Developing a Travel Time Estimation Method of Freeway Based …downloads.hindawi.com/journals/jat/2019/8582761.pdf · 2019. 7. 30. · JournalofAdvancedTransportation 0 20 40 60 80

Research ArticleDeveloping a Travel Time Estimation Method of Freeway Basedon Floating Car Using Random Forests

Juan Cheng Gen Li and Xianhua Chen

School of Transportation Southeast University Nanjing 211189 China

Correspondence should be addressed to Xianhua Chen chenxhseueducn

Received 28 May 2018 Revised 2 November 2018 Accepted 18 December 2018 Published 3 January 2019

Guest Editor Ali Tizghadam

Copyright copy 2019 Juan Cheng et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Travel time of traffic flow is the basis of traffic guidance To improve the estimation accuracy a travel time estimationmodel based onRandomForests is proposed 7 influence variables are viewed as candidates in this paper Data obtained fromVISSIM simulation areused to verify themodel Different fromothermachine learning algorithmas black boxes RandomForests can provide interpretableresults through variable importance The result of variable importance shows that mean travel time of floating car 119905119891 traffic stateparameter 119883 density of vehicle 119870119886119897119897 and median travel time of floating car 119905119898119890119899119891 are important variables affecting travel time oftraffic flow meanwhile other variables also have a certain influence on travel time Compared with the BP (Back Propagation)neural network model and the quadratic polynomial regression model the proposed Random Forests model is more accurate andthe variables contained in the model are more abundant

1 Introduction

Along with economic and populations grow the number ofcars has increased dramatically causing a series of problemssuch as traffic congestion traffic accidents and environ-mental pollution [1ndash3] To tackle these issues IntelligentTransportation System (ITS) is applied to the road systemThrough the harmonious and close cooperation of peo-ple vehicles and roads ITS can improve the efficiency oftransportation ease traffic congestion improve road networkcapacity reduce traffic accidents lower energy consumptionand decrease environmental pollution Travel time is themost intuitionistic index to reflect the running conditionwhich is an important foundation for constructing ITS [4]Obtaining accurate travel time information on the one handtrafficdepartments improve trafficmanagement decisions onthe other hand travelers can make better travel choices [5]Therefore the accurate travel time of traffic flow is paid moreattention by travelers traffic managers and scholars As thebasis of ITS some researchers have conducted special studieson travel time

Travel time can be achieved directly or indirectly Directmethods measure travel time using probe vehicle recordsat toll stations tracking of cell phones and many other

technologies [6 7] Indirect methods infer travel time usingmeasured traffic volume speed and occupancy in pointsensors (eg loop detector and video camera) along thevehicle trajectory [8]

Recently GPS on the vehicles and smartphones carriedby occupants of motor vehicles can provide data support fortravel time [9] Therefore travel time estimation using GPSdata has been carried out [10ndash12] Over the past few decadesa great number ofmodels for travel time estimation have beendeveloped includingmodels based onmathematical statisticsand models based on artificial intelligence technology

(1) Models based on mathematical statistics These mod-els provide interpretable parameters and a simple modelstructure [7 13] eg a piecewise truncated quadratic speedtrajectory to estimate travel time was proposed by Sun[14] The speed value can be selected between the highestand lowest which was selected as the basis of the runningcondition of the vehicle The method was more accuratewhen the vehicle is in the state of transition and congestionNevertheless in the state of free-flow the advantages ofthe proposed model were not obvious Taken the numberof single lanes the speed limitation and the instantaneousspeed as independent variables a multiple linear regressionmodel based on the floating car was raised by Bobba [15]

HindawiJournal of Advanced TransportationVolume 2019 Article ID 8582761 13 pageshttpsdoiorg10115520198582761

2 Journal of Advanced Transportation

The model was applicable during peak and off-peak periodsYet the road section studied was the section between twosignalized intersections (exclude signalized intersections)which was different from most current researches Choosingdifferent parameters a linear regressionmodel and amultiplelinear regression model were developed by Faria [16] Themultiple linear regression model was more accurate but theaccuracy of the model is limited only 60 Using the GPSdata with lower frequency two mathematical models wereproposed by Sanaullah [17] The two models were based onthe number of map matched points connectivity of linksand spatial and temporal travel time components of the linkrespectively The experimental results indicate that vehiclepenetration rates data sampling frequencies vehicle coverageon the links and time window lengths all influence theaccuracy of link travel time estimation Zhan [18] used GPS-OD data from New York taxis to estimate travel time of roadnetwork segments The impact of the single lane of the roadon the driving vehicle was taken into account When the roadsection was wider the number of lanes may be more and thesingle lane may not portray the fineness of the road networkUsing the same data a Bayesian model to estimate short-termtravel time was presented by Zhan [19] However to reducethe modeling complexity several assumptions were posedBecause of easy to implementation and low computationaleffort models based on mathematical statistics are widelyused However the accuracy is generally low

(2) Models based on artificial intelligence technologyThese models do not assume any particular model structureof the data but treat it as unknown Some successful modelsinclude Fuzzy reasoning [20] machine learning [21] and thehybrid model [22 23] Such as a three-layer Artificial NeuralNetwork (ANN) model was presented to estimate link traveltime by Zheng [24] In the proposed model individual probevehiclersquos positions link IDs timestamps and speed wereused as input information Compared with Hellingarsquos modelthe ANN model performed quite well under different trafficconditions However the ANNmodelwas applied to estimatetravel time based on one car with GPS Using the sparse andlarge-scale GPS trajectories Tang [25] presented a tensor-based context-aware approach to estimate personalized traveltime The model was comprised of map matching traveltime tensor construction context-ware feature extractionand travel time tensor factorization The proposed modelconsiders the spatial correlation between different roadsegments the deviation between different drivers the fine-grain temporal correlation between different time slots andthe coarse-grain temporal correlation between recent andhistorical traffic conditions A bus travel time predictionmodel based on SVMwas proposed byReddy [26]Themodelused V-Support vector regression as a linear kernel functionand used the data collected by public bus equipped with aGPS system to validate The result showed that accuracy ofthe model was significantly improved under the condition ofhigh variance Although these models need large amounts ofcomputation the high accuracy drives scholars to shift theirresearch focus on artificial intelligence technology method

In summary a wide range of models has been developedfor travel time estimation Although these models have

their own advantages the number of independent variablesselected is limited and the influence of traffic flow parameterson travel time has not been thoroughly considered

In recent years data mining and machine learninghave gradually come into sight The development of trafficinformation acquisition technology (such as data of GPStrajectories) has provided us with a large amount of trafficdata which offer an opportunity to develop a more accuratetravel time estimation based on data mining Compared withtraditional parametric models data mining algorithm canbe deeply explored implicit relationships between variablesIn view of this the paper introduces a new data miningtechnique called Random Forests for travel time estimationThe influence of variables on travel time can be deeplyexcavated through Random Forests

The rest of the paper is structured as followed The nextsection will give the methodology of Random Forests to builda travel time estimation model followed by Section 3 whichdescribes the data used in this paper Results and discussionsare presented in Section 4 Finally the conclusions areoutlined in Section 5

2 Methodology of Random Forests

Random Forests is an integrated learning algorithm basedon decision tree proposed by Breiman in 2001 [27] RandomForests is a high-precision algorithm in machine learningwhich can overcome the shortcomings of a single predictionor classification model

21eory Random Forests is a combination model consist-ing of a set of regression decision trees Equation (1) showsthe definition of Random Forests [28]

ℎ (119909 120579119905) 119905 = 1 2 119879 (1)where ℎ(119909 120579119905) is a tree-structured classifier and 120579119905 is

independent identically distributed random vectors 119909 isthe independent variable 120579119905 is the independent distributedrandom variable 119879 represents the number of decision trees

Use the idea of ensemble learning to take the average ofeach decision tree as a regression prediction result which isshown in

ℎ = 1119879119879

sum119894=1

ℎ (119909 120579119905) (2)

where ℎ(119909 120579119905) is output based on 119909 and 120579In order to overcome the problem that the decision tree

model is not high in accuracy and is prone to overfitting theidea of bagging and stochastic subspace was introduced inRandom Forests [28 29]

(1) Bagging Bagging is a Bootstrap sampling techniqueproposed in 1996 [28] Assuming that 119878 is the original sampleand119873 is the number of samples in 119878The probability that eachsample in 119878 is not extracted is (1 minus 1119873)119873

If119873 997888rarr infin then

lim119873997888rarrinfin

(1 minus 1119873)119873

= 1119890 asymp 0368 (3)

Journal of Advanced Transportation 3

TrainingDataset

Bootstrap

Training datasubset

Training datasubset hellip Training data

subset

hellip

Decision tree 1 Decision tree 2 hellip Decision tree m

Generatingforest

TestDataset

hellip


Weightedaverage

Result

Making decision

Figure 1 The process of establishing a Random Forests

Equation (3) indicates that about 368 of the samples arenot extracted each time which is called OOB (Out-of-Bag)data

(2) Stochastic Subspace In the process of constructing theregression decision tree each split node randomly extractsthe feature subspace from the total feature space as thecandidate feature set of the node and selects the optimalfeature for splitting The method ensures that the featuresubsets are not only different among trees but also theindependence and diversity of the tree and further improvethe randomness in node splitting of Random Forests Deter-mining the stochastic subspace is to choose the numberof explanatory variables to be checked for the splittingprocess

In Random Forests the final predictive performance ofthe model is determined by the number of trees in the forest

(T) and the number of explanatory variables to be checkedfor the splitting process (m)

Figure 1 is the flowchart of the classifier and the flowof training and testing phases which shows the process ofestablishing a Random Forests

22 Generalization Error Generalization error reflects theability of the model to predict data outside the training setand is an important indicator for judging the quality of themodel

Definition 1 It is assumed that the training sets are extractedfrom the independent and identically distributed randomvectors (119883 119884) and the formed training sets are independentof each otherThen themean squared error of the output ℎ(119883)is 119864119883119884(119884 minus ℎ(119883))2


In Random Forests when there are enough regressiondecision trees and ℎ119905(119883) = ℎ(119883 120579119905) according to the largenumber theorem Theorem 2 can be obtained

Theorem2 When 119905 997888rarr infin mean square generalization errorconverges on

119864119883119884 (119884 minus ℎ (119883 120579119905))2 997888rarr 119864119883119884 (119884 minus 119864120579 (119883 120579))2 = 119875119864lowast (4)

where 120579119905 is a random variable of the 119905 minus 119905ℎ regressiondecision subtree 119864120579 is a mathematical expectation 119875119864lowast isgeneralization error of Random Forests

Theorem 2 shows that with the increase of the regressiondecision subtree 119905 Random Forests gradually converges andgeneralization error will eventually tend to a limit valueAlthough Random Forests has been proven not prone tooverfitting in mathematics [27] in the actual applicationprocess the parameters of the Random Forests are optimizedby experiments to further avoid overfitting

3 Data

31 Traffic Simulation Soware To collect enough data fortraining and testing traffic simulation software is used Trafficsimulation software is widely used in the study of trafficplanning and traffic flow The microscopic traffic simulationsoftware can describe the road network and simulate thetraffic flow through different models Many types of trafficsimulation software can be used to collect travel time data[30 31]

(1) VISSIM VISSIM is a microscopic traffic simulationsoftware developed by PTV of Germany which is a sim-ulation system based on traffic behavior model It uses adiscrete random microscopic model with a time step of01s The longitudinal movement of the vehicle adopts thepsychophysical car-following model proposed by ProfessorWiedemann and the lane-changing behavior of the vehicleadopts a rule-based algorithm After an open COM interfaceVISSIM has a good secondary development capability

(2) CORSIM CORSIM is developed by the US FederalHighway Administration (FHWA) and consists of two mod-els FRESIM and NETSIM FRESIM is mainly used for thesimulation of highways and expressways while NETSIMis used for the simulation of urban road networks It haslane change and car-following model simulation module andsimulates the state of traffic flow in the road network with 1ssimulation step The software has functions such as analogtiming dynamic filter control and cooperative filteringcontrol However CORSIM lacks an allocation algorithm andit is difficult to evaluate the traffic volume transfer caused byramp control accidents and travel information

(3) PARAMICS Developed by British Quadstone PARAM-ICS can be applied to traffic simulation at different levelsfrom a single road network to a large-scale urban roadnetwork PARAMICS supports multiuser parallel computing

Airport InterchangeLukou Interchange

104828m

Figure 2 The study area

with a powerful application interface However PARAMICSlacks a model of mixed traffic and complex traffic flow

(4) SimTraffic SimTraffic is originally developed as trans-portation software for signal optimization timing and trafficmodel building With the development of traffic simulationtechnology SimTraffic has gradually developed into matureand fully functional microscopic traffic simulation softwareIt adds ramps roundabouts and highway modeling toolsbased on the original functions Nevertheless SimTraffic doesnot have a dedicated lane as well as bus and car parking spots

Through the above description it can be found thatthe traffic simulation software has its own advantages anddisadvantages However VISSIM has the ability to pro-pose separate file output parameters high traffic descriptionaccuracy and simulated traffic has diverse characteristicsTherefore data produced by VISSIM simulation software areused to verify the proposed travel time estimation model inthis paper

32 e Source of Data

321 Selection of the Simulation Section Nanjing Airportfreeway between the Airport Interchange and Lukou Inter-change with the length of 104828m and 4 lanes in onedirection is selected as the research area Time detectors areset at both ends of the selected freeway section The routediagram is presented in Figure 2

322 Determination of the Simulation Parameters

(1) Simulation Traffic The VISSIM simulation software iscalibrated according to actual hourly traffic flow in NanjingAirport freeway from Nanjing to Airport investigated by air-port toll station at 900-1500 onAugust 22 2017 Since the realtraffic flow does not include congestion in order to cover thestate of free-flow transition and congestion in the freewaythe traffic flow increased 600Vehh from the real measuredvalue of the previous period during 15 00-17 00 whichreflect the state of congestion Only increasing the number ofvehicles does not necessarily result in congestion Howeverbased on the state of transition the authors guarantee that allvariables are constant and continue to increase the traffic flowto characterize the state of congestion The input traffic flowis shown in Table 1

(2) Vehicle Type The user-defined taxi type is 1 and thevehicle color is blue the truck type is 2 and the vehicle coloris yellow the bus type is 3 and the vehicle color is blue the


Table 1 The input traffic flow

time segments(s) 900-930 930-1000 1000-1030 1030-1100

Simulationtime segments(s)

0-1800 1800-3600 3600-5400 5400-7200

traffic flow(vehh) 800 1200 1600 2000

time segments(s) 1100-1130 1130-1200 1200-1230 1230-1300


7200-9000 9000-10800 10800-12600 12600-14400


time segments(s) 1300-1330 1330-1400 1400-1430 1430-1500


1400-16200 16200-18000 18000-19800 19800-21600


time segments(s) 1500-1530 1530-1600 1600-1630 1630-1700


21600-23400 23400-25200 25200-27000 27000-28800


car type is 4 and the vehicle color is redThe user-defined taxiis chosen as the floating car in this paper

(3) Speed Distribution On the freeway the expected speedof car truck and bus is 120100 and 100 kmh The speeddistribution of cars trucks buses and taxis is shown inFigure 3

(4) Vehicle Proportion Through investigation the vehicleproportion on the airport freeway section is car truck bustaxi =04201202602

(5) Time Detector In the freeway section time detectors areset up to collect travel time of the individual floating car andtravel time of the traffic flowThemean and median values oftravel time are calculated by the collection travel time of anindividual floating car

33 Design of Experimental Scheme In the process of exper-iment the dynamic changing process of the freeway trafficflow was simulated by changing the input traffic flow includ-ing the state of free-flow transition and congestion

Using different random seed number the experimentsimulated 133 times and the simulation time was 28800s Atlast 133 sets of data were obtained representing 133 daysrsquo dataof 900-1700

Travel time was obtained at the sampling interval of 300seconds At the same time travel time of the floating cars wasacquired at the sampling interval of 1 second

34 Variables of the Model

341 Traffic State Parameter In the Highway Capacity Man-ual [32] traffic state of the freeway was divided into six levels(namely A to F) according to the average speed and densityAs we all know speed density and traffic flow are threebasic parameters which are interrelated If values for two ofthese parameters are known the third can be computed Thestandard of traffic state classification of a freeway is shown inTable 2

In this paper traffic state parameter refer to the standardof traffic state classification of a freeway let 119909 = 1 119905119900 6 forrepresenting the traffic state A to F of the freeway respectivelyThe paper combined existing traffic state levels and describedthe freeway at a lower level Therefore traffic state of thefreeway was divided into three categories The state of free-flow includes level A and B namely 119909119891 = 1 2 the stateof transition includes level C and D namely 119909119905 = 3 4the state of congestion includes level E and F namely 119909119888 =5 6 which is presented in Table 3 The traffic parameter is119883 = 119909119891 119909119905 119909119888


0

20

40

60

80

100

120

140Ve

loci

ty (k

mh

)

02 04 06 08 1000Cumulative percentage

(a) The speed distributions of cars

0

20

40

60

80

100

Velo

city

(km

h)


(b) The speed distributions of trucks

0

20

40

60

80

100

Velo

city

(km

h)


(c) The speed distributions of buses

0

20

40

60

80

100

120

Velo

city

(km

h)


(d) The speed distributions of taxis

Figure 3 The speed distributions

Table 2 The standard of traffic state classification of a freeway [32]

Trafficstate

Density Range Design speed (mih)75 65

(pcmiln) Speed (mih) Traffic flow(pchln) Speed (mih) traffic flow

(pchln)A 11 75 820 65 710B 18 748 1350 65 1170C 26 706 1830 646 1680D 35 622 2170 597 2090E 45 533 2400 522 2350F gt45 lt533 gt2400 lt522 gt2350Note in order to keep the data neat the unit used pcmiln and mih in Table 2 Table 2 can change into pckmln and kmh by 1mi = 1609km The numberin Table 2 is the maximum value of each level

342 Travel Time Calculation of the Floating Car On anyfreeway section Δ119909119899 there are 119904 floating cars within the timeinterval 119905119894 to 119905119894+1 which is shown in Figure 4

Assuming that travel time of each floating car on thefreeway section is 119905119892 (g = 1 2 3 s) since the mean valueexpressed as 119905 and the median value denoted by 119905119898119890119899 canrepresent the general level of the whole data The travel time

of the floating car is being calculated by the mean value andmedian value respectively

343 Variables of the Model In the process of VISSIMsimulation 14 traffic variables can be obtained that isnumber of floating car 119873119891 occupancy of floating car 119877119891number of vehicle 119873119886119897119897 occupancy of vehicle 119877119886119897119897 density of


Direction of the vehicles

Δxn

Figure 4 The distribution of floating cars on the freeway

Table 3 The table of traffic state parameter

traffic state traffic stateparameter

traffic state ofthe paper

A 1 free-flowB 2C 3 transitionD 4E 5 congestionF 6

floating car119870119891 speed of floating car119881119891 traffic flow of floatingcar 119876119891 density of vehicle 119870119886119897119897 speed of vehicle 119881119886119897119897 trafficflow of vehicle 119876119886119897119897 ratio of floating car 119877119886119905119894119900119891 travel timeof floating car (mean value 119905119891 and median value 119905119898119890119899) andtraffic state parameter 119883

4 Results and Discussions

Using the data obtained from VISSIM and the variablesdiscussed above the Random Forests model for travel timeestimation was established

SPM 82 data mining software developed by SalfordSystems was used to establish the Random Forests model[33] although Random Forests can use the OOB error toevaluate the model However in order to compare with othermodels in this paper 133 sets of data were trained andvalidated different models in two scenarios Total data of132 simulations were selected as training data and the 5thsimulation data were selected as test data which used tocompare with the mathematical statistics model Meanwhilein order to contrast with machine learning model data of 133days were divided into two data sets in which 27-133 days ofdata were used as training data sets and 1-26 days of data wereused as test data sets

Mean Square Error (MSE) Mean Absolute Deviation(MAD) and Relative Error (RE) were selected as evaluationcriteria

119872119878119864 = 1119899119899

sum119894=1

(119910119894 minusand119910119894) (5)

119872119860119863 = 1119899119899

sum119894=1

1003816100381610038161003816100381610038161003816119910119894 minusand119910119894

1003816100381610038161003816100381610038161003816 (6)

119877119864 = 119910119894 minusand119910119894

119910119894(7)

where in (5)-(7) 119899 is the total number of samples 119910119894 is thereal value of travel time and

and119910119894 is the estimation value of travel

time

41 Parameter Determination There are 2 parameters to beascertained in Random Forests namely the number of treesin the forest (T) and the number of explanatory variables tobe checked for the splitting process (m)

(1) e Number of Trees in the Forest (T) In Random Forestsdecision trees are not pruned It is demonstrated that increas-ing the number of trees would not increase the precision butbrings the computational burden However insufficient treesare generated the calculated variables importance may notbe accurate enough The number of trees in the forest wasdetermined by 10-fold cross-validation Table 4 shows the 10-fold cross-validation errors with a different number of treesin the forest

It can be seen from Table 4 that the number of trees was500 and 600with the same minimum test errorThe fewer thetrees are the smaller the computational burden is thereforethe number of trees was 500 in the Random Forests model

(2) e Number of Explanatory Variables to Be Checked forthe Splitting Process (m) In Random Forests only a subset ofindependent variables is checked to find the best splits whichmakes the forest development more efficient Beriman [27]has shown that randomly selecting a subset of independentvariables to find the best split makes the process faster andleads to accurate results Ghasri [34] adopted the squareroot of the number of independent variables in each splitThere are other methods such as twice the square rootand half the square root of the number of independentvariables in each split When the number of explanatoryvariables to be checked for the splitting process is determinedby 10-fold cross-validation error the effect is not obviousRandom Forests can use OOB (Out-of-Bag) error estimatesas unbiased estimates of generalization error without runninga cross-validation procedure to measure the Random Forestsmodel [28 34ndash36] Therefore the OOB error was used todetermine the number of explanatory variables to be checkedfor the splitting process In this paper the OOB errors areobtained using a different number of explanatory variables tobe checked for the splitting process respectively and finallychoose the number of independent variables with the smallestvalue of OOB error Table 5 shows the OOB errors with adifferent number of independent variables in each split

Finally the number of explanatory variables to be checkedfor the splitting process was 3 in the Random Forests model

42 Variable Importance Using the training data to trainthe model the order of variables importance can be gained


Table 4 10-fold cross-validation errors with a different number of trees in the forest

trees 100 200 300Data sets Learn Test Learn Test Learn TestRMSE 22149 26889 22153 26857 22179 26789MAD 09228 11243 09189 12112 09163 11165trees 400 500 600Data sets Learn Test Learn Test Learn TestRMSE 22126 26752 22144 26703 22144 26703MAD 09141 11163 09152 11151 09152 11151

Table 5 The OOB errors with a different number of independent variables in each split

m 1 2 3 4 5 6 7OOB errors 10283 7219 6342 6936 6591 6474 7230m 8 9 10 11 12 13 14OOB errors 7306 7235 7300 7260 7282 7395 7302

Table 6 Variable importance

Variable Variableimportance

mean travel time of floating car 119905119891 5898density of vehicle119870119886119897119897 3558traffic state parameter119883 2995median travel time of floating car 119905119898119890119899119891 1572density of floating car119870119891 539speed of vehicle119881119886119897119897 474occupancy of vehicle 119877119886119897119897 275speed of floating car 119881119891 168traffic flow of vehicle 119876119886119897119897 022number of vehicle119873119886119897119897 022occupancy of floating car 119877119891 021traffic flow of floating car 119876119891 015number of floating car119873119891 007ratio of floating car 119877119886119905119894119900119891 005

Variable importance explains the influence of independentvariables on the dependent variable The higher the value ofthe variable importance is the stronger the influence on themodel is Variable importance is shown in Table 6

It can be seen from Table 6 that mean travel time of float-ing car 119905119891 density of vehicle 119870119886119897119897 traffic state parameter 119883andmedian travel time of floating car 119905119898119890119899119891 are the importantfactors which are much greater than other variables It isindicated that travel time of traffic flow is closely related totravel time of floating car density of vehicle and traffic stateparameter

43 Filtering Feature Variables As can be seen from Table 6in the established Random Forests model much variableimportance has low values such as the ratio of floating carindicating that there are some redundant variables in themodel and the variables need to be screened The literature

[37] uses the variable importance obtained by the model tofilter the feature variables which is presented as follows

(1) Create a Random Forests model using a set of featurevariables containing 119899 variables and rank the variableimportance of the 119899 feature variables in descendingorder

(2) Delete the variable with the lowest variable impor-tance among the 119899 feature variables and get thefeature variable set containing 119899-1 variables

(3) Create a Random Forests model using a set of fea-ture variables containing 119899-1 variables and rank thevariable importance of the 119899-1 feature variables indescending order

(4) Delete the variable with the lowest variable impor-tance among the 119899-1 feature variables and get thefeature variable set containing 119899-2 variables

(5) Repeat steps (3) and (4) until there is one remainingfeature variable

(6) The Random Forests models are established contain-ing 119899 119899-1 119899-2 sdot sdot sdot 1 variables OOB errors are rankedin order and the Random Forests model with thesmallest OOB error and the feature variable set isselected

According to the method described above a set of featurevariables and a Random Forests model containing 7 featurevariables are obtained The training result of the model isshown in Figure 5 and the variable importance is shown inTable 7

From Figure 5 reducing the number of feature variablesdoes not reduce the performance of the model however theOOB error decreases from 6342 to 5586 It can be observedfrom Table 7 that mean travel time of floating car 119905119891 trafficstate parameter 119883 density of vehicle 119870119886119897119897 and median traveltime of floating car 119905119898119890119899119891 are still the most important factorswhich is much greater than the other three variables

In all the 7 variables 119905119891 and 119905119898119890119899119891 enter the model at thesame time but the variable importance of 119905119891 is much larger


80

70

60

50

40

30

20

10

0

MSE

Number of Trees

500 (5586)

5004003002001000

Figure 5 The result of Random Forests

Table 7 Variable importance after filtering feature variables


mean travel time of floating car 119905119891 11369traffic state parameter119883 4507density of vehicle119870119886119897119897 4138median travel time of floating car 119905119898119890119899119891 1346speed of vehicle119881119886119897119897 488density of floating car119870119891 117speed of floating car 119881119891 094

than 119905119898119890119899119891 In the previous research due to the correlationof variables the two parameters were generally not includedin the model at the same time However the mean value andmedian value can represent the general level of the whole datawith different statistical significance Therefore the RandomForests model uses both 119905119891 and 119905119898119890119899119891 as variables to take fulladvantage of different variables

Density of vehicle119870119886119897119897 and density of floating car119870119891 havedifferent effects on the Random Forests model Density isthe most important parameter of traffic flow and it is anevaluation index of traffic demand The higher the densityis the slower the speed is and the longer the travel timeis Density is an important indicator that affects travel time119870119886119897119897 is much more important than 119870119891 which is simple tounderstand The paper uses travel time of the floating carto calculate travel time of traffic flow but 119870119886119897119897 represents thecondition of all vehicles which is a more intuitive reflectionon travel time of traffic flow

Speed of vehicle 119881119886119897119897 and speed of floating car 119881119891 havean influence on the estimated travel time because speedis the most intuitive reflection of travel time The variableimportance value of 119881119891 is the lowest (094) but it is alsoan important factor affecting travel time of traffic flow Thereason is that the travel time estimation model is based ontravel time of floating car and speed of floating car is closelyrelated to travel time of floating car

Traffic state parameter 119883 is the second most importantinfluence variable in the Random Forests model As a newlyintroduced parameter in this paper119883 is an intuitive indicatorthat directly reflects traffic states

To sum up the paper uses travel time of floating car toreflect travel time of traffic flow Travel time of floating car(both 119905119891 and 119905119898119890119899119891) is an indispensable factor in the RandomForests model Speed and density are the most intuitivereflection of travel time therefore 119870119886119897119897 119870119891 119881119886119897119897 and 119881119891 are

the selected influence variable of the Random Forests modelThe variable of 119883 is selected in the Random Forests modelbecause it directly reflects the traffic states

44 Accuracy of the Established Model To test the accuracyof the model presented in this paper a quadratic polyno-mial regression model with different states was establishedaccording to the method of [38] Consistent with the RandomForests model the total data of 132 simulations were selectedfor quadratic polynomial regression and the 5th simulationdata were selected as validation data The quadratic polyno-mial regression model is provided in

119879119891119897119900119908

=

002751198792119891 minus 12203119879119891 + 455727 119891119903119890119890 minus 119891119897119900119908000581198792119898119890119899119905 + 00902119879119898119890119899119905 + 371768 119905119903119886119899119904119894119905119894119900119899minus000341198792119888 + 20308119879119888 minus 650968 119888119900119899119892119890119904119905119894119900119899

(8)

where 119879119891119897119900119908 is travel time of traffic flow 119879119891 is mean traveltime of floating car in the state of free-flow 119879119898119890119899119905 is mediantravel time of floating car in the state of transition 119879119888 is meantravel time of floating car in the state of congestion

Equation (8) is a regression model with different statesAlthough there are no separate states to establish the RandomForests model the introduced traffic state parameter 119883 candistinguish different traffic states The errors of differentmodels are presented in Table 8

Meanwhile BP (Back Propagation) neural networkmodel was also established by using the data of 27-133 daysof data as training data sets BP neural network [39] isa multilayer feedforward network trained by error inversepropagation algorithm which was proposed by a team ofscientists led by Rumelhart and McCelland in 1986

The topology of BP neural network includes input layerhidden layer and output layer which are divided intoinformation forward propagation and error back propagation[40] BP neural network model with a three-layer feedfor-ward Perceptron algorithm is used to estimate travel timeFigure 6 is the network structure of the three-layer BP neuralnetwork model designed in this paper

In order to a fair comparison with the Random Forestsmodel the input variable in the BP neural network model isthe selected variables in Section 43 and the output variable isthe estimated travel time The function of the hidden layer islogistic in the BP neural network The network structure is 7-6-1 that is the number of input layer nodes is 7 the number ofhidden layer nodes is 6 and the number of output layer nodesis 1 Then the model was tested using 1-26 days of data setsThe training and test errors of different models are shown inTable 9

Figure 7 is travel time obtained by different modelsFigure 8 shows the comparison between travel time of the5th day in the test data sets (real travel time) and travel timeobtained with various models

Several conclusions can be drawn based onTables 8-9 andFigures 7-8


hellip

hellip

hellip

Information forward propagation

Input layer Hidden layer Output layer

Estimated travel time

Error back propagation

Vf

tf

X

Kall

Figure 6 The network structure of the three-layer BP neural network model

Table 8 The MAD of Random Forests model and reference [38] model

MAD Random Forests model model of reference [38]free-flow 05295 06556transition 06640 12326congestion 17573 68407average 08047 55113

Table 9 TheMAD of Random Forests model and BP neural network model

Data set Traffic state Random Forests model BP Neural Network model

Training Data

free-flow 05264 05414transition 05768 06003congestion 12856 18827average 08043 08987

Test Data


Firstly it can be seen from Table 8 that the accuracyof the Random Forests model is much greater than that ofthe quadratic polynomial regression model In addition totravel time (mean and median) of floating car the proposedmodel has selected another six variables which indicate thatRandom Forests are not sensitive to the interaction betweenvariables Therefore the Random Forests model can choose aricher impact variable

Secondly Table 9 shows the comparison between theRandomForestsmodel and theBPneural networkmodel it isfound that the error of the Random Forestsmodel is generallyless than the BP neural network model in both training datasets and test data sets The reason may be different from themachine learning algorithm as black boxes (such as BPneuralnetwork and SVM) Random Forests has capabilities of data

mining The relationship between variables can be deeplyexploited through Random Forests

Thirdly it revealed that in Table 9 when traffic flow isoperating in the state of free-flow with high speed traveltime obtained by the two models is close to the real valuein both the two data sets While in the state of transitionand congestion with the lower speed error of the proposedmodel is obviously less than the BP neural network model inboth two data sets It is shown that the model proposed inthis paper has more advantages in the state of transition andcongestion

Fourthly as indicated in Figures 7-8 that travel timeobtained in this paper is consistent with the real travel timewhich indicates that the proposed Random Forests model iseffective


Table 10 The variables entering the model after eliminating multicollinearity

traffic state variables

free-flow mean travel time of floating car 119879119891 traffic state parameter119883119891 occupancy of vehicle 119877119886119897119897119891 numberof floating car119873119891

transition median travel time of floating car 119879119898119890119899119905 traffic state parameter119883119905 occupancy of vehicle 119877119886119897119897119905number of floating car119873119905

congestion mean travel time of floating car 119879119888 traffic state parameter119883119888 occupancy of vehicle 119877119886119897119897119888 numberof floating car119873119888

020406080

100120140160180200220

Trav

el T

ime (

s)

Travel time

Random ForestsBP Neural NetworkModel of reference [38]True

10 20 30 40 50 60 70 80 90 1000Time Series

Figure 7 The estimated travel time

minus8minus6minus4minus2

02468

10

Rela

tive E

rror

()

Error

Random ForestsBP Neural NetworkModel of reference [38]

10 20 30 40 50 60 70 80 90 1000Time Series

Figure 8 The relative error of the models

In addition the paper established a multiple linearregression model for different states using the 14 variablesmentioned in Section 343 Before establishing a regressionmodel the multicollinearity between independent variablesis tested firstly Multicollinearity (collinearity for short) pro-posed by Freund [41] refers to a precise correlation or ahigh degree of correlation between the variables in the linearregressionmodel whichmakes themodel difficult to estimateaccurately After eliminating multicollinearity the variablesentering the model are shown in Table 10

It can be seen from Table 10 that due to the mul-ticollinearity of variables when the regression model is

established only 4 variables are selected and some of thevariables that affect travel time are ignored such as speeddensity etc However Random Forests is not affected bymulticollinearity of variables The relationship between traveltime and variables can be deeply excavated through RandomForests

5 Conclusion

In this paper Random Forests is proposed for travel timeestimation which is a hotspot algorithm in machine learningand can deeply excavate the complex relationships betweenvariables The proposedmodel is established with 7 variablesnamely mean travel time of floating car 119905119891 traffic stateparameter 119883 density of vehicle 119870119886119897119897 median travel time offloating car 119905119898119890119899119891 speed of vehicle 119881119886119897119897 density of floating car119870119891 and speed of floating car119881119891 Using different random seednumber the experiment simulates 133 times with VISSIMsimulation software Total data of 132 simulations are selectedas training data and the 5th simulation data are selected as testdata which used to compare with the quadratic polynomialregression model Meanwhile data of 133 days are dividedinto two data sets in which 27-133 days of data are used astraining data sets and 1-26 days of data are used as test datasets in order to contrast with the BP neural network modelComparison results show that the Random Forests modelis more accurate than the quadratic polynomial regressionmodel and the BP neural network model The includedvariables are more abundant in the Random Forests model


However data are obtained by VISSIM which limited thediversity of data In future research the variables of weathercharacters of drivers and other variables which affect traveltime will be considered in the Random Forests model

Data Availability

The data of the study was simulated by VISSIM and can beobtained up request

Conflicts of Interest

The author declares that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This study is supported by theNationalNatural Science Foun-dation of China under Grants nos 51478114 and 51778136

References

[1] E Jenelius and H N Koutsopoulos ldquoTravel time estimation forurban road networks using low frequency probe vehicle datardquoTransportation Research Part B Methodological vol 53 pp 64ndash81 2013

[2] J F Xi Z H Zhao W Li and Q Wang ldquoA traffic accidentcausation analysis method based on AHP-apriorirdquo ProcediaEngineering vol 137 pp 680ndash687 2016

[3] T Yi and BMWilliams ldquoDynamic traffic flowmodel for traveltime estimationrdquo Transportation Research Record vol 2526 pp70ndash78 2015

[4] W-H Lee S-S Tseng and S-H Tsai ldquoA knowledge based real-time travel time prediction system for urban networkrdquo ExpertSystems with Applications vol 36 no 3 pp 4239ndash4247 2009

[5] D M Miranda and S V Conceicao ldquoThe vehicle routingproblem with hard time windows and stochastic travel andservice timerdquo Expert Systems with Applications vol 64 pp 104ndash116 2016

[6] D Woodard G Nogin P Koch D Racz M Goldszmidtand E Horvitz ldquoPredicting travel time reliability using mobilephone GPS datardquo Transportation Research Part C EmergingTechnologies vol 75 pp 30ndash44 2017

[7] M Rahmani E Jenelius and H N Koutsopoulos ldquoNon-parametric estimation of route travel time distributions fromlow-frequency floating car datardquo Transportation Research PartC Emerging Technologies vol 58 pp 343ndash362 2015

[8] L Lu J Wang Z He and C-Y Chan ldquoReal-time estimation offreeway travel time with recurrent congestion based on sparsedetector datardquo IET Intelligent Transport Systems vol 12 no 1pp 2ndash11 2018

[9] M Rahmani H N Koutsopoulos and E Jenelius ldquoTravel timeestimation from sparse floating car data with consistent pathinference A fixed point approachrdquoTransportation Research PartC Emerging Technologies vol 85 pp 628ndash643 2017

[10] C-H Wu J-M Ho and D T Lee ldquoTravel-time predictionwith support vector regressionrdquo IEEETransactions on IntelligentTransportation Systems vol 5 no 4 pp 276ndash281 2004

[11] C A Quiroga and D Bullock ldquoTravel time studies with globalpositioning and geographic information systems an integrated

methodologyrdquo Transportation Research Part C Emerging Tech-nologies vol 6 no 1-2 pp 101ndash127 1998

[12] J Tang F Liu Y Wang and H Wang ldquoUncovering urbanhuman mobility from large scale taxi GPS datardquo Physica AStatistical Mechanics and Its Applications vol 438 pp 140ndash1532015

[13] Z Ma H N Koutsopoulos L Ferreira and M MesbahldquoEstimation of trip travel time distribution using a general-ized Markov chain approachrdquo Transportation Research Part CEmerging Technologies vol 74 pp 1ndash21 2017

[14] L Sun J Yang and H Mahmassani ldquoTravel time estimationbasedonpiecewise truncatedquadratic speed trajectoryrdquoTrans-portation Research Part A Policy and Practice vol 42 no 1 pp173ndash186 2008

[15] R Bobba Predicting Speeds on Urban Streets Using Real TimeGPSData University of Texas at ArlingtonArlingtonVaUSA2002

[16] D Faria ldquoA framework to transform real-time GPS derivedfrom transit vehicles to determine speed-flowrdquo 2003

[17] I Sanaullah M Quddus and M Enoch ldquoDeveloping traveltime estimation methods using sparse GPS datardquo Journal ofIntelligent Transportation Systems Technology Planning andOperations vol 20 no 6 pp 532ndash544 2016

[18] X Zhan S Hasan S V Ukkusuri and C Kamga ldquoUrbanlink travel time estimation using large-scale taxi data withpartial informationrdquo Transportation Research Part C EmergingTechnologies vol 33 pp 37ndash49 2013

[19] X Zhan S V Ukkusuri and C Yang ldquoA Bayesian mixturemodel for short-term average link travel time estimation usinglarge-scale limited information trip-based datardquo Automation inConstruction vol 72 pp 237ndash246 2016

[20] Y Li and M McDonald ldquoLink travel time estimation usingsingle GPS equipped probe vehiclerdquo in Proceedings of the5th IEEE International Conference on Intelligent TransportationSystems ITSC 2002 pp 932ndash937 Singapore September 2002

[21] A Hofleitner R Herring and A Bayen ldquoArterial travel timeforecast with streaming data A hybrid approach of flow mod-eling and machine learningrdquo Transportation Research Part BMethodological vol 46 no 9 pp 1097ndash1122 2012

[22] S Lee B Lee and Y Yang ldquoEstimation of link speed usingpattern classification of GPS probe car datardquo in Proceedings ofthe International Conference on Computational Science and ItsApplications vol 3981 pp 495ndash504 2006

[23] B A Kumar L Vanajakshi and S C Subramanian ldquoA hybridmodel based method for bus travel time estimationrdquo Journalof Intelligent Transportation Systems Technology Planning andOperations vol 22 no 5 pp 390ndash406 2017

[24] F Zheng and H van Zuylen ldquoUrban link travel time estimationbased on sparse probe vehicle datardquo Transportation ResearchPart C Emerging Technologies vol 31 pp 145ndash157 2013

[25] K Tang S Chen and A J Khattak ldquoPersonalized travel timeestimation for urban road networks A tensor-based context-aware approachrdquo Expert Systems with Applications vol 103 pp118ndash132 2018

[26] K K Reddy B A Kumar and L Vanajakshi ldquoBus travel timeprediction under high variability conditionsrdquo Current Sciencevol 111 no 4 pp 700ndash711 2016

[27] L Breiman ldquoRandom forestsrdquoMachine Learning vol 45 no 1pp 5ndash32 2001

[28] L Breiman ldquoBagging predictorsrdquoMachine Learning vol 24 no2 pp 123ndash140 1996


[29] T K Ho ldquoThe random subspace method for constructingdecision forestsrdquo IEEE Transactions on Pattern Analysis andMachine Intelligence vol 20 no 8 pp 832ndash844 1998

[30] A Louati S Darmoul S Elkosantini and L ben Said ldquoAnartificial immune network to control interrupted flow at asignalized intersectionrdquo Information Sciences vol 433434 pp70ndash95 2018

[31] J Wu M Brackstone and M McDonald ldquoThe validation of amicroscopic simulation model a methodological case studyrdquoTransportation Research Part C Emerging Technologies vol 11no 6 pp 463ndash479 2003

[32] National Research CouncilHCM2010 Highway Capacity Man-ual Transportation Research Board 5th edition 2010

[33] M Gualtieri C A Rowan and K TaKeaways ldquoThe ForresterWave Big Data Predictive Analytics Solutions Q1rdquo ForresterResearch 2013

[34] M Ghasri T Hossein Rashidi and S T Waller ldquoDeveloping adisaggregate travel demand systemofmodels using dataminingtechniquesrdquoTransportation Research Part A Policy and Practicevol 105 pp 138ndash153 2017

[35] L Cheng X Chen J De Vos X Lai and F Witlox ldquoApplyinga random forest method approach to model travel mode choicebehaviorrdquo Travel Behaviour and Society vol 14 pp 1ndash10 2019

[36] J Bao P Liu X Qin and H Zhou ldquoUnderstanding the effectsof trip patterns on spatially aggregated crashes with large-scaletaxi GPS datardquoAccident Analysis amp Prevention vol 120 pp 281ndash294 2018

[37] RGenuer J-M Poggi andC Tuleau-Malot ldquoVariable selectionusing random forestsrdquoPattern Recognition Letters vol 31 no 14pp 2225ndash2236 2010

[38] JW Li Estimation and Prediction of Link Travel Time for UrbanTrunk and Secondary Stress Jilin University 2012

[39] Y-K Liu F Xie C-L Xie M-J Peng G-H Wu and H XialdquoPrediction of time series of NPP operating parameters usingdynamic model based on BP neural networkrdquoAnnals of NuclearEnergy vol 85 pp 566ndash575 2015

[40] X Yu J Han L Shi Y Wang and Y Zhao ldquoApplication of a BPneural network in predicting destroyed floor depth caused byunderground pressurerdquo Environmental Earth Sciences vol 76no 15 Article ID 535 2017

[41] R J Freund and R C Littell SAS System for Regression SASPublishing 3rd edition 2000

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

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Active and Passive Electronic Components

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

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Journal of

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Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

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Volume 2018

Control Scienceand Engineering

Journal of



Journal ofEngineeringVolume 2018

SensorsJournal of



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Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018


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Submit your manuscripts atwwwhindawicom


The model was applicable during peak and off-peak periodsYet the road section studied was the section between twosignalized intersections (exclude signalized intersections)which was different from most current researches Choosingdifferent parameters a linear regressionmodel and amultiplelinear regression model were developed by Faria [16] Themultiple linear regression model was more accurate but theaccuracy of the model is limited only 60 Using the GPSdata with lower frequency two mathematical models wereproposed by Sanaullah [17] The two models were based onthe number of map matched points connectivity of linksand spatial and temporal travel time components of the linkrespectively The experimental results indicate that vehiclepenetration rates data sampling frequencies vehicle coverageon the links and time window lengths all influence theaccuracy of link travel time estimation Zhan [18] used GPS-OD data from New York taxis to estimate travel time of roadnetwork segments The impact of the single lane of the roadon the driving vehicle was taken into account When the roadsection was wider the number of lanes may be more and thesingle lane may not portray the fineness of the road networkUsing the same data a Bayesian model to estimate short-termtravel time was presented by Zhan [19] However to reducethe modeling complexity several assumptions were posedBecause of easy to implementation and low computationaleffort models based on mathematical statistics are widelyused However the accuracy is generally low

(2) Models based on artificial intelligence technologyThese models do not assume any particular model structureof the data but treat it as unknown Some successful modelsinclude Fuzzy reasoning [20] machine learning [21] and thehybrid model [22 23] Such as a three-layer Artificial NeuralNetwork (ANN) model was presented to estimate link traveltime by Zheng [24] In the proposed model individual probevehiclersquos positions link IDs timestamps and speed wereused as input information Compared with Hellingarsquos modelthe ANN model performed quite well under different trafficconditions However the ANNmodelwas applied to estimatetravel time based on one car with GPS Using the sparse andlarge-scale GPS trajectories Tang [25] presented a tensor-based context-aware approach to estimate personalized traveltime The model was comprised of map matching traveltime tensor construction context-ware feature extractionand travel time tensor factorization The proposed modelconsiders the spatial correlation between different roadsegments the deviation between different drivers the fine-grain temporal correlation between different time slots andthe coarse-grain temporal correlation between recent andhistorical traffic conditions A bus travel time predictionmodel based on SVMwas proposed byReddy [26]Themodelused V-Support vector regression as a linear kernel functionand used the data collected by public bus equipped with aGPS system to validate The result showed that accuracy ofthe model was significantly improved under the condition ofhigh variance Although these models need large amounts ofcomputation the high accuracy drives scholars to shift theirresearch focus on artificial intelligence technology method

In summary a wide range of models has been developedfor travel time estimation Although these models have

their own advantages the number of independent variablesselected is limited and the influence of traffic flow parameterson travel time has not been thoroughly considered

In recent years data mining and machine learninghave gradually come into sight The development of trafficinformation acquisition technology (such as data of GPStrajectories) has provided us with a large amount of trafficdata which offer an opportunity to develop a more accuratetravel time estimation based on data mining Compared withtraditional parametric models data mining algorithm canbe deeply explored implicit relationships between variablesIn view of this the paper introduces a new data miningtechnique called Random Forests for travel time estimationThe influence of variables on travel time can be deeplyexcavated through Random Forests

The rest of the paper is structured as followed The nextsection will give the methodology of Random Forests to builda travel time estimation model followed by Section 3 whichdescribes the data used in this paper Results and discussionsare presented in Section 4 Finally the conclusions areoutlined in Section 5

2 Methodology of Random Forests

Random Forests is an integrated learning algorithm basedon decision tree proposed by Breiman in 2001 [27] RandomForests is a high-precision algorithm in machine learningwhich can overcome the shortcomings of a single predictionor classification model

21eory Random Forests is a combination model consist-ing of a set of regression decision trees Equation (1) showsthe definition of Random Forests [28]

ℎ (119909 120579119905) 119905 = 1 2 119879 (1)where ℎ(119909 120579119905) is a tree-structured classifier and 120579119905 is

independent identically distributed random vectors 119909 isthe independent variable 120579119905 is the independent distributedrandom variable 119879 represents the number of decision trees

Use the idea of ensemble learning to take the average ofeach decision tree as a regression prediction result which isshown in

ℎ = 1119879119879

sum119894=1

ℎ (119909 120579119905) (2)

where ℎ(119909 120579119905) is output based on 119909 and 120579In order to overcome the problem that the decision tree

model is not high in accuracy and is prone to overfitting theidea of bagging and stochastic subspace was introduced inRandom Forests [28 29]

(1) Bagging Bagging is a Bootstrap sampling techniqueproposed in 1996 [28] Assuming that 119878 is the original sampleand119873 is the number of samples in 119878The probability that eachsample in 119878 is not extracted is (1 minus 1119873)119873

If119873 997888rarr infin then

lim119873997888rarrinfin

(1 minus 1119873)119873

= 1119890 asymp 0368 (3)


TrainingDataset

Bootstrap

Training datasubset


subset

hellip


Generatingforest

TestDataset

hellip


Weightedaverage

Result

Making decision















3 Data






104828m





32 e Source of Data







time segments(s) 900-930 930-1000 1000-1030 1030-1100


0-1800 1800-3600 3600-5400 5400-7200


time segments(s) 1100-1130 1130-1200 1200-1230 1230-1300


7200-9000 9000-10800 10800-12600 12600-14400


time segments(s) 1300-1330 1330-1400 1400-1430 1430-1500


1400-16200 16200-18000 18000-19800 19800-21600


time segments(s) 1500-1530 1530-1600 1600-1630 1630-1700


21600-23400 23400-25200 25200-27000 27000-28800













0

20

40

60

80

100

120

140Ve

loci

ty (k

mh

)



0

20

40

60

80

100

Velo

city

(km

h)



0

20

40

60

80

100

Velo

city

(km

h)



0

20

40

60

80

100

120

Velo

city

(km

h)





Trafficstate










Δxn











119872119878119864 = 1119899119899

sum119894=1

(119910119894 minusand119910119894) (5)

119872119860119863 = 1119899119899

sum119894=1

1003816100381610038161003816100381610038161003816119910119894 minusand119910119894

1003816100381610038161003816100381610038161003816 (6)

119877119864 = 119910119894 minusand119910119894

119910119894(7)



time





























80

70

60

50

40

30

20

10

0

MSE

Number of Trees

500 (5586)

5004003002001000












119879119891119897119900119908

=


(8)









hellip

hellip

hellip





Vf

tf

X

Kall






Training Data


Test Data













020406080

100120140160180200220

Trav

el T

ime (

s)

Travel time


10 20 30 40 50 60 70 80 90 1000Time Series



02468

10

Rela

tive E

rror

()

Error


10 20 30 40 50 60 70 80 90 1000Time Series





5 Conclusion




Data Availability




Acknowledgments


References














































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



TrainingDataset

Bootstrap

Training datasubset


subset

hellip


Generatingforest

TestDataset

hellip


Weightedaverage

Result

Making decision















3 Data






104828m





32 e Source of Data







time segments(s) 900-930 930-1000 1000-1030 1030-1100


0-1800 1800-3600 3600-5400 5400-7200


time segments(s) 1100-1130 1130-1200 1200-1230 1230-1300


7200-9000 9000-10800 10800-12600 12600-14400


time segments(s) 1300-1330 1330-1400 1400-1430 1430-1500


1400-16200 16200-18000 18000-19800 19800-21600


time segments(s) 1500-1530 1530-1600 1600-1630 1630-1700


21600-23400 23400-25200 25200-27000 27000-28800













0

20

40

60

80

100

120

140Ve

loci

ty (k

mh

)



0

20

40

60

80

100

Velo

city

(km

h)



0

20

40

60

80

100

Velo

city

(km

h)



0

20

40

60

80

100

120

Velo

city

(km

h)





Trafficstate










Δxn











119872119878119864 = 1119899119899

sum119894=1

(119910119894 minusand119910119894) (5)

119872119860119863 = 1119899119899

sum119894=1

1003816100381610038161003816100381610038161003816119910119894 minusand119910119894

1003816100381610038161003816100381610038161003816 (6)

119877119864 = 119910119894 minusand119910119894

119910119894(7)



time





























80

70

60

50

40

30

20

10

0

MSE

Number of Trees

500 (5586)

5004003002001000












119879119891119897119900119908

=


(8)









hellip

hellip

hellip





Vf

tf

X

Kall






Training Data


Test Data













020406080

100120140160180200220

Trav

el T

ime (

s)

Travel time


10 20 30 40 50 60 70 80 90 1000Time Series



02468

10

Rela

tive E

rror

()

Error


10 20 30 40 50 60 70 80 90 1000Time Series





5 Conclusion




Data Availability




Acknowledgments


References














































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia








3 Data






104828m





32 e Source of Data







time segments(s) 900-930 930-1000 1000-1030 1030-1100


0-1800 1800-3600 3600-5400 5400-7200


time segments(s) 1100-1130 1130-1200 1200-1230 1230-1300


7200-9000 9000-10800 10800-12600 12600-14400


time segments(s) 1300-1330 1330-1400 1400-1430 1430-1500


1400-16200 16200-18000 18000-19800 19800-21600


time segments(s) 1500-1530 1530-1600 1600-1630 1630-1700


21600-23400 23400-25200 25200-27000 27000-28800













0

20

40

60

80

100

120

140Ve

loci

ty (k

mh

)



0

20

40

60

80

100

Velo

city

(km

h)



0

20

40

60

80

100

Velo

city

(km

h)



0

20

40

60

80

100

120

Velo

city

(km

h)





Trafficstate










Δxn











119872119878119864 = 1119899119899

sum119894=1

(119910119894 minusand119910119894) (5)

119872119860119863 = 1119899119899

sum119894=1

1003816100381610038161003816100381610038161003816119910119894 minusand119910119894

1003816100381610038161003816100381610038161003816 (6)

119877119864 = 119910119894 minusand119910119894

119910119894(7)



time





























80

70

60

50

40

30

20

10

0

MSE

Number of Trees

500 (5586)

5004003002001000












119879119891119897119900119908

=


(8)









hellip

hellip

hellip





Vf

tf

X

Kall






Training Data


Test Data













020406080

100120140160180200220

Trav

el T

ime (

s)

Travel time


10 20 30 40 50 60 70 80 90 1000Time Series



02468

10

Rela

tive E

rror

()

Error


10 20 30 40 50 60 70 80 90 1000Time Series





5 Conclusion




Data Availability




Acknowledgments


References














































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




time segments(s) 900-930 930-1000 1000-1030 1030-1100


0-1800 1800-3600 3600-5400 5400-7200


time segments(s) 1100-1130 1130-1200 1200-1230 1230-1300


7200-9000 9000-10800 10800-12600 12600-14400


time segments(s) 1300-1330 1330-1400 1400-1430 1430-1500


1400-16200 16200-18000 18000-19800 19800-21600


time segments(s) 1500-1530 1530-1600 1600-1630 1630-1700


21600-23400 23400-25200 25200-27000 27000-28800













0

20

40

60

80

100

120

140Ve

loci

ty (k

mh

)



0

20

40

60

80

100

Velo

city

(km

h)



0

20

40

60

80

100

Velo

city

(km

h)



0

20

40

60

80

100

120

Velo

city

(km

h)





Trafficstate










Δxn











119872119878119864 = 1119899119899

sum119894=1

(119910119894 minusand119910119894) (5)

119872119860119863 = 1119899119899

sum119894=1

1003816100381610038161003816100381610038161003816119910119894 minusand119910119894

1003816100381610038161003816100381610038161003816 (6)

119877119864 = 119910119894 minusand119910119894

119910119894(7)



time





























80

70

60

50

40

30

20

10

0

MSE

Number of Trees

500 (5586)

5004003002001000












119879119891119897119900119908

=


(8)









hellip

hellip

hellip





Vf

tf

X

Kall






Training Data


Test Data













020406080

100120140160180200220

Trav

el T

ime (

s)

Travel time


10 20 30 40 50 60 70 80 90 1000Time Series



02468

10

Rela

tive E

rror

()

Error


10 20 30 40 50 60 70 80 90 1000Time Series





5 Conclusion




Data Availability




Acknowledgments


References














































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



0

20

40

60

80

100

120

140Ve

loci

ty (k

mh

)



0

20

40

60

80

100

Velo

city

(km

h)



0

20

40

60

80

100

Velo

city

(km

h)



0

20

40

60

80

100

120

Velo

city

(km

h)





Trafficstate










Δxn











119872119878119864 = 1119899119899

sum119894=1

(119910119894 minusand119910119894) (5)

119872119860119863 = 1119899119899

sum119894=1

1003816100381610038161003816100381610038161003816119910119894 minusand119910119894

1003816100381610038161003816100381610038161003816 (6)

119877119864 = 119910119894 minusand119910119894

119910119894(7)



time





























80

70

60

50

40

30

20

10

0

MSE

Number of Trees

500 (5586)

5004003002001000












119879119891119897119900119908

=


(8)









hellip

hellip

hellip





Vf

tf

X

Kall






Training Data


Test Data













020406080

100120140160180200220

Trav

el T

ime (

s)

Travel time


10 20 30 40 50 60 70 80 90 1000Time Series



02468

10

Rela

tive E

rror

()

Error


10 20 30 40 50 60 70 80 90 1000Time Series





5 Conclusion




Data Availability




Acknowledgments


References














































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




Δxn











119872119878119864 = 1119899119899

sum119894=1

(119910119894 minusand119910119894) (5)

119872119860119863 = 1119899119899

sum119894=1

1003816100381610038161003816100381610038161003816119910119894 minusand119910119894

1003816100381610038161003816100381610038161003816 (6)

119877119864 = 119910119894 minusand119910119894

119910119894(7)



time





























80

70

60

50

40

30

20

10

0

MSE

Number of Trees

500 (5586)

5004003002001000












119879119891119897119900119908

=


(8)









hellip

hellip

hellip





Vf

tf

X

Kall






Training Data


Test Data













020406080

100120140160180200220

Trav

el T

ime (

s)

Travel time


10 20 30 40 50 60 70 80 90 1000Time Series



02468

10

Rela

tive E

rror

()

Error


10 20 30 40 50 60 70 80 90 1000Time Series





5 Conclusion




Data Availability




Acknowledgments


References














































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia
























80

70

60

50

40

30

20

10

0

MSE

Number of Trees

500 (5586)

5004003002001000












119879119891119897119900119908

=


(8)









hellip

hellip

hellip





Vf

tf

X

Kall






Training Data


Test Data













020406080

100120140160180200220

Trav

el T

ime (

s)

Travel time


10 20 30 40 50 60 70 80 90 1000Time Series



02468

10

Rela

tive E

rror

()

Error


10 20 30 40 50 60 70 80 90 1000Time Series





5 Conclusion




Data Availability




Acknowledgments


References














































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



80

70

60

50

40

30

20

10

0

MSE

Number of Trees

500 (5586)

5004003002001000












119879119891119897119900119908

=


(8)









hellip

hellip

hellip





Vf

tf

X

Kall






Training Data


Test Data













020406080

100120140160180200220

Trav

el T

ime (

s)

Travel time


10 20 30 40 50 60 70 80 90 1000Time Series



02468

10

Rela

tive E

rror

()

Error


10 20 30 40 50 60 70 80 90 1000Time Series





5 Conclusion




Data Availability




Acknowledgments


References














































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



hellip

hellip

hellip





Vf

tf

X

Kall






Training Data


Test Data













020406080

100120140160180200220

Trav

el T

ime (

s)

Travel time


10 20 30 40 50 60 70 80 90 1000Time Series



02468

10

Rela

tive E

rror

()

Error


10 20 30 40 50 60 70 80 90 1000Time Series





5 Conclusion




Data Availability




Acknowledgments


References














































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia








020406080

100120140160180200220

Trav

el T

ime (

s)

Travel time


10 20 30 40 50 60 70 80 90 1000Time Series



02468

10

Rela

tive E

rror

()

Error


10 20 30 40 50 60 70 80 90 1000Time Series





5 Conclusion




Data Availability




Acknowledgments


References














































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




Data Availability




Acknowledgments


References














































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Documents

Developing a Travel Time Estimation Method of Freeway Based …downloads.hindawi.com/journals/jat/2019/8582761.pdf · 2019. 7. 30. · JournalofAdvancedTransportation 0 20 40 60 80