A data mining based approach for travel time prediction in freeway
with non-recurrent congestion
Chi-Sen Li, Mu-Chen Chen
nDepartment of Transportation and Logistics Management, National Chiao Tung University, 4F, No. 118, Section 1, Chung-Hsiao W. Road, Taipei 100, Taiwan, ROC
a r t i c l e i n f o
Article history:Received 17 July 2013 Received in revised form 13 November 2013 Accepted 16 November 2013 Communicated by Manoj Kumar Tiwari Available online 9 January 2014 Keywords:
Travel time prediction Non-recurrent congestion K-means
Classification and regression tree Neural networks
a b s t r a c t
This study integrates three data mining techniques, K-means clustering, decision trees, and neural networks, to predict the travel time of freeway with non-recurrent congestion. By creating dummy variables and identifying important variables, not only is the prediction performance increased without increasing investment in equipment, but also important variables are obtained concerning the important locations of equipment in order to effectively assist public transit agencies with system maintenance. The experimental results for a segment of 36.1 km of National Freeway No. 1, Taiwan, with non-recurrent congestion show that, whether or not the data generated by the Electronic Toll Collection (etc) system is used as input variables, the travel time prediction method developed in this study is able to improve the prediction performance. Meanwhile, the proposed approach also reduces the percentage of samples with mean absolute percentage error (MAPE)420%. Furthermore, in this study, important variables are extracted from the decision tree in order to predict the travel time. Finally, the prediction models constructed in accordance with six scenarios are highly accurate due to the low MAPE values, which are from 6% to 9%.
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1. Introduction
According to a report by the International Energy Agency in 2011 [1], the transport industry made the second largest global contribu-tion to CO2emissions, accounting for 23%, following the electricity
generation industry, which accounted for 41%. Roads are the main source of CO2emissions in the transport industry. Joumard et al.[2]
found that CO2emissions from vehicles traveling at low speed in
urban areas are higher than those from vehicles traveling at high speed. Furthermore, cold engines consume more fuel and generate more pollution than engines that are fully warmed up. Therefore,
increasing or maintaining smooth traffic flows for reducing the
conditions of stop and go while drivers travel on roads not only reduces the social costs, but also makes an important contribution to reduce greenhouse gas emissions. However, the speed of con-struction of additional roads generally cannot match the increase in the number of vehicles. Thus, construction of additional roads may be difficult to efficiently ease traffic congestion. In view of this, intelligent transportation systems (ITSs) provide a viable
solution that can improve the efficiency and service standard of
the existing transportation system and relieve or resolve the road congestion problem. Therefore, in recent decades, ITS has become
a mainstream research area. Advanced traveler information systems
(ATIS) and advanced traffic management systems (ATMS) are
technologies that are often used in ITS to improve the efficiency of the road system. Many studies (e.g.,[3,4]) have also pointed out that providing travel time information is an important factor in encouraging the success of ATIS and ATMS. Therefore, in order to
relieve traffic congestion or reduce CO2 emissions, travel time
prediction is an important issue. According to the Oak Ridge National Laboratory[5], 55% of the delays encountered by drivers on American freeways are caused by non-recurrent events, of which 72% are freeway accidents[6]. Therefore, in recent years, in order to improve the applicable timing of travel time prediction models, related studies (e.g.,[7,8]) have extended the research from explor-ing general traffic flow conditions to how to improve the prediction performance in the case of non-recurrent congestion.
From the study by Golob et al.[9], there exists a close relation-ship between traffic flow conditions and traffic accidents (crashes), by type of crash. For example, the congestionflow is apt to result in more serious crashes. In recent years, ATIS and ATMS have been widely utilized to ensure the efficiency of road system and to avoid the congestionflow. From the study by Vanderschuren[10], intel-ligent transport systems (ITS) can reduce (potential) crashes, and thisfinding is also demonstrated in Mitretek Systems[11]. Mitretek Systems reported that there are six major objectives/benefits of ITS identified in the literature, which consist of safety, mobility, effi-ciency, productivity, energy/environment and customer satisfaction. Contents lists available atScienceDirect
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http://dx.doi.org/10.1016/j.neucom.2013.11.029
nCorresponding author.
Therefore, forecasting travel time, particularly in the freeway with non-recurrent congestion, with a high degree of accuracy, can improve safety and efficiency.
Many studies related to prediction of freeway travel time have
shown concrete results. Kwon et al.[12] used a liner model to
collect loop detector data in order to predict travel time. Oda[13]
and Van Arem et al.[14]used autoregressive integrated moving
average (ARIMA) models to obtain appropriate results of travel time prediction in general traffic conditions. Van Arem et al.[14]
found that the ARIMA model is applicable to normal traffic
congestion, but shows larger deviations in non-recurring conges-tion. There are also many studies that predict travel time through
Kalman filtering [15–20]. Fei et al. [7] developed the Bayesian
inference-based dynamic linear model (DLM) and further con-structed the adaptive dynamic linear model (ADLM) to predict the travel time in two traffic conditions of recurrent and non-recurrent
congestion. Fei et al. [7] divided the data into two data sets,
morning and afternoon, and performed travel time prediction with both data sets. The prediction performance of the proposed ADLM is between highly accurate prediction and good prediction.
Moreover, in order to construct the prediction model of actual travel time, previous studies mainly obtain the actual travel time
information through probe vehicles [21] and automatic vehicle
identification (AVI) [16,22–25]. Petty et al.[21] developed a speed calibrated model through single-loop loop detectors, and then estimated the travel time accordingly. The study by Petty et al.[21]
confirmed that the developed stochastic model is applicable in
congestion conditions, but not including non-recurrent congestion. Meanwhile, Petty et al.[21]used the travel time data collected by four probe vehicles as the model validation target. Chien and Kuchipudi [16]found that the percentage of probe vehicles in the total traffic flow is a critical factor, which affects the prediction accuracy when using AVI data to predict the travel time. In recent years, neural networks (NNs)[22,26–32]have been utilized to predict traffics with various degrees of success due to their modelingflexibility, predictive ability, and generalization potential[33]. The above-mentioned
stu-dies also confirmed that NNs have good prediction capability when
applied to the analysis of complex traffic characteristics.
Although previous studies have predicted the short-term travel
time with various degrees of success, scientific research with
regard to travel time reliability focuses on four fundamental issues as follows:
1. Enhancing the prediction capability with existing equipment. 2. Identifying the important detectors and the critical variables in
order to enable the authority to obtain the target detectors and develop the effective imputation methods for missing data. 3. Providing the robust and accurate prediction model which is
also applicable in the case of non-recurrent congestion. 4. Classifying different categories of traffic characteristics in order
to predict the travel time.
Previous studies (e.g.,[16,17,24,25]) mainly focused on thefirst issue mentioned above, but there are few studies on the third issue. However, for the transportation management unit, there is a trade-off
between costs and output benefits. How to improve the prediction
performance and applicable timing under the premise of reducing the system implementation cost and operational cost is an important goal of travel time prediction. Therefore, the objective of this study is to use a systematic structure to integrate a variety of data mining methods in order to develop an effective solution to thefirst three issues mentioned above. For thefirst issue, there is no doubt that there is a significant positive relationship between improving the
explanatory power of traffic characteristics and enhancing the
performance of travel time prediction. The previous travel time studies (e.g.,[15–17,24,25]) were mainly focused on enhancing the
explanatory power of traffic characteristics irrespective of whether the data were derived through model inference, system simulation, parameter calibration, or nonlinear model construction. Therefore, identifying the traffic characteristics at time t could help with improving the accuracy of travel time prediction. Furthermore, collecting more comprehensive traffic data could reflect the traffic characteristics better. For example, stronger explanatory power of traffic characteristics could be obtained when a vehicle detector is set up every kilometer than when one is set up every 10 km. However, more devices will result in higher equipment and maintenance costs. Therefore, increasing devices and enhancing the explanatory power of traffic characteristics have been a trade-off for long time. In order to solve this problem, this study proposes a solution which attempts to avoid the cost of increasing devices and improve the explanatory power of traffic characteristics at the same time. Furthermore, the performance of travel time prediction is expected to be enhanced. In this study, to achieve the above goals, we use K-means to categorize the traffic characteristics in every 5 min and create a dummy variable to mark the cluster ID of each 5-min sample.
With regard to the second issue, when compared with collect-ing data manually, there is no denycollect-ing that collectcollect-ing data through a device is better for long-term data collection and makes it easier to control the error. However, it cannot prevent the occurrence of
missing data. Therefore, researchers [34–38] have studied the
processing of missing data in order to understand the exact traffic characteristics. However, in terms of freeway travel time predic-tion, relatively few previous studies focused on identifying impor-tant device locations and critical variables. For example, if rainfall at detection point A, the spot speed at detection point B, heavy
vehicle volume at detection point C, etc. are identified as the
critical variables for analyzing traffic characteristics and predicting travel time, managers not only can clearly understand the target detectors but also can develop an imputation method for missing data for a specific variable collected at a particular detection point. In addition, this can also have the benefits of reducing investment in equipment, decreasing maintenance cost and enhancing the applications of model. In this regard, in this study, we use the
classification and regression tree (CART) to provide an effective
solution to identify important device locations and critical vari-ables for travel time prediction.
For the third issue, in order to construct a robust model which is
able to predict freeway travel time in traffic with non-recurrent
congestion, a method integrating K-means, CART and NN is pro-posed in this study. Furthermore, in this study, the raw data of the ETC system (vehicle charging time and ID) are used to calculate the actual travel time (ATT), which is used as a target in training the prediction model. This study develops a robust model for predicting the travel time in the case of non-recurrent congestion. With this model, the prediction performance can be improved with existing equipment, and critical variables at important locations
can be identified such that the management unit can have a clear
objective in operating and maintaining equipment.
The rest of this paper is organized as follows.Section 2presents the details of the freeway segment in this study and data
collec-tion.Section 3describes the method of constructing the model of
travel time prediction. The experimental design and results are presented inSection 4. Finally, conclusions and suggestions of this study are made inSection 5.
2. Data
2.1. The freeway segment in this study
Two freeways, National Freeways No. 1 and No. 3, form the main inter-city transportation corridor between the south and the
north of Taiwan. According to the data reported by Taiwan Area
National Freeway Bureau (MOTC) in 2009, the total annual traffic
volume of these two freeways was 539,568,273 vehicles, while the
annual total traffic volume of National Freeway No. 1 was
329,743,228 vehicles, which accounts for approximately 61.11%. Therefore, National Freeway No. 1 is the main freeway for inter-city transportation in Taiwan. In this study, the data were collected at 5-minute intervals between the Yangmei Toll Station and Taishan Toll Station of the freeway in the northward direction from 16 September to 16 October 2009. The studied segment is a
one-way three-lane freeway. From Fig. 1, there are eight
inter-changes including two system interinter-changes, the Pingzhen System Interchange and the Airport System Interchange in this segment. Its length is 36.1 km accounting for 9.7% of National Freeway No. 1 with a service population of 9,382,332 people accounting for 40.58% of the total population of Taiwan. Furthermore, according to the statistics of September and October 2009 reported by Taiwan Area National Freeway Bureau MOTC, the average daily
traffic volume in this freeway segment was 336,895 vehicles,
which is the sum of the daily traffic volumes at Yangmei Toll
Station and Taishan Toll Station. It accounts for 23.5% of the
average daily traffic volume of National Freeway No. 1. With the
above information, the segment in this study is the busiest and most complicated segment in National Freeway No. 1.
2.2. Data collection
Considering the methodologies for short-term traffic
predic-tion, NNs are classified as nonparametric statistical methods[39]. Looking for critical variables through the process of establishing the NN-based prediction model is the key to developing an accurate prediction model. Therefore, according to the suggestions of previous studies (cite references), we collected data of critical variables of travel time prediction. Furthermore, the data relia-bility of automated data collection is dependent on system stability and calibration accuracy. Therefore, in order to enhance
the accuracy of travel time prediction in the areas with compli-cated traffic characteristics, collecting data of critical variables for
effectively analyzing traffic characteristics and ensuring data
reliability have become the important issues.
According to previous travel time prediction studies[7,40–43], spot speed, rainfall, historical travel time, and the day of the week and time (AM or PM) are important variables for improving the performance of travel time prediction. Therefore, in this study, spot speeds were collected by 11 dual loop vehicle detectors every 5 min. The rainfall data of three areas were collected every 10 min by rainfall detectors, and the data were transformed into those of 5-min intervals using the arithmetic mean method.
According to Petty et al.[21]and Chien and Kuchipudi[16], ATT can be obtained through a probe vehicle or AVI system, and ATT helps with establishing a robust prediction model. However, due to the high system construction cost, the studied segment and samples are limited. In Taiwan, the ETC system was established in 2006 and covers the entire National Freeway No. 1. Up to the end of October 2009, the utilization rate reached 36.48%, and there were a total of 16,247,908 charging records in October 2009, with a charging success rate of 99.9984%. Therefore, through the ETC system, the travel time data can be collected on a long road segment and the sample size can also be increased considerably to ensure sample representativeness. Furthermore, in order to obtain the actual travel time (ATT) and the historical travel time (HTT) respectively as the target and input variable of the prediction model, the vehicle charging time and ID were collected by ETC in this study. ATT and HTT were calculated by the methods presented inSection 3. In addition, Li and Chen [8] pointed out that encoding the days of the week as 1–7 and the time attribute as AM (0:00–12:00) or PM (12:00–24:00) can improve the performance of freeway travel time prediction in the case of non-recurrent congestion. To sum up, in this study, the spot speed, rainfall, day of the week, time (AM or PM), and HTT obtained from ETC were collected and used as input variables of the travel time prediction model.
In addition, to ensure data reliability, the raw data were collected from the database of Taiwan Area National Freeway
Bureau, MOTC, the database of the Central Weather Bureau, and the accident database of the National Highway Police Bureau. The rainfall data were collected from three rainfall detectors. The above-mentioned three databases are established by Taiwan0s governmental agencies to permanently collect the most complete real-time data for information dissemination, management, and research use. Because ATT was used as the target for the model training and test, and HTT was used as the input variable, in order to avoid inconsistency between the result of model training and the actual condition as a result of data imputation error, the sample at time t with missing values of ATT and HTT were removed. Finally, 7908 samples were collected in this study.
2.3. Characteristics of non-recurrent congestion
It is undeniable that accidents and rainfall are the main causes of non-recurrent congestion, and are difficult to predict accurately. There were a total of 76 accidents with 176 vehicles damaged and
six people injured in the time span of this study (see Fig. 2).
In addition, 94.7% of accidents involved only vehicle damage without injuries to people. It is noteworthy that although fewer accidents occurred on the freeway section between Taoyuan interchange and Linkou interchange than on the freeway section between Jungli interchange and Neili interchange, more vehicles were damaged in accidents occurring in the former section than in the latter. Thus, the impact of accidents on traffic flow is greater in the freeway section between Taoyuan interchange and Linkou interchange.
The traffic flow of Tuesday can be taken as an example (see
Fig. 3) to explain the impact of accident and rainfall on traffic flow. Observing the distribution of travel time of 13 October shown in Fig. 3(a), the morning peak hour of the freeway segment in this
study occurred at about 7:00–8:20 AM, when there were no
accidents or rainfall, whereas the peak time was prolonged, when there was rainfall. This can be approved in the cases of 29 September and 6 October. Due to the intermittent shower
occurring during the period 5:25–6:40 AM on 29 September (see
Fig. 3(b)), the morning peak hour of this day occurred at 7:20– 8:50 AM. Furthermore, the intermittent rainfall during the period
7:15–8:50 AM on 6 October resulted in a morning peak hour of
7:00–9:30 AM.
According toFig. 3, in the freeway segment in this study, the afternoon peak on Tuesdays was not obvious if there was no accident. However, when there were accidents, the travel time of this freeway segment increased significantly. Taking 29 September as an example, accidents occurred consecutively between 15:10
and 18:45 (seeFig. 3(c)), and accordingly there was a peak hour
from 16:30 to 18:45 in this freeway segment (see Fig. 3(a)).
Furthermore, there was an accident involving three vehicles between 10:40 and 11:27 AM in the morning of 22 September, which resulted in a morning peak hour lasting from 7:15 to 11:25 AM. Hence, the accident and rainfall are critical factors
resulting in non-recurrent congestion. The occurrence of accident has randomness as well as the important variables such as accident occurrence time, number of closed lanes and accident
removal time used to estimate the impact of accident on traffic
flow cannot be acquired in real time due to the limitation of
notification scheme. Therefore, this study attempts to develop a
robust model of travel time prediction in the case of non-recurrent congestion without the real time accident related information.
3. The proposed procedure of travel time prediction
In order to establish a robust travel time prediction model for the freeway with non-recurrent congestion, and to obtain the critical variables of important detector locations for the manage-ment unit with existing equipmanage-ment, this study tries to achieve the
research objectives based on the procedure as shown in Fig. 4.
Each step is described as follows. 3.1. Step 1: input data
In this study, raw data such as spot speed, rainfall, day of the week, time (AM or PM), and vehicle charging time and ID of ETC are collected from the databases established by Taiwan0s govern-mental agencies. Furthermore, ATT, HTT, dummy variables, impor-tant detectors, and critical variables are obtained through the following steps.
3.2. Step 2: compute ATT and HTT
The Southwest Research Institute [44] developed two
algo-rithms, TransGuide and TranStar, by using the AVI system to calculate the actual travel time. Both these algorithms use the concept of rolling average to automatically calculate the travel time which meets the threshold-based criterion. Furthermore, TransGuide and TranStar both set 0.2 (20%) as the threshold value. That is, if the travel time of vehicle i is 20% more or less than the previous average travel time BttABt, it is regarded as an abnormal
trip, and this sample is removed. For the further details, readers are referred to Dion and Rakha[24]. In addition, differing from the rolling average algorithm, the Transmit algorithm constantly makes the calculation with the travel times from those samples within 15-min intervals. The travel time is the time difference (tBitAi) between downstream point B, tBi, and the upstream point
A, tAi. Furthermore, the Transmit algorithm collects the travel
time samples of two AVI readers, N, in each constant time interval t, with an upper limit of 200 samples, to calculate the average
travel time ρABtwithin the time interval by using the following
equation[45]: ρABt¼∑
N
i¼ 1ðtBitAiÞ
N ð1Þ
In this study, the charging times and ID of northbound vehicles passing through Yangmei Toll Station and Linkou Toll Station were collected through the ETC system. A total of 1,679,868 data points were collected, and the Transmit algorithm was employed to compute HTT and ATT at 5-min intervals without the restriction of 200 samples. The computation of historical travel time (HTTABt)
is expressed by the following equation:
HTTABt¼ tBitAijt trrtBirt and BttABtð10:4Þ rtBitAirBttABtð1þ0:4Þ
ð2Þ In Eq.(2), with the time of vehicle i passing through point B, tBi, as
the judgment basis, data of vehicles passing through point B during an interval offive minutes are collected, and the completed trips between upstream point A and downstream point B are utilized as the samples to compute the average travel time as the historical travel time (HTTABt). Although HTT does not represent
the ATT (ATTABt) of vehicle i traveling in the freeway section AB
from upstream point A, it may imply the historical traffic
char-acteristics of the freeway section AB. According to Fei et al.[7], HTT can be used to effectively adjust the real time prediction model.
Thus, in this study, HTTABtis used as an input variable of the
NN-based prediction model.
The computation of actual travel time (ATTABt) is expressed by
the following equation:
ATTABt¼ tBitAijt trrtAirt and BttABtð10:4Þ
rtBitAirBttABtð1þ0:4Þ ð3Þ
In Eq.(3), with the time of vehicle i passing through point A, tAi, as
the judgment basis, data of vehicles passing through point A during an interval of 5 min are collected, and the average travel time of vehicles completing the freeway section AB is computed. This travel time represents the ATT taken by vehicle i after passing through point A to enter the freeway section AB. The actual travel
time (ATTABt) is taken as the target of prediction model. The
threshold value of checking whether it is a continuous trip is set to 0.4. For example, if the average travel time at time t–1 is 30 min and the travel time of sample i at time t is more than or equal to 18 min or less than or equal to 42 min, it is regarded as a continuous trip. This sample can be used to compute the travel time. Furthermore, both HTTABtand ATTABtapply the same
thresh-old value, 0.4. For different areas, the threshthresh-old value may be Fig. 3. Analysis of travel time, accident and rainfall on Tuesday. (a) Travel time, (b) rainfall and (c) distribution of number of vehicles involved in accidents and duration of accidents.
different. The threshold value of 0.4 is used by Taiwan Area National Freeway Bureau, MOTC.
3.3. Step 3: partition data
After processing the data with Step 2, the processed data were divided into the training data set and the test data set in the ratio of 7:3 in order to build the travel time prediction model. However, selecting 70% of the data randomly as the training data set and the remaining 30% as the test data set is not applicable because non-recurrent congestion is considered in this study. If the data are directly divided in a random manner, the samples of non-recurrent congestion may be grouped mainly into either the training data set or the test data set. Such a situation may result in over- or under-estimation in the prediction model. Thus, in this
study, all the samples werefirstly clustered by using K-means.
Then, each cluster was randomly divided into the training data set and test data set in the ratio of 7:3. The clustering is used to ensure
that the samples of various traffic characteristics are randomly
selected in the training data set and test data set for avoiding the error in implementing the prediction model.
3.4. Step 4: create dummy variable by K-means
In this study, clustering is used to assign samples which have
the same traffic characteristics to the same group, and then
generate a dummy variable to the samples. The training data set was clustered through K-means, and a dummy variable was added to the input variables to represent the cluster ID in order to build the travel time prediction model. Firstly, the samples of training
data set were used to construct the CART-based classification
model by utilizing the input variables obtained in the previous steps as the attributes of classification, and the group ID as the class label. Secondly, the cluster ID (e.g., group 1, group 2, etc.) of each sample in the test data set was labeled through the con-structed classification model. To summarize, the process of creat-ing the dummy variable is illustrated inFig. 5. The cluster ID was taken as the dummy variable for building the model of travel time prediction with the training data set, and the built model was used to predict the travel time of the test data set.
3.5. Step 5: identify critical detectors and variables by CART
The CART-based classification model can be used not only to
predict the cluster ID of each sample in the test data set, but also to identify the important variables, which appear in the decision tree.
The identified important variables can be used to construct the
NN-based model of travel time prediction. This prediction model could be used in real-time data forecasting, information
publish-ing, or traffic management. The procedure described above is
illustrated inFig. 6.
3.6. Step 6: build NN-based prediction model
After adding the dummy variable and identifying the important variables, various NN-based models of travel time prediction with different combinations of variables can be constructed to analyze the prediction performance. In order to analyze the impact of HTT, dummy variable and identified critical variables on the prediction performance, six experimental combinations are designed, and the three-layer NN is used to construct the prediction model. Further-more, each experimental combination uses the training data set to construct the best NN-based prediction model. Then, it is tested with the test data set.
In this study, SAS Enterprise Miner 5.3 is used to construct the back-propagation neural network (BPN) with three layers, input, hidden and output layers, CART, and K-means. The detailed algorithm of BPN can be found in[46], and the detailed algorithms
of K-means and CART can be found in[47].
4. Experimentation 4.1. Experimental design
This study focused on exploring how to establish a robust model to predict the travel time of freeway with non-recurrent Fig. 4. Procedure of travel time prediction.
congestion by using existing or even simplified equipment. Six scenarios were designed for to investigate the performance of proposed prediction approach in this study. Scenario 1 uses spot speeds collected by 11 vehicle detectors, rainfalls collected by detectors in three locations, day of the week, and time (AM or PM) as input variables to build the NN-based model of travel time prediction. Because the number of hidden nodes is an important parameter for the BPN-based prediction model, various numbers of hidden nodes were investigated to select the best model for predicting the travel time. The experimental details of BPN can be
found in [8]. In contrast with Scenario 1, Scenario 2 adds HTT
calculated from ETC as the input variable. Scenario 3 adds the dummy variable (i.e., cluster ID) generated by K-means clustering with the input variables of Scenario 1. The input variables of Scenario 4 include the variables in Scenario 2 and cluster ID. Scenario 5 takes the cluster ID as the class label of the classi fica-tion in Scenario 3, and the CART is adopted to select the important variables for predicting the travel time with NN. The prediction procedure of Scenario is described in Step 5 inSection 3. The input variables in Scenario 6 include the important variables identified by using CART with the variables in Scenario 4. These six scenarios are summarized inTable 1.
From the above discussion, the important variables in Scenarios 5 and 6 are all selected by using CART. Observing the decision trees in Scenarios 5 and 6, the same important variables are identified,
which include time (AM or PM), the day of the week, and the spot speed collected by the VD located at 51.6 km, which is denoted as speed 5160.
4.2. Experimental results
The general traffic flow contains the morning peak and
after-noon peak, and a after-noon peak in the areas with the complicated or special traffic flow. Moreover, the traffic management unit usually distinguishes the midnight off-peak traffic characteristic from the Fig. 6. The procedure of identifying important variables and constructing travel time prediction model.
Table 1
Summary of six scenarios.
Scenario Description of input variables
1 Spot speeds collected by 11 VDs, rainfalls from three detectors, the day of the week, and time (AM or PM)
2 The input variables of S1, and HTT calculated from ETC
3 The input variables of S1, and the dummy variable (i.e., cluster ID) 4 The input variables of S2, and the dummy variable (i.e., cluster ID) 5 The important variables identified by CART with the variables
in Scenario 3
6 The important variables identified by CART with the variables in Scenario 4
general off-peak condition. Therefore, it is common to divide the traffic characteristics into eight groups in the areas with
compli-cated traffic flow, and to develop corresponding management
strategies according to their traffic characteristics. In this study,
the data of traffic flow are also divided into eight groups.
Furthermore, before clustering and classification, the data are
standardized by using δij¼(εjφij)/εj, where δij represents the
standardized value of ith sample0s variable j, φij represents
the original value of ith sample0s variable j, andεjrepresents the
maximum value of all samples of variable j plus 20%, that is εj¼max{φi} 1.2. In the CART-based classification, the training
data set are randomly the ratio 7:3 divided into the training stage and the validation stage with the ratio of 7:3. From the results of decision trees, the classification accuracy rates of the training stage and validation stage for Scenarios 3 and 4 are above 99.85% for both S3 and S4. Therefore, the constructed CART-based models are able to effectively differentiate the traffic characteristics of the samples collected in this study.
In order to assess the performance of prediction models, the mean absolute percentage error (MAPE) is adopted as the perfor-mance metric, and it is expressed by the following equation[48]: MAPE¼1n ∑n i¼ 1 ATTiPTTi ATTi ð5Þ
where ATTi represents the actual travel time of ith sample, PTTi
represents the predicted travel time of ith sample, and n is the number of samples. Therefore, the smaller MAPE is, the higher
prediction accuracy is. MAPE was proposed by Lewis[48]and has
been widely used as a performance metric of prediction. In the
case of MAPEr10%, the model has the “highly accurate prediction
capability”. In the case of 11%oMAPE r20%, the model has a
“good prediction capability”. In the case of 21%oMAPE r50%, the
model has a “reasonable prediction capability”. In the case of
MAPE451%, the model has an “inaccurate prediction capability”.
Therefore, if we can construct a model with a“highly accurate
prediction” capability and a smaller number of samples with
MAPE421%, the prediction model not only can help with
satisfy-ing the road users0requirements regarding the travel time predic-tion but also have a positive effect on ITS implementapredic-tion.
According to the experimental results as shown inTable 2, the MAPE values of the six scenarios are between 6% and 9%. Thus, the prediction models of freeway travel time constructed in this study all have“highly accurate prediction” capability. FromTable 2, the MAPE of Scenario 1 (6.68%) is higher than that of Scenario 3 (6.49%) as well as the MAPE of Scenario 2 (6.41%) is close to that of Scenario 4 (6.47%), it is demonstrated that additionally including
the cluster ID as the input variable can enhance the model0s
prediction capability in the environment of having an ETC system or in the environment of having traditional VD detectors.
Furthermore, from Table 2, the percentage of samples with
MAPE420% is lower in Scenario 3 (2.62%) compared to that
Scenario 1 (3.74%). The percentage of samples with MAPE420%
is lower in Scenario 4 (2.74%) compared to Scenario 2 (2.99%). Therefore, additionally including the cluster ID as the input variable can effectively lower the percentage of samples with
MAPE420%. No matter there is AVI or ETC, the dummy variable
(i.e., cluster ID) can improve the performance of travel time prediction. In particular, in the case of collecting the traffic data
only with VDs, the dummy variable can more significantly improve
the performance of travel time prediction, and notably reduce the
percentage of samples with MAPE420%.
In addition, if the prediction models (Scenarios 5 and 6) are constructed only with important variables, the percentage of
samples with MAPE420% increases two to four times compared
with other scenarios. The prediction model containing more
important variables increases the understanding of traffic
char-acteristics and enhances the prediction performance. Therefore, the experimental results of Scenarios 5 and 6 are not unusual. From the results of Scenarios 5 and 6, the day of the week, time (AM or PM) and speed 5160 are extracted as the important variables. Two of these three important variables, the day of the week and time (AM or PM), can be collected by VDs. Therefore, for effective management, speed 5160, i.e., the spot speed collected by the VD at 51.6 km, is a critical element requiring careful main-tenance. With the important variables extracted in Scenarios 5 and 6, only one out of 14 detectors (11 VDs and 3 rainfall detectors) is identified as the important detector such that the operational cost
and maintenance cost can be significantly reduced. Furthermore,
the management unit can maintain and calibrate the data collec-tion system, and develop the imputacollec-tion method of missing data based on the experimental results. Although the models of travel time prediction constructed in Scenarios 5 and 6 perform worse than the models of other scenarios, the models of Scenarios 5 and 6 have the“highly accurate prediction capability” according to the classification defined by Lewis[46]. From the results of Scenarios
5 and 6, time (AM or PM) is also identified as an important
variable by CART, it is similar to the finding in Fei et al. [7]
confirming that the traffic characteristics with non-recurrent
congestion in the morning and afternoon are indeed different. Therefore, taking time (AM or PM) as the input variable or partitioning the data with respect to time (AM or PM) and analyzing accordingly can improve the performance of travel time prediction in the case of non-recurrent congestion.
5. Conclusions and suggestions
Predicting the travel time of freeway with non-recurrent congestion is essential in the area of traffic and transportation, but it is a challenge to achieve a high degree of prediction accuracy with less data and lower cost. Furthermore, the ability to (1) enhance the model prediction capability with existing equip-ment and (2) obtain important variables in important locations in order to reduce the equipment maintenance cost and retain the prediction accuracy is an important issue that has been paid much attention by management and research organizations. In this study, about several million data collected by ETC have been used to obtain the actual travel time for predicting the travel time. In addition, following the empirical analysis of National Freeway No. 1 between the Yangmei Toll Station and Taishan Toll Station in the northward direction, we found that a robust travel time prediction model with non-recurrent congestion could be con-structed by integrating K-means, decision tree, and neural network. From the experimental results of this study, the performance of freeway travel time prediction with non-recurrent congestion could be improved by the added dummy variables and the proposed method of extracting important variables. According to the results of this study, increasing the number of dummy Table 2
The performance of six scenarios.
Scenario MAPE (%) The percentage of samples
with MAPE420% 1 6.68 3.74 2 6.41 2.99 3 6.49 2.62 4 6.47 2.74 5 8.94 10.22 6 8.94 10.22
variables and using them as input variables could enhance the prediction capability of model and lower the percentage of the
sample whose MAPE420% without increasing the amount of
equipment needed. This could enhance public acceptance of travel time prediction. For example, in the six-lane two-way freeway, in a
specific direction (outbound or inbound), if the travel time
information is updated every 5 min, the travel time prediction model runs continuously for 30 days, and there are 600 PCU (the total in three lanes) passing each changeable message sign (CMS) every 5 min and two passengers in each vehicle, then there will be 10,368,000 passengers in total receiving travel time information from each CMS within a month. Even if we only eliminate 0.1% of
the sample whose MAPE420%, this could reduce negative
per-ception of the prediction model by 10,368 people every month. If we set up a number of CMSs, n, along the freeway in two bounds
at the same time, it will influence 2n passengers (10,368 2n
people). Furthermore, it is confirmed by this study that the
important variable extraction method with decision tree can not
only maintain high prediction accuracy but also significantly
reduce the cost of equipment maintenance and operation to comply with the demand of management organization.
Increasing the speed of shock wave and calculating the distance of queue may improve the accuracy of travel time forecasting. The future work can take them into consideration in forecasting travel
time. Reducing the percentage of samples whose MAPE420% has
a significant impact on the road users0 satisfaction. Although the method proposed in this study can reduce the percentage of
samples whose MAPE420%, reducing the percentage of samples
whose MAPE420% is an issue which needs to be addressed
continuously, and it is worth to be further studied in the future.
Acknowledgments
This work is partially supported by National Science Council,
Taiwan, ROC, under Grant NSC 100–2410-H-009–013-MY3.
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Chi-Sen Li is a Ph.D. candidate in the Department of Transportation and Logistics Management at National Chiao Tung University, Taipei, Taiwan. He received his M.Sc. degree in the Department of Civil Engineering from National Central University and B.S. degree in Department of Transportation Engineering from Feng Chia University. His research interests include Data Mining, Travel Time Prediction and Logistics Management.
Mu-Chen Chen is a professor of Department of Trans-portation and Logistics Management in National Chiao Tung University, Taipei, Taiwan. He received his Ph.D. and M.Sc. degrees both in Industrial Engineering and in Management from National Chiao Tung University, and his B.S. degree in Industrial Engineering from Chung Yuan Christian University. His teaching and research interests include Data Mining, Logistics and Supply Chain Management and Meta-heuristics.
