent of the monitoring system, the magnitude of congestion and the frequency of unrecurrent incidents vary from one place to another as well as the attractiveness of alternative routes, and the type of control used on the road. This all makes all the cases unique and the difficulty of the prediction task very different in different places. The models were based on one-minute observations and the results were conducted assuming that the travel time information on VMS would be updated every minute. However, this may not be realistic in all real-life applications. It is possible that the data from the measurement system are received more seldom or that the message on VMS is not changed according to every little change in the output of the prediction model. The current models gave correct forecasts over 97 percent of the time, and the best models gave correct forecasts clearly over 80 percent during the congested flow. If the target was set to be able to predict over 90 percent of also the congested travel times correctly, the model for link DA was the only one fit for real life application. However, the results obtained so far are promising and even now the new prediction models could be used to improve the present information system.

ACKNOWLEDGEMENTS The research was funded by the Ministry of Transport and Communications and by the Finnish Road Administration. The study is a part of the Finnish National Research and Development Program on Transport Telematics Infrastructure (TETRA) 1998 – 2000 and the Finnish Research and Development Programme on Intelligent Transport Systems (FITS) 2001 – 2004.

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8th World Congress on Intelligent Transportation Systems Sydney, Australia, 30 Sept. – 4 Oct. 2001

The author wants to thank Professor Matti Pursula from Helsinki University of Technology and the referees for their valuable comments during the preparation of this paper. The neural network computing has been done with the computers of CSC – Center for Scientific Computing Ltd. in Finland.

REFERENCES (1)

Haugen T (1996) Section Data. Possibilities and experiences. SINTEF Civil and Environmental Engineering, Transport Engineering, Norway. 16 p. (2) Innamaa S (1999) Automaattiset liikenteenohjaus- ja liikenneinformaatiojärjestelmät (Automatic traffic control and information systems). Finnra Reports 28/1999. Finnish National Road Administration, Helsinki. 136 p. (3) Finnra (2000) Vt 4 Lahti-Heinola matka-ajan seuranta- ja informaatiojärjestelmän toiminnan arviointi (Main Road 4 Lahti-Heinola Journey Time Monitoring and Information System Functional Analysis). Finnra Reports 58/2000. Häme District of Finnish National Road Administration, Tampere. 46 + 61 p. (4) Park D, Rilett L (1997). Forecasting Freeway Link Travel Times with a Feedforward Neural Network. Journal of Microcomputers in Civil Engineering on Advanced Computer Technologies in Transportation Engineering. (5) Lee S, Kim D, Kim J, Cho B (1998) Comparison of Models for Predicting Short-Term Travel Speeds. Proceedings of 5th World Congress on Intelligent Transport Systems, Seoul, Korea. 9 p. (6) Smith B, Demetsky M (1994) Short-Term Traffic Flow Prediction: Neural Network Approach. Transportation Research Record 1453. Pp. 98 - 104. (7) Smith B, Demetsky M (1997) Traffic Flow Forecasting: Comparison of Modeling Approaches. Journal of Transportation Engineering, Vol. 123, No. 4, July / August 1997. Pp. 261 - 266. (8) Innamaa S, Pursula M (2000) Liikennemäärän ja nopeuden lyhyen aikavälin ennustaminen (Short-term Prediction of Flow and Speed). Finnra Reports 54/2000. Finnish National Road Administration, Helsinki. 101 + 3 p. (9) Demuth H, Beale M (1998) Neural Networks Toolbox for Use with Matlab. User’s Guide, Version 3. The Math Works Inc. Pp. 5-1 – 5-58. (10) Park D, Rilett L, Han G (1999) Spectral Basis Neural Networks for Real-Time Travel Time Forecasting. Journal of Transportation Engineering, November/December 1999. Pp. 515 – 523.

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