unidirectionalandbidirectionallstmmodelsforshort-term ...2021/01/12 · where σ g is the gate...

Research ArticleUnidirectional and Bidirectional LSTM Models for Short-TermTraffic Prediction

Rusul L Abduljabbar 1 Hussein Dia1 and Pei-Wei Tsai2

1Department of Civil and Construction Engineering Swinburne University of Technology Melbourne Australia2Department of Computer Science and Software Engineering Swinburne University of Technology Melbourne Australia

Correspondence should be addressed to Rusul L Abduljabbar rabduljabbarswineduau

Received 12 January 2021 Revised 31 January 2021 Accepted 20 February 2021 Published 26 March 2021

Academic Editor Jinjun Tang

Copyright copy 2021 Rusul L Abduljabbar et al is is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

is paper presents the development and evaluation of short-term traffic prediction models using unidirectional and bidirectionaldeep learning long short-term memory (LSTM) neural networks e unidirectional LSTM (Uni-LSTM) model provides highperformance through its ability to recognize longer sequences of traffic time series data In this work Uni-LSTM is extended tobidirectional LSTM (BiLSTM) networks which train the input data twice through forward and backward directions e paperpresents a comparative evaluation of the two models for short-term speed and traffic flow prediction using a common dataset offield observations collected from multiple freeways in Australia e results showed BiLSTM performed better for variableprediction horizons for both speed and flow Stacked and mixed Uni-LSTM and BiLSTM models were also investigated for 15-minute prediction horizons resulting in improved accuracy when using 4-layer BiLSTM networkse optimized 4-layer BiLSTMmodel was then calibrated and validated for multiple prediction horizons using data from three different freeways e validationresults showed a high degree of prediction accuracy exceeding 90 for speeds up to 60-minute prediction horizons For flow themodel achieved accuracies above 90 for 5- and 10-minute prediction horizons and more than 80 accuracy for 15- and 30-minute prediction horizons ese findings extend the set of AI models available for road operators and provide them withconfidence in applying robust models that have been tested and evaluated on different freeways in Australia

1 Introduction

Freeway short-term traffic prediction models have beenresearched extensively in the literature [1ndash8] e stronginterest in these models is that they can be used to provideroad operators with predictive intelligence tools to helpthem optimize freeway operations and avoid traffic break-downs ese models have been developed from a variety oftheoretical backgrounds including statistical techniques andartificial intelligence (AI) methods based on neural networks[9] With the development of big data and complex com-putational intelligence AI methods can predict future trafficmore accurately than statistical models In particular deeplearning networks can represent traffic dynamic behaviourand have recently achieved massive success in time seriesmodelling An example of recent models is the

unidirectional long short-term memory (Uni-LSTM) re-current neural network and its extension bidirectional longshort-termmemory (BiLSTM) Previous research has shownthat the Uni-LSTM model has an effective prediction inhandling long-term dependencies as it remembers usefulinformation from inputs that has already passed throughusing ldquoadditional gatesrdquo incorporated in its architecture[10ndash12] However in more recent years a bidirectionalLSTM (BiLSTM) model has been investigated which offersan additional training capability as the output layer receivesinformation from past (backwards) and future (forward)instances simultaneously and it provides better predictionaccuracy [13ndash16] In this paper we assess the performance ofUni-LSTM and BiLSTM for different time horizons usingspeed and flow field data for multiple freeways in Australiae main research questions are as follows

HindawiJournal of Advanced TransportationVolume 2021 Article ID 5589075 16 pageshttpsdoiorg10115520215589075

(1) Will results be improved if speed and flow data aretrained from both directions (forward direction andbackward direction)

(2) How adding layers or mixing both LSTM andBiLSTM as one model affects the modelperformance

(3) If the model is trained and tested for one freewaywill it achieve a good accuracy if validated only(without retraining) on an independent dataset froma different freeway

is paper aims to address these questions and dem-onstrate the feasibility of using advanced AI techniquesbased on deep learning Uni-LSTM and BiLSTM models topredict speed and flow for multiple prediction horizons Itprovides a comparative performance analysis of both Uni-LSTM and BiLSTM based on a common dataset of fieldmeasurements e models are developed using historicaldata extracted from sensors embedded in pavements onthree freeways in Australia the Pacific Motorway betweenBrisbane and the Gold Coast in Queensland TullamarineFreeway in Melbourne and South Eastern Freeway inMelbourne is paper also investigates whether additionallayers of training improve prediction accuracies for bothspeed and flow To our knowledge there have been limitedpapers targeting the BiLSTM model for future traffic pre-diction and this paper shows the robust performance of thisextension of the Uni-LSTMmodel Also this paper validatesthe performance of a developed model on different freewayswhich makes this work a valuable contribution to knowledgein the intelligent transport systems and network operationsfields is provides road operators and transport agencieswith confidence that they can apply these models on dif-ferent freeways even if they have not embarked on com-prehensive historical data collection efforts for the targetfreeways is also helps them with reducing the cost ofdeployment of these algorithms by avoiding the need topreprocess new data and calibrate and validate new modelswhich is a time-consuming undertaking that requires sub-stantial resources and experienced and well-trained AI staffand specialists

is paper is organized as follows Section 2 provides ascan of previous research work Section 3 presents themethodology including data collection and modellingframeworks Section 4 presents the results of the compar-ative evaluation of different models Section 5 presents theperformance of stacked and mixed Uni-LSTM and BiLSTMmodels Section 6 shows the model validation results andfinally Section 7 presents the conclusions and future re-search directions

2 Literature Review

e prediction and forecasting of short-term (1 to 60minutes into the future) traffic conditions plays an im-portant role in the success of intelligent transport systems(ITSs) such as travel information systems adaptive trafficmanagement systems public transportation scheduling andcommercial vehicle operations [17ndash19] Due to the wide

body of literature on this topic we focus the literature scan inthis section on traffic prediction using LSTM models whichused field traffic data collected from inductive loop detectorsCCTV probe vehicles and incident reports A compre-hensive review of other models including those that usedsimulated data can be found in [17] Increasingly roadoperators have more confidence in models that have beendeveloped using real-life data and hence our focus in thiswork on model development and evaluations using datafrom real-world environments

Methodologies used for flow and speed prediction can beclassified into two broad parametric and nonparametricapproaches [20] Examples of commonly used parametricmethods include linear models such as autoregressive in-tegrated moving average model (ARIMA) [21] seasonalARIMA ie SARIMA model [22] exponential smoothingmodel [23] and ARIMA with Kalman filter (KF) [24 25]ese parametric methods perform poorly with dynamictraffic patterns which limits their application in complextraffic prediction compared to nonparametric methodsNonparametric methods are more capable of predicting astochastic pattern of input traffic data and are better athandling noisy data

With the recent advancements in machine learningmany models have shown a promising potential in solvingnonlinear problems and handling long-term dependenciesExamples include LSTM and BiLSTMmodels ese modelswere previously used to forecast future traffic speeds [10]travel times [18] and traffic flows [11] In one study the longshort-termmemory (LSTM) structure was applied for futurespeed prediction and showed that it provides higher per-formance compared to classical methods [10] Another studyshowed that using LSTM models is promising for irregulartravel time prediction models as the error for 1-step-aheadprediction error is relatively small [18] Other studies haveshown that flow prediction using LSTM achieved high ac-curacy compared to other models for different predictionhorizons [11] Also LSTM models have been developed inother studies on car-followingmodels to predict accelerationand deceleration on different road hierarchies [26]

Short-term traffic flow using LSTM has also been in-vestigated where the dependency relationships of time seriesdata were fully considered and experimental results showeda very good performance with an error of 54 whencompared with other models [27] In other studies an end-to-end deep learning model has been investigated to predictfuture traffic flows [28] where one BiLSTM layer was addedand the results showed that the model was capable of solvingstochastic flow characteristics and overcoming overfittingproblems [28] Similarly stacking BiLSTM and Uni-LSTMmodels were developed in another study to predict network-wide traffic speeds e results showed that the stackedarchitecture outperforms both BiLSTM and Uni-LSTMmodels [29]

In another study different models were developed thatshowed superior performance when using deeper BiLSTMlayers for urban traffic prediction [30] Other researchershave also used LSTM and RNN approaches for speed pre-diction models under various urban driving conditions with

2 Journal of Advanced Transportation

credible and accurate results [31] LSTM and gated recurrentunits (GRUs) were also applied in recent studies to predictthe general condition of driving speed in consideration ofthe road geometry and temporal evolution of traffic demande results showed superior LSTM model performancecompared to regression models [32] Similarly superiormodel performance has been shown from using LSTM andGRUmodels when compared to ARIMA and support vectorregression (SVR) models for the track flow prediction [33]

In other studies a variational long short-term memoryencoder was examined to predict traffic flow which providedbetter prediction in comparison to other conventionalmethods used [34] Similarly a long short-term memory-genetic algorithm support vector regression (LSTM-GASVR) short-term traffic flow prediction algorithm wasreported to predict future traffic flows with better accuraciesthan LSTM GRU convolutional neural networks (CNNs)stacked autoencoder (SAE) ARIMA and support vectorregression (SVR) models tested in the same study [35]

Furthermore LSTM models have also been developedfor momentary traffic stream forecasts which aim to helptransport authorities in decision-making during rush hourfor gridlock prediction since the model remembers infor-mation for longer periods of time than other models [36]Also the validity of LSTM models has been verified instudies on prediction of short-term traffic flow and werefound to provide high prediction accuracies for flow data[37] Other studies have documented superior performancewhen ARIMA and long short-term memory (LSTM) neuralnetworks were combined for short-term traffic flow pre-diction [38] In another recent study type-2 fuzzy LSTM(T2F-LSTM) was developed for long-term traffic volumeprediction and extraction of spatial-temporal characteristicsof traffic volumes and was found to achieve high predictionaccuracies [39]

In summary a substantial number of studies in theliterature have addressed short-term traffic prediction withrobust LSTM models However only few studies haveaddressed the promising potential of BiLSTM models fortraffic time series future prediction that consider thebackward temporal dependencies Another importantcontribution in this work is the comparison of stacked andmixed BiLSTM and LSTM layers for model accuracy im-provement In addition this paper discusses the modelapplicability when being developed on parameters of onelocation and validated only (without retraining) on differentlocations Furthermore the models are developed using fielddata that comprised diverse and complex traffic character-istics (including peak nonpeak weekday weekend incidentand nonincident data) Another important factor in thiswork is that the data used for model development have beenmethodically screened preprocessed and validated in a largenumber of previous studies [40 41]

3 Study Methodology

is section of the paper presents the study methodologyincluding data collection model development evaluationtests and analyses

31 Data for Model Development Neural network appli-cations require large amounts of data that are needed formodel development [41 42] e data are typically dividedinto a training dataset used for model calibration and atesting dataset used for model verification e validity ofthe model is tested on an independent dataset not used inmodel training referred to as the testing dataset In thisresearch the data used for model development includedtraffic speed and flow measurements collected fromsensors installed on a number of freeways in Australiaedata were collected over a number of years and timeperiods including peak nonpeak weekday and weekendconditions Another unique characteristic of the data isthat they include incident traffic conditions which areusually difficult to capture for model development Suchincidents which include road crashes broken down ve-hicles and similar nonrecurrent events typically result ina significant capacity reduction of the freeway and last forlong durations Including these data in model training andvalidation improves the robustness of the predictionmodels

311 Dataset 1 Pacific Motorway Queensland is datasetwas collected from a section of the Pacific Motorway be-tween Brisbane and the Gold Coast in Queensland [40] elength of the section is around 15 km Speed and flow datawere gathered from 4 detection stations (S0ndashS3) whichinclude inductive loop sensors installed at approximately500m interval as shown in Figure 1 ese data were col-lected for a period of 5 hours (2 hours peak and 3 hours off-peak traffic conditions) e data comprised normal trafficconditions that did not include any incidents A total of1667 observations were gathered For this study the datawere divided into 1000 observations for training (60 of thetotal dataset) and 667 observations for testing (40 of thetotal dataset)

312 Dataset 2 Tullamarine Freeway Melbourne isdataset was collected from a section of the TullamarineFreeway in Melbourne as shown in Figure 2 e freewayconnects the city to the airport and the northern suburbs andis considered one of the busiest roads in Melbourne edata comprised lane-by-lane loop-detector data consisting ofspeed flow and occupancy measurements in 1-minutecycles [41] Detector station spacing ranged between 450mand 1070m with an average spacing of about 580m for the14 detector stations A total of 21123 observations weregathered and for this research they were divided into 60for training (12674 observations) and 40 for testing (8449observations) is dataset was unique in that it comprised atotal of 75 incidents that occurred on the freeway undervariable traffic conditions While such data make it verychallenging to be able to predict future conditions (becauseof the randomness of incidents) they are most useful as theyallow the prediction algorithms to be trained on a wide rangeof traffic data including both incident and nonincidentconditions

Journal of Advanced Transportation 3

313 Dataset 3 South Eastern Freeway Melbourne isdataset was collected from a section of the South EasternFreeway inMelbourne as shown in Figure 3e data consistedof speed and flow measurements in 1-minute cycles alsocollected from inductive loops embedded in the pavement Atotal of 3147 observations were gathered For this work thedata were divided into 60 for training (1888 observations)and 40 for testing (1259 observations) Similarly these data

included a total of 25 incidents which would allow the pre-diction algorithm to be trained on a variety of traffic dataincluding incident and nonincident conditions

e data from the two Melbourne freeways are alsoimportant in that each freeway carries more than 100000vehicles per day e incident data collected from thesefreeways (100 in total) had varying characteristics that in-cluded a representative range of incidents on freeways Forexample four incidents resulted in blocking one lane oftraffic 77 resulted in blocking 2 lanes and 19 resulted inblocking three lanes Five of the incidents occurred duringlow-flow conditions (below 700 vphpl) 58 during heavy-flow conditions (above 1550 vphpl) and 37 during moderateflow conditions Twenty-five incidents also occurred duringpeak-hour traffic conditions As for the distribution of in-cident duration 26 incidents lasted for less than 30 minutes32 lasted between 30 and 60 minutes 30 lasted between 60and 90 minutes and 12 lasted more than 90 minutes [41]

Samples of speed and flow data for the three freeways areshown in Figures 4 and 5 respectivelyese figures representa small portion of the data for illustrative purposes Figure 4shows speed patterns in kmh during AM peak between 530and 800 AMe figure demonstrates that the South EasternFreeway is the most congested freeway with a speed lowerthan 20 kmh followed by the Pacific Motorway and Tulla-marine Freeway As for Figure 5 the flow patterns are il-lustrated in vehh for the period from 9 AM to 12 PM efigure shows that each freeway behaves differently during thesame period of time as the flow ranges between 7 and 56vehicles per hour for the three freeways In summary the real-life datasets used in this study are considered to be one of themost diverse and representative field traffic datasets availableparticularly in the Australian context ey are also unique inthat they have been meticulously screened cleaned pre-processed and validated in a large number of studies [15]

32 Modelling Framework Unidirectional LSTM has re-ceived considerable attention in recent years for its superiorperformance compared to the state-of-the-art recurrentneural networks (RNNs) Even though RNNs provide goodaccuracy they have been found to underperform for long-term memory as RNNs are unable to use information fromdistant past Also LSTM can learn patterns with long

Gold coast hishwayHelansvla interchange

To brisbane

Pacific highway to gold coast

485m 490m 515m

S0 S1 S2 S3

Figure 1 Schematic of the Pacific Motorway section used for collecting dataset 1 [40]

S0

S1

S3

S4

S5

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S8

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S11S12S13

S14

MT alexander RD

Ormond RD

Dean ST

Wilson

Albion ST

Moreland RD

Reynard ST

Bell ST

Pascoe vale RD

Napier ST

Bulla RD

Brunswick RD

Victoria ST

Dawson ST

S2Mebourne city

Tullamarine airport

Figure 2 Schematic diagram of the Tullamarine Freeway used forcollecting dataset 2 [41]


dependencies when compared with traditional RNNs thatare not able to function for long-term patterns ereforeLSTM has generally been found to outperform RNNs in timeseries data forecasting [43] e inclusion of additional datatraining has resulted in some model extensions of LSTMnow known as bidirectional LSTM (BiLSTM) is modeltrains the input time series data twice through forward andbackward directions e architectures of these models arepresented in Figures 6 and 7

In these models the following formulae are used tocalculate the predicted values

input gate It( 1113857 σg WiXt + Rihtminus1 + bi( 1113857

forget gate ft( 1113857 σg WfXt + Rfhtminus1 + bf1113872 1113873

cell candidate Ct( 1113857 σc WcXt + Rchtminus1 + bc( 1113857

output gate ot( 1113857 σg WoXt + Rohtminus1 + bo( 1113857

(1)

S1

E B

urnl

eyM

ary

stree

tE

Chu

rch

StCu

bbit

road

OB IB

453m

238m

620m

Gib

don

St O

P

457m

474m

E Y

arra

Blv

dE

Hey

ingt

on

533m

N Y

arra

Blv

d

313m

S0 Batm

an st

reet

785m

S8S9

N Y

arra

Blv

d 421m

S11

S12

St K

evin

s 550m

Gle

nfer

rie ro

ad

585m

603m

Kooy

ong

park

Toor

ak ro

ad

S10

S2S3

S4S5

S6S7

S8

IB

OB

Figure 3 Schematic of the South Eastern Freeway


where σg is the gate activation function andWi Wf Wc andWo are input weight matrices

Ri Rf Rc andRoare recurrent weight matrices Xt is theinput and htminus1 is the output at the previous time (tminus 1)bi bf bc and bo are bias vectors e forget gate determineshow much of the prior memory values should be removedfrom the cell state Similarly the input gate specifies new

input to the cell state en the cell state Ct and the outputHt of the LSTM at time t are calculated as follows

Ct ft⊙ ct⊙ 1 + it⊙gt

Ht ot⊙ σc(ct)(2)

where ⊙ denotes the Hadamard product (element-wisemultiplication of vectors)

In this work the unidirectional and bidirectional LSTMnetworks were implemented in MATLAB R2020b First thedata were arranged as two column values the first columncorresponds to speedflow at time t and the second columncorresponds to the expected output (t+ n) where n rangesfrom 5 minutes to 60 minutes into the future en the datawere partitioned into training and testing sets e modelswere trained on the first 60 of the sequence and tested onthe last 40 To prevent model overfitting the trainingtesting data were standardized to have zero mean and unitvariancee LSTMnetworks were created using four layerssequence input layer (number of features 1) Uni-LSTMBiLSTM layers (number of hidden units 300) fully con-nected layer (number of responses 1) and a regressionlayer e model hyperparameter settings are presented inTable 1 Multiple sets of hyperparameters were tested withthe aim to find the right combination of values which resultin the best accuracy Table 1 shows the parameters thatprovided the optimal results e tanh and sigmoid func-tions were used for state and gate activation functions

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Tullamarine freewayPacific motorwaySouth eastern freeway

Figure 4 Samples of speed data for the three freeways


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Figure 5 Samples of flow data for the three freeways

o (t)F (t)

c (t)

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+

o

o

o

Xt h (t ndash 1) Xt h (t ndash 1)

Xt Xth (t ndash 1) h (t ndash 1)

c (t ndash 1) c (t)

h (t)

σc

Figure 6 LSTM architecture


respectively e LSTM experiments were also implementedin MATLAB R2020b with the Deep Learning Toolboxfunctions of trainNetwork training options andpredictAndUpdateState

4 Comparative Evaluation of Uni-LSTMand BiLSTM

e first set of results in this paper was for speed and flowdata for the Tullamarine Freeway in Melbourne (Table 2)and the Pacific Motorway in Brisbane (Table 3) e datafrom both freeways were divided into 60 training data and40 testing data e mean absolute percentage error(MAPE) is used to calculate the accuracy of the modelprediction for different time horizons MAPE calculates theaverage absolute difference between the predicted outputfrom the model (Y1) and expected true output (Y)

MAPE() 1n

1113944

n

i1

|Y minus Y1|

Y⎛⎝ ⎞⎠ times 100

accuracy() (100 minus MAPE)

(3)

e speed prediction results showed that BiLSTM andUni-LSTM achieve high prediction results up to 60 minutes

into the future BiLSTM outperforms Uni-LSTM with ac-curacies above 926 up to 60 minutes for the TullamarineFreeway For a prediction horizon up to 60 minutes ac-curacy improvements over Uni-LSTM were 7 for 5minutes 6 for 10 minutes 7 for 15 minutes 13 for 30minutes and 15 and 16 for 45 and 60 minutes re-spectively For the Pacific Motorway BiLSTM outperformsUni-LSTM up to 15 minutes and then Uni-LSTM presentsbetter results up to 60 minutes however the two modelsproduce similar results for the 60-minute prediction horizon(eg 936 versus 927 as shown in Table 2

For the Pacific Motorway the results showed thatBiLSTM outperformed Uni-LSTM for up to 45 minuteswith an accuracy improvement of 14 for 5 minutes 14for 10 minutes 9 for 15 minutes 8 for 30 minutesand 2 for 45 minutes For 60-minute prediction ho-rizons the percentage differences in accuracies betweenUni-LSTM and BiLSTM were found to be minimal(001) as reported in Table 3 In Tables 2 and 3 the cellshighlighted in green denote best-performing models andcells highlighted in yellow denote second best-per-forming models

5 Deep and Mixed Unidirectional andBidirectional LSTM

In this section the results for multiple Uni-LSTM andBiLSTM layers to improve the results for both speed andflow are presented Also results for combining bothLSTM and BiLSTM layers are presented for the 15-minute horizon for the Tullamarine Freeway and PacificMotorway To our knowledge limited publications havetested deep architectures of BiLSTM and mixed modelsto measure the backward dependency of traffic speed andflow prediction

e results provided in Tables 4 and 5 show that deepBiLSTM with combined layers outperforms Uni-LSTM and

Input Input

Output Output

Hidden layer

Hidden layerForward

Forward

Backward

Uni-LSTM BiLSTM

Figure 7 Uni-LSTMBiLSTM architecture

Table 1 Model hyperparameters for Uni-LSTM and BiLSTMGradient decay factor 09Initial learning rate 0005Minimum batch size 128Maximum epochs 300

Training optimizer Adaptive moment estimationoptimizer

Dropping learning rate duringtraining Piecewise

Learning rate drop period 125Factor for learning ratedropping 02


deep Uni-LSTM models for 15-minute prediction horizonson both freeways For speed 3-BiLSTM layers and 4-BiLSTM layers provide the best accuracy of 98 on theTullamarine Freeway while LSTM layers provide the lowestaccuracy of around 94 e 4-layered BiLSTM modeloutperformed other models with 925 accuracy for 15-minute prediction horizons on the Tullamarine FreewaySimilarly Pacific Motorway experiments show that the 4-layer BiLSTM model outperformed other models with anaccuracy of 9999 as shown in Tables 4 and 5

Figures 8 and 9 present the speed and flow results for the15-minute prediction horizon using the best-performing4-layered BiLSTM model ese figures compare the targetor expected values (blue trendline) with the predicted valuesfrom the model (orange trendline) Figure 8 shows thesuperior performance of the model for predicting both speedand flow with accuracies of 98 and 9250 for 15-minuteprediction horizons on the Tullamarine Freeway Similarly

Figure 9 shows a remarkable prediction performance for the4-layered BiLSTM model on the Pacific Motorway with aprediction accuracy of 9999 for both speed and flow for15-minute prediction horizons

6 Deep BiLSTM Model Validationand Transferability

is section of the paper presents results for model vali-dation and potential for transferability to other freewayswithout the need for recalibration and retraining If this canbe achieved even at the expense of a depreciated accuracy itcan provide road operators and transport agencies withconfidence that they can apply existing models on differentfreeways even if they have not embarked on comprehensivehistorical data collection efforts is also helps them withreducing the cost of deployment of these algorithms by

Table 2 Speed performance for different prediction horizons for the Tullamarine Freeway


avoiding the need to preprocess new data and calibrate andvalidate newmodels which is a time-consuming undertakingthat requires substantial resources and experienced and well-trained AI staff and specialists

e model validation experimental design is shown inFigure 10 e learning obtained from the previous com-parative evaluations was used to develop robust speed andflow prediction models using data combined from the two

Table 3 Flow performance for different prediction horizons for the Tullamarine Freeway


largest datasets (Tullamarine and South Eastern Freeways inMelbourne) e data used in model development included24270 observations and were divided into two sets trainingset comprising 60 of the data (14562 observations) andtesting set comprising 40 of the data (9708 observations)e validation dataset included 1667 observations from thethird freeway (Pacific Motorway in Brisbane) e modeldevelopment results are provided in the first set of columnsin Table 6 (Tullamarine and South Eastern Freeways) Forspeed the model accuracy ranged from 997 for 5-minuteforecasting horizons to 918 for 60-minute forecastinghorizons For flow the model accuracy ranged from 996for 5-minute forecasting horizons to 712 for 60-minuteforecasting horizons emodel was then validated (withoutretraining) on the third independent dataset from the PacificMotorway in Brisbane

e validation results are shown in the right side col-umns of Table 6 For speed the modelrsquos accuracy rangedfrom 997 for 5-minute forecasting horizons to 902 for60-minute forecasting horizons For traffic flow the modelrsquosaccuracy ranged from 972 for 5-minute forecasting ho-rizons to 821 for 30-minute forecasting horizons eperformance degrades to 7919 for 45-minute and 7345for 60-minute prediction horizons as shown in Table 6ese findings are also depicted in Figures 11ndash16

In Figures 11ndash16 the blue trendline represents thetargeted real data compared to the orange trendline whichrepresents the results generated from the model In Fig-ure 13 the difference between targeted and predicted resultsfor both speed and flow is minimal as theMAPE percentagesbetween the two are 027 and 283 respectively InFigure 14 the speed results for 10-minute prediction

Table 4 Speed and flow performance for different prediction horizons for the Tullamarine Freeway

Table 5 Speed and flow performance for different prediction horizons for the Pacific Motorway


horizons also demonstrate a low MAPE percentage error of302 compared to 926 for flow As expected it can benoted that the error increases as the prediction horizonincreases In Figure 15 theMAPE percentage error increasesminimally for 15-minute prediction horizons for speed(463 increase) compared to a high increase in error forflow (1749) e same behaviour is observed for 30-

minute prediction horizons as the errors for speed and flowincrease to 628 and 1791 as shown in Figure 16 eseresults suggest that the model is able to accurately validatespeed to multiple prediction horizons e flow predictionresults also showed good accuracies higher than 80 for 510 15 and 30 minutes into the future using the 4-layeredBiLSTM model

TargetPrediction (4 BiLSTM)

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Figure 8 Tullamarine Freeway speed and flow prediction results for 15-minute horizons using the 4-BiLSTM model


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339

365

391

417

443

469

495

521

547

573

599

625

651

Flow

(veh

h)

Time (minutes)

(b)

Figure 9 Pacific Motorway speed and flow prediction results for 15-minute horizons using the 4-BiLSTM model


Report speed and flow accuracy () for multiple prediction horizons up to 60minutes into the future

Validate the model using pacific motorway data without retraining

Save the model

Predict future speed and flow using the 4-layer BiLSTM model

Training (60) and testing (40) of data collected from tullamarine andsouth eastern freeway

Figure 10 Validation experiment design

Table 6 Speed and flow validation results for different prediction horizons

Prediction horizonsTullamarine Freeway + South Eastern Freeway Validation on the Pacific MotorwaySpeed (kmh) Flow (vehh) Speed (kmh) Flow (vehh)

MAPE () Accuracy () MAPE () Accuracy () MAPE () Accuracy () MAPE () Accuracy ()5mins 030 9970 038 9962 027 9973 283 971710mins 261 9739 415 9585 302 9698 926 907415mins 306 9694 682 9318 463 9537 1749 825130mins 814 9186 1126 8874 628 9372 1791 820945mins 774 9226 1901 8099 784 9216 2081 791960mins 817 9183 2877 7123 983 9017 2655 7345

0

20

40

60

80

100

120

1 74 147

220

293

366

439

512

585

658

731

804

877

950

1023

1096

1169

1242

1315

1388

1461

1534

1607

Spee

d (k

mh

)

Time (minutes)

Validation targetValidation prediction

(a)


0

10

20

30

40

50

60

70

80

90

1 77 153

229

305

381

457

533

609

685

761

837

913

989

1065

1141

1217

1293

1369

1445

1521

1597

Flow

(veh

h)

Time (minutes)

(b)

Figure 11 Speed and flow validation results for 5 minutes



0

20

40

60

80

100

120

1 61 121

181

241

301

361

421

481

541

601

661

721

781

841

901

961

1021

1081

1141

1201

1261

1321

1381

1441

1501

1561

1621

Spee

d (k

mh

)

Time (minutes)

(a)


0

10

20

30

40

50

60

70

80

90

1 63 125

187

249

311

373

435

497

559

621

683

745

807

869

931

993

1055

1117

1179

1241

1303

1365

1427

1489

1551

1613

Flow

(veh

h)

Time (minutes)

(b)



0

20

40

60

80

100

120

1 73 145

217

289

361

433

505

577

649

721

793

865

937

1009

1081

1153

1225

1297

1369

1441

1513

1585

Spee

d (k

mh

)

Time (minutes)

(a)


0102030405060708090

1 70 139

208

277

346

415

484

553

622

691

760

829

898

967

1036

1105

1174

1243

1312

1381

1450

1519

1588

Flow

(veh

h)

Time(Minutes)

(b)



0

20

40

60

80

100

120

1 73 145

217

289

361

433

505

577

649

721

793

865

937

1009

1081

1153

1225

1297

1369

1441

1513

1585

Spee

d (k

mh

)

Time (minutes)

(a)


10

20

30

40

50

60

70

80

1 70 139

208

277

346

415

484

553

622

691

760

829

898

967

1036

1105

1174

1243

1312

1381

1450

1519

1588

Flow

(veh

h)

Time (minutes)

(b)



7 Conclusions Contributions and FutureResearch Directions

In this paper unidirectional and bidirectional LSTM net-works were developed to predict speed and flow on freewaysfor forecasting horizons up to 60 minutes into the futuree models were evaluated based on historical field datacollected from inductive loop sensors on a number offreeways in Australia A comprehensive and rigorous pro-cedure was adopted to evaluate the suitability of differentarchitectures and modelling parameters e results showeda superior performance for the bidirectional compared tounidirectional LSTM e results also demonstrated thechallenges of predicting traffic flow compared to speediswas a result of the noisy nature of flow measurementscompared to speed observations For the TullamarineFreeway the BiLSTM model was able to achieve speedpredictions up to 60 minutes into the future with an ac-curacy above 90 For the flow prediction the accuracy wasabove 80 up to 45min forecasting horizons outperformingthe Uni-LSTM model For the Pacific Motorway BiLSTMalso outperformed Uni-LSTMwith accuracies above 88 forspeed and above 80 for flow up to 60-minute predictionhorizons

is study also extended the models and evaluated theirperformance when adding multiple Uni-LSTM and BiLSTMlayers or mixing both LSTM and BiLSTM as one model for

15-minute prediction horizons e experiments showedthat the 4-layered BiLSTM outperformed other models forboth speed and flow on Tullamarine and Pacific Motorwaydatasets Another contribution of this work was to examinemodel validation and its potential for transferability eevaluation was undertaken on a combined dataset from theTullamarine and South Eastern Freeways in Melbourneisapproach enabled us to train the models on a large datasetwith different patterns and variable traffic conditions in-cluding peak nonpeak weekday weekend and incidentdata Once optimized the model was validated by testingonly (without retraining) on an independent dataset from athird freeway e validation results showed speed predic-tion accuracies ranging from 997 for 5-minute forecastinghorizons to 902 for 60-minute forecasting horizons eflow validation prediction accuracies were lower and rangedbetween 74 and 97 While it is acknowledged that morecomprehensive testing is required on much larger numbersof freeways this contribution demonstrates the potential todevelop transferable models provided sufficient data areavailable to represent more diverse traffic conditions fromdifferent cities around the world

Future directions in this research include collection ofmore field data from other real-life freeways in differentcities both in Australia and overseas such as those reportedin [44] e use of microsimulation to generate edge casedata that are difficult to measure in the field is also

0

50

100

150

1 79 157

235

313

391

469

547

625

703

781

859

937

1015

1093

1171

1249

1327

1405

1483

1561

Spee

d (k

mh

)

Time (minutes)


(a)


020406080

100

1 70 139

208

277

346

415

484

553

622

691

760

829

898

967

1036

1105

1174

1243

1312

1381

1450

1519

1588

Flow

(veh

h)

Time (minutes)

(b)



0

50

100

150

1 78 155

232

309

386

463

540

617

694

771

848

925

1002

1079

1156

1233

1310

1387

1464

1541

Spee

d (k

mh

)

Time (minutes)

(a)


10

30

50

70

90

1 68 135

202

269

336

403

470

537

604

671

738

805

872

939

1006

1073

1140

1207

1274

1341

1408

1475

1542

Flow

(veh

h)

Time (minutes)

(b)



recommended [45 46] As was shown in this paper trainingthe models on different patterns and variable traffic con-ditions enabled us to develop robust models that can per-form well on an independent dataset With more data usedfor training and model development it is expected that theaccuracy will improve e AI field is also witnessing a fastpace of developments and breakthroughs providing futureopportunities to test new architectures to further improvethe model performance and accuracy

Data Availability

To ensure transparency and allow other researchers to auditand reproduce the results reported in this study the fielddata used in this work can be found at httpsbitly2Ka0RiS

Conflicts of Interest

e authors declare no conflicts of interest

Acknowledgments

e first author would like to acknowledge her PhDscholarship provided by the Iraqi Government and Swin-burne University of Technology in Melbourne Australia

References

[1] H Dia D Harney and A Boyle ldquoDynamics of driversrsquo routechoice decisions under advanced traveller information sys-temsrdquo Road amp Transport Research vol 10 no 4 p 3 2001

[2] R Abduljabbar and H DIA ldquoPredictive intelligence a neuralnetwork learning system for traffic condition prediction andmonitoring on freewaysrdquo Journal of the Eastern Asia Societyfor Transportation Studies vol 13 pp 1785ndash1800 2019

[3] R Abduljabbar and H Dia ldquoA deep learning approach forfreeway vehicle speed and flow predictionrdquo in Proceedings ofthe Australasian Transport Research Forum (ATRF) 41st2019 Canberra ACT Australia October 2019

[4] K omas H Dia and N Cottman ldquoJanuary Simulation ofarterial incident detection using neural networksrdquo in Pro-ceedings of the 8th World Congress on ITS Sydney AustraliaOctober 2001

[5] S Nigarnjanagool and H Dia ldquoEvaluation of a dynamic signaloptimisation control model using traffic simulationrdquo IATSSResearch vol 29 no 1 pp 22ndash30 2005

[6] K omas and H Dia ldquoComparative evaluation of freewayincident detection models using field datardquo IEE Proceedings-Intelligent Transport Systems vol 153 no 3 pp 230ndash2412006

[7] J Tang F Liu Y ZouW Zhang and YWang ldquoAn improvedfuzzy neural network for traffic speed prediction consideringperiodic characteristicrdquo IEEE Transactions on IntelligentTransportation Systems vol 18 no 9 pp 2340ndash2350 2017

[8] J Tang X Chen Z Hu F Zong C Han and L Li ldquoTrafficflow prediction based on combination of support vectormachine and data denoising schemesrdquo Physica A StatisticalMechanics and Its Applications vol 534 Article ID 1206422019

[9] H Dia G Rose and A Snell ldquoComparative performance offreeway automated incident detection algorithmsrdquo in Instituteof Transport and Logistics Studies Working Paper ITS-WP-96-

15e University of Sydney Sydney Australia 1996 httpsseslibraryusydeduauhandle212319426

[10] X Ma Z Tao Y Wang H Yu and Y Wang ldquoLong short-term memory neural network for traffic speed predictionusing remote microwave sensor datardquo Transportation Re-search Part C Emerging Technologies vol 54 pp 187ndash1972015

[11] Z Zhao W Chen X Wu P C Y Chen and J Liu ldquoLSTMnetwork a deep learning approach for short-term trafficforecastrdquo IET Intelligent Transport Systems vol 11 no 2pp 68ndash75 2017

[12] D Kang Y Lv and Y Y Chen ldquoShort-term traffic flowprediction with LSTM recurrent neural networkrdquo in Pro-ceedings of the 2017 IEEE 20th International Conference onIntelligent Transportation Systems (ITSC) pp 1ndash6 IEEEYokohama Japan October 2017

[13] H Zou Y Wu H Zhang and Y Zhan ldquoShort-term trafficflow prediction based on PCC-BiLSTMrdquo in Proceedings of the2020 International Conference on Computer Engineering andApplication (ICCEA) pp 489ndash493 IEEE Guangzhou ChinaMarch 2020

[14] J Wang F Hu and L Li ldquoDeep bi-directional long short-termmemory model for short-term traffic flow predictionrdquo inProceedings of the International Conference on Neural Infor-mation Processing pp 306ndash316 Springer Guangzhou ChinaNovember 2017

[15] T Sun C Yang K Han W Ma and F Zhang ldquoBidirectionalspatial-temporal network for traffic prediction with multi-source datardquo Transportation Research Record Journal of theTransportation Research Board vol 2674 no 8 pp 78ndash892020

[16] S Siami-Namini N Tavakoli and A S Namin ldquoe per-formance of LSTM and BiLSTM in forecasting time seriesrdquo inProceedings of the 2019 IEEE International Conference on BigData (Big Data) pp 3285ndash3292 IEEE Los Angeles CA USADecember 2019

[17] R Abduljabbar H Dia S Liyanage and S A BagloeeldquoApplications of artificial intelligence in transport an over-viewrdquo Sustainability vol 11 no 1 p 189 2019

[18] Y Duan Y Lv and F Y Wang ldquoTravel time prediction withLSTM neural networkrdquo in Proceedings of the 2016 IEEE 19thInternational Conference on Intelligent Transportation Systems(ITSC) pp 1053ndash1058 IEEE Rio de Janeiro Brazil No-vember 2016

[19] G Song M Shuai K Xie and X Ma ldquoAn on-road wirelesssensor network approach for urban traffic state monitoringrdquoin Proceedings of the 2008 11th International IEEE Conferenceon Intelligent Transportation Systems pp 1195ndash1200 IEEEBeijing China October 2008

[20] R Lund ldquoTime series analysis and its applications with Rexamplesrdquo Journal of the American Statistical Associationvol 102 no 479 p 1079 2007

[21] M G Karlaftis and E I Vlahogianni ldquoMemory propertiesand fractional integration in transportation time-seriesrdquoTransportation Research Part C Emerging Technologiesvol 17 no 4 pp 444ndash453 2009

[22] G Fusco C Colombaroni and N Isaenko ldquoShort-term speedpredictions exploiting big data on large urban road networksrdquoTransportation Research Part C Emerging Technologiesvol 73 pp 183ndash201 2016

[23] C Chen J Hu Q Meng and Y Zhang ldquoShort-time trafficflow prediction with ARIMA-GARCHmodelrdquo in Proceedingsof the 2011 IEEE Intelligent Vehicles Symposium (IV)pp 607ndash612 Baden-Baden Germany June 2011


[24] J Guo W Huang and B M Williams ldquoAdaptive Kalmanfilter approach for stochastic short-term traffic flow rateprediction and uncertainty quantificationrdquo TransportationResearch Part C Emerging Technologies vol 43 pp 50ndash642014

[25] M Lippi M Bertini and P Frasconi ldquoShort-term traffic flowforecasting an experimental comparison of time-seriesanalysis and supervised learningrdquo IEEE Transactions on In-telligent Transportation Systems vol 14 no 2 pp 871ndash8822013

[26] J Morton T A Wheeler and M J Kochenderfer ldquoAnalysisof recurrent neural networks for probabilistic modeling ofdriver behaviorrdquo IEEE Transactions on Intelligent Trans-portation Systems vol 18 no 5 pp 1289ndash1298 2016

[27] H Shao and B H Soong ldquoTraffic flow prediction with longshort-term memory networks (LSTMs)rdquo in Proceedings of the2016 IEEE Region 10 Conference (TENCON) pp 2986ndash2989IEEE Singapore November 2016

[28] Q Zhaowei L Haitao L Zhihui and Z Tao ldquoShort-termtraffic flow forecasting method with MB-LSTM hybrid net-workrdquo IEEE Transactions on Intelligent Transportation Sys-tems pp 1ndash11 2020

[29] Z Cui R Ke Z Pu and Y Wang ldquoDeep bidirectional andunidirectional LSTM recurrent neural network for network-wide traffic speed predictionrdquo 2018 httpsarxivorgabs180102143

[30] M Lu J Pang and J Li ldquoDeepBSTN a deep bidirectionnetwork model for urban traffic predictionrdquo in Proceedings ofthe 2019 5th International Conference on Big Data Computingand Communications (BIGCOM) pp 1ndash6 IEEE QingDaoChina August 2019

[31] K Yeon K Min J Shin M Sunwoo and M Han ldquoEgo-vehicle speed prediction using a long short-term memorybased recurrent neural networkrdquo International Journal ofAutomotive Technology vol 20 no 4 pp 713ndash722 2019

[32] Y Chen Y Chen and B Yu ldquoSpeed distribution prediction offreight vehicles on mountainous freeway using deep learningmethodsrdquo Journal of Advanced Transportation vol 2020Article ID 8953182 14 pages 2020

[33] W Wang H Zhang T Li et al ldquoAn interpretable model forshort term traffic flow predictionrdquo Mathematics and Com-puters in Simulation vol 171 pp 264ndash278 2020

[34] M Farahani M Farahani M Manthouri and O KaynakldquoShort-term traffic flow prediction using variational LSTMnetworksrdquo 2020 httpsarxivorgabs200207922

[35] J Zhou H Chang X Cheng and X Zhao ldquoA multiscale andhigh-precision LSTM-GASVR short-term traffic flow pre-diction modelrdquo Complexity vol 2020 Article ID 143408017 pages 2020

[36] P Poonia and V K Jain ldquoShort-term traffic flow predictionusing LSTMrdquo in Proceedings of the 2020 International Con-ference on Emerging Trends in Communication Control andComputing (ICONC3) pp 1ndash4 IEEE Sikar India February2020

[37] C Kang and Z Zhang ldquoApplication of LSTM in short-termtraffic flow predictionrdquo in Proceedings of the 2020 IEEE 5thInternational Conference on Intelligent Transportation Engi-neering (ICITE) pp 98ndash101 Beijing China September 2020

[38] S Lu Q Zhang G Chen and D Seng ldquoA combined methodfor short-term traffic flow prediction based on recurrentneural networkrdquo Alexandria Engineering Journal vol 60no 1 pp 87ndash84 2020

[39] R Li Y Hu and Q Liang ldquoT2F-LSTMmethod for long-termtraffic volume predictionrdquo IEEE Transactions on Fuzzy Sys-tems vol 28 no 12 2020

[40] H Dia ldquoAn object-oriented neural network approach toshort-term traffic forecastingrdquo European Journal of Opera-tional Research vol 131 no 2 pp 253ndash261 2001

[41] H Dia and G Rose ldquoDevelopment and evaluation of neuralnetwork freeway incident detection models using field datardquoTransportation Research Part C Emerging Technologies vol 5no 5 pp 313ndash331 1997

[42] D T Larose and C D LaroseDiscovering Knowledge in Dataan Introduction to Data Mining Vol 4 John Wiley amp SonsHoboken NJ USA 2014


[44] C Sutandi and H Dia ldquoPerformance evaluation of an ad-vanced traffic control system in a developing countryrdquo inProceedings of the 6th EASTS Conference vol 5 pp 1572ndash1584 Bangkok ailand September 2005

[45] S Panwai and H Dia ldquoDevelopment and evaluation of areactive agent-based car following modelrdquo in Proceedings ofthe Intelligent Vehicles and Road Infrastructure Conference(IVRI rsquo05) Melbourne Australia February 2005

[46] K omas H Dia and N Cottman ldquoSimulation of arterialincident detection using neural networksrdquo in Proceedings ofthe 8th World Congress on Intelligent Transport SystemsSydney Australia 2001


(1) Will results be improved if speed and flow data aretrained from both directions (forward direction andbackward direction)

(2) How adding layers or mixing both LSTM andBiLSTM as one model affects the modelperformance

(3) If the model is trained and tested for one freewaywill it achieve a good accuracy if validated only(without retraining) on an independent dataset froma different freeway

is paper aims to address these questions and dem-onstrate the feasibility of using advanced AI techniquesbased on deep learning Uni-LSTM and BiLSTM models topredict speed and flow for multiple prediction horizons Itprovides a comparative performance analysis of both Uni-LSTM and BiLSTM based on a common dataset of fieldmeasurements e models are developed using historicaldata extracted from sensors embedded in pavements onthree freeways in Australia the Pacific Motorway betweenBrisbane and the Gold Coast in Queensland TullamarineFreeway in Melbourne and South Eastern Freeway inMelbourne is paper also investigates whether additionallayers of training improve prediction accuracies for bothspeed and flow To our knowledge there have been limitedpapers targeting the BiLSTM model for future traffic pre-diction and this paper shows the robust performance of thisextension of the Uni-LSTMmodel Also this paper validatesthe performance of a developed model on different freewayswhich makes this work a valuable contribution to knowledgein the intelligent transport systems and network operationsfields is provides road operators and transport agencieswith confidence that they can apply these models on dif-ferent freeways even if they have not embarked on com-prehensive historical data collection efforts for the targetfreeways is also helps them with reducing the cost ofdeployment of these algorithms by avoiding the need topreprocess new data and calibrate and validate new modelswhich is a time-consuming undertaking that requires sub-stantial resources and experienced and well-trained AI staffand specialists

is paper is organized as follows Section 2 provides ascan of previous research work Section 3 presents themethodology including data collection and modellingframeworks Section 4 presents the results of the compar-ative evaluation of different models Section 5 presents theperformance of stacked and mixed Uni-LSTM and BiLSTMmodels Section 6 shows the model validation results andfinally Section 7 presents the conclusions and future re-search directions

2 Literature Review

e prediction and forecasting of short-term (1 to 60minutes into the future) traffic conditions plays an im-portant role in the success of intelligent transport systems(ITSs) such as travel information systems adaptive trafficmanagement systems public transportation scheduling andcommercial vehicle operations [17ndash19] Due to the wide

body of literature on this topic we focus the literature scan inthis section on traffic prediction using LSTM models whichused field traffic data collected from inductive loop detectorsCCTV probe vehicles and incident reports A compre-hensive review of other models including those that usedsimulated data can be found in [17] Increasingly roadoperators have more confidence in models that have beendeveloped using real-life data and hence our focus in thiswork on model development and evaluations using datafrom real-world environments

Methodologies used for flow and speed prediction can beclassified into two broad parametric and nonparametricapproaches [20] Examples of commonly used parametricmethods include linear models such as autoregressive in-tegrated moving average model (ARIMA) [21] seasonalARIMA ie SARIMA model [22] exponential smoothingmodel [23] and ARIMA with Kalman filter (KF) [24 25]ese parametric methods perform poorly with dynamictraffic patterns which limits their application in complextraffic prediction compared to nonparametric methodsNonparametric methods are more capable of predicting astochastic pattern of input traffic data and are better athandling noisy data

With the recent advancements in machine learningmany models have shown a promising potential in solvingnonlinear problems and handling long-term dependenciesExamples include LSTM and BiLSTMmodels ese modelswere previously used to forecast future traffic speeds [10]travel times [18] and traffic flows [11] In one study the longshort-termmemory (LSTM) structure was applied for futurespeed prediction and showed that it provides higher per-formance compared to classical methods [10] Another studyshowed that using LSTM models is promising for irregulartravel time prediction models as the error for 1-step-aheadprediction error is relatively small [18] Other studies haveshown that flow prediction using LSTM achieved high ac-curacy compared to other models for different predictionhorizons [11] Also LSTM models have been developed inother studies on car-followingmodels to predict accelerationand deceleration on different road hierarchies [26]

Short-term traffic flow using LSTM has also been in-vestigated where the dependency relationships of time seriesdata were fully considered and experimental results showeda very good performance with an error of 54 whencompared with other models [27] In other studies an end-to-end deep learning model has been investigated to predictfuture traffic flows [28] where one BiLSTM layer was addedand the results showed that the model was capable of solvingstochastic flow characteristics and overcoming overfittingproblems [28] Similarly stacking BiLSTM and Uni-LSTMmodels were developed in another study to predict network-wide traffic speeds e results showed that the stackedarchitecture outperforms both BiLSTM and Uni-LSTMmodels [29]

In another study different models were developed thatshowed superior performance when using deeper BiLSTMlayers for urban traffic prediction [30] Other researchershave also used LSTM and RNN approaches for speed pre-diction models under various urban driving conditions with






3 Study Methodology












To brisbane


485m 490m 515m

S0 S1 S2 S3


S0

S1

S3

S4

S5

S6

S7

S8

S9

S10

S11S12S13

S14

MT alexander RD

Ormond RD

Dean ST

Wilson

Albion ST

Moreland RD

Reynard ST

Bell ST

Pascoe vale RD

Napier ST

Bulla RD

Brunswick RD

Victoria ST

Dawson ST

S2Mebourne city

Tullamarine airport









(1)

S1

E B

urnl

eyM

ary

stree

tE

Chu

rch

StCu

bbit

road

OB IB

453m

238m

620m

Gib

don

St O

P

457m

474m

E Y

arra

Blv

dE

Hey

ingt

on

533m

N Y

arra

Blv

d

313m

S0 Batm

an st

reet

785m

S8S9

N Y

arra

Blv

d 421m

S11

S12

St K

evin

s 550m

Gle

nfer

rie ro

ad

585m

603m

Kooy

ong

park

Toor

ak ro

ad

S10

S2S3

S4S5

S6S7

S8

IB

OB







Ht ot⊙ σc(ct)(2)



0

20

40

60

80

100

120

530

00

533

00

536

00

539

00

542

00

545

00

548

00

551

00

554

00

557

00

600

00

603

00

606

00

609

00

612

00

615

00

618

00

621

00

624

00

627

00

630

00

633

00

636

00

639

00

642

00

645

00

648

00

651

00

654

00

657

00

700

00

703

00

706

00

709

00

712

00

715

00

718

00

721

00

724

00

727

00

730

00

733

00

736

00

739

00

742

00

745

00

748

00

751

00

754

00

757

00

Spee

d (k

mh

)

Period




0

10

20

30

40

50

60

900

00

903

00

906

00

909

00

912

00

915

00

918

00

921

00

924

00

927

00

930

00

933

00

936

00

939

00

942

00

945

00

948

00

951

00

954

00

957

00

100

000

100

300

100

600

100

900

101

200

101

500

101

800

102

100

102

400

102

700

103

000

103

300

103

600

103

900

104

200

104

500

104

800

105

100

105

400

105

700

110

000

110

300

110

600

110

900

111

200

111

500

111

800

112

100

112

400

112

700

Flow

(veh

h)

Period


o (t)F (t)

c (t)

I (t)C (t)

+

o

o

o



c (t ndash 1) c (t)

h (t)

σc






MAPE() 1n

1113944

n

i1

|Y minus Y1|

Y⎛⎝ ⎞⎠ times 100


(3)







Input Input

Output Output

Hidden layer

Hidden layerForward

Forward

Backward

Uni-LSTM BiLSTM



























0

20

40

60

80

100

120

140

131

462

794

012

5315

6618

7921

9225

0528

1831

3134

4437

5740

7043

8346

9650

0953

2256

3559

4862

6165

7468

8772

0075

1378

2681

39

Spee

d (k

mh

)

Time (minutes)

(a)

0

5

10

15

20

25

30

35

40

45

50

137

374

511

1714

8918

6122

3326

0529

7733

4937

2140

9344

6548

3752

0955

8159

5363

2566

9770

6974

4178

1381

8585

5789

29

Flow

(veh

h)

Time (minutes)


(b)



0

20

40

60

80

100

120

1 26 51 76 101

126

151

176

201

226

251

276

301

326

351

376

401

426

451

476

501

526

551

576

601

626

651

Spee

d (k

mh

)

Time (minutes)

(a)


0

10

20

30

40

50

60

70

80

90

1 27 53 79 105

131

157

183

209

235

261

287

313

339

365

391

417

443

469

495

521

547

573

599

625

651

Flow

(veh

h)

Time (minutes)

(b)





Save the model







0

20

40

60

80

100

120

1 74 147

220

293

366

439

512

585

658

731

804

877

950

1023

1096

1169

1242

1315

1388

1461

1534

1607

Spee

d (k

mh

)

Time (minutes)


(a)


0

10

20

30

40

50

60

70

80

90

1 77 153

229

305

381

457

533

609

685

761

837

913

989

1065

1141

1217

1293

1369

1445

1521

1597

Flow

(veh

h)

Time (minutes)

(b)




0

20

40

60

80

100

120

1 61 121

181

241

301

361

421

481

541

601

661

721

781

841

901

961

1021

1081

1141

1201

1261

1321

1381

1441

1501

1561

1621

Spee

d (k

mh

)

Time (minutes)

(a)


0

10

20

30

40

50

60

70

80

90

1 63 125

187

249

311

373

435

497

559

621

683

745

807

869

931

993

1055

1117

1179

1241

1303

1365

1427

1489

1551

1613

Flow

(veh

h)

Time (minutes)

(b)



0

20

40

60

80

100

120

1 73 145

217

289

361

433

505

577

649

721

793

865

937

1009

1081

1153

1225

1297

1369

1441

1513

1585

Spee

d (k

mh

)

Time (minutes)

(a)


0102030405060708090

1 70 139

208

277

346

415

484

553

622

691

760

829

898

967

1036

1105

1174

1243

1312

1381

1450

1519

1588

Flow

(veh

h)

Time(Minutes)

(b)



0

20

40

60

80

100

120

1 73 145

217

289

361

433

505

577

649

721

793

865

937

1009

1081

1153

1225

1297

1369

1441

1513

1585

Spee

d (k

mh

)

Time (minutes)

(a)


10

20

30

40

50

60

70

80

1 70 139

208

277

346

415

484

553

622

691

760

829

898

967

1036

1105

1174

1243

1312

1381

1450

1519

1588

Flow

(veh

h)

Time (minutes)

(b)








0

50

100

150

1 79 157

235

313

391

469

547

625

703

781

859

937

1015

1093

1171

1249

1327

1405

1483

1561

Spee

d (k

mh

)

Time (minutes)


(a)


020406080

100

1 70 139

208

277

346

415

484

553

622

691

760

829

898

967

1036

1105

1174

1243

1312

1381

1450

1519

1588

Flow

(veh

h)

Time (minutes)

(b)



0

50

100

150

1 78 155

232

309

386

463

540

617

694

771

848

925

1002

1079

1156

1233

1310

1387

1464

1541

Spee

d (k

mh

)

Time (minutes)

(a)


10

30

50

70

90

1 68 135

202

269

336

403

470

537

604

671

738

805

872

939

1006

1073

1140

1207

1274

1341

1408

1475

1542

Flow

(veh

h)

Time (minutes)

(b)




Data Availability




Acknowledgments


References






















































3 Study Methodology












To brisbane


485m 490m 515m

S0 S1 S2 S3


S0

S1

S3

S4

S5

S6

S7

S8

S9

S10

S11S12S13

S14

MT alexander RD

Ormond RD

Dean ST

Wilson

Albion ST

Moreland RD

Reynard ST

Bell ST

Pascoe vale RD

Napier ST

Bulla RD

Brunswick RD

Victoria ST

Dawson ST

S2Mebourne city

Tullamarine airport









(1)

S1

E B

urnl

eyM

ary

stree

tE

Chu

rch

StCu

bbit

road

OB IB

453m

238m

620m

Gib

don

St O

P

457m

474m

E Y

arra

Blv

dE

Hey

ingt

on

533m

N Y

arra

Blv

d

313m

S0 Batm

an st

reet

785m

S8S9

N Y

arra

Blv

d 421m

S11

S12

St K

evin

s 550m

Gle

nfer

rie ro

ad

585m

603m

Kooy

ong

park

Toor

ak ro

ad

S10

S2S3

S4S5

S6S7

S8

IB

OB







Ht ot⊙ σc(ct)(2)



0

20

40

60

80

100

120

530

00

533

00

536

00

539

00

542

00

545

00

548

00

551

00

554

00

557

00

600

00

603

00

606

00

609

00

612

00

615

00

618

00

621

00

624

00

627

00

630

00

633

00

636

00

639

00

642

00

645

00

648

00

651

00

654

00

657

00

700

00

703

00

706

00

709

00

712

00

715

00

718

00

721

00

724

00

727

00

730

00

733

00

736

00

739

00

742

00

745

00

748

00

751

00

754

00

757

00

Spee

d (k

mh

)

Period




0

10

20

30

40

50

60

900

00

903

00

906

00

909

00

912

00

915

00

918

00

921

00

924

00

927

00

930

00

933

00

936

00

939

00

942

00

945

00

948

00

951

00

954

00

957

00

100

000

100

300

100

600

100

900

101

200

101

500

101

800

102

100

102

400

102

700

103

000

103

300

103

600

103

900

104

200

104

500

104

800

105

100

105

400

105

700

110

000

110

300

110

600

110

900

111

200

111

500

111

800

112

100

112

400

112

700

Flow

(veh

h)

Period


o (t)F (t)

c (t)

I (t)C (t)

+

o

o

o



c (t ndash 1) c (t)

h (t)

σc






MAPE() 1n

1113944

n

i1

|Y minus Y1|

Y⎛⎝ ⎞⎠ times 100


(3)







Input Input

Output Output

Hidden layer

Hidden layerForward

Forward

Backward

Uni-LSTM BiLSTM



























0

20

40

60

80

100

120

140

131

462

794

012

5315

6618

7921

9225

0528

1831

3134

4437

5740

7043

8346

9650

0953

2256

3559

4862

6165

7468

8772

0075

1378

2681

39

Spee

d (k

mh

)

Time (minutes)

(a)

0

5

10

15

20

25

30

35

40

45

50

137

374

511

1714

8918

6122

3326

0529

7733

4937

2140

9344

6548

3752

0955

8159

5363

2566

9770

6974

4178

1381

8585

5789

29

Flow

(veh

h)

Time (minutes)


(b)



0

20

40

60

80

100

120

1 26 51 76 101

126

151

176

201

226

251

276

301

326

351

376

401

426

451

476

501

526

551

576

601

626

651

Spee

d (k

mh

)

Time (minutes)

(a)


0

10

20

30

40

50

60

70

80

90

1 27 53 79 105

131

157

183

209

235

261

287

313

339

365

391

417

443

469

495

521

547

573

599

625

651

Flow

(veh

h)

Time (minutes)

(b)





Save the model







0

20

40

60

80

100

120

1 74 147

220

293

366

439

512

585

658

731

804

877

950

1023

1096

1169

1242

1315

1388

1461

1534

1607

Spee

d (k

mh

)

Time (minutes)


(a)


0

10

20

30

40

50

60

70

80

90

1 77 153

229

305

381

457

533

609

685

761

837

913

989

1065

1141

1217

1293

1369

1445

1521

1597

Flow

(veh

h)

Time (minutes)

(b)




0

20

40

60

80

100

120

1 61 121

181

241

301

361

421

481

541

601

661

721

781

841

901

961

1021

1081

1141

1201

1261

1321

1381

1441

1501

1561

1621

Spee

d (k

mh

)

Time (minutes)

(a)


0

10

20

30

40

50

60

70

80

90

1 63 125

187

249

311

373

435

497

559

621

683

745

807

869

931

993

1055

1117

1179

1241

1303

1365

1427

1489

1551

1613

Flow

(veh

h)

Time (minutes)

(b)



0

20

40

60

80

100

120

1 73 145

217

289

361

433

505

577

649

721

793

865

937

1009

1081

1153

1225

1297

1369

1441

1513

1585

Spee

d (k

mh

)

Time (minutes)

(a)


0102030405060708090

1 70 139

208

277

346

415

484

553

622

691

760

829

898

967

1036

1105

1174

1243

1312

1381

1450

1519

1588

Flow

(veh

h)

Time(Minutes)

(b)



0

20

40

60

80

100

120

1 73 145

217

289

361

433

505

577

649

721

793

865

937

1009

1081

1153

1225

1297

1369

1441

1513

1585

Spee

d (k

mh

)

Time (minutes)

(a)


10

20

30

40

50

60

70

80

1 70 139

208

277

346

415

484

553

622

691

760

829

898

967

1036

1105

1174

1243

1312

1381

1450

1519

1588

Flow

(veh

h)

Time (minutes)

(b)








0

50

100

150

1 79 157

235

313

391

469

547

625

703

781

859

937

1015

1093

1171

1249

1327

1405

1483

1561

Spee

d (k

mh

)

Time (minutes)


(a)


020406080

100

1 70 139

208

277

346

415

484

553

622

691

760

829

898

967

1036

1105

1174

1243

1312

1381

1450

1519

1588

Flow

(veh

h)

Time (minutes)

(b)



0

50

100

150

1 78 155

232

309

386

463

540

617

694

771

848

925

1002

1079

1156

1233

1310

1387

1464

1541

Spee

d (k

mh

)

Time (minutes)

(a)


10

30

50

70

90

1 68 135

202

269

336

403

470

537

604

671

738

805

872

939

1006

1073

1140

1207

1274

1341

1408

1475

1542

Flow

(veh

h)

Time (minutes)

(b)




Data Availability




Acknowledgments


References
























































To brisbane


485m 490m 515m

S0 S1 S2 S3


S0

S1

S3

S4

S5

S6

S7

S8

S9

S10

S11S12S13

S14

MT alexander RD

Ormond RD

Dean ST

Wilson

Albion ST

Moreland RD

Reynard ST

Bell ST

Pascoe vale RD

Napier ST

Bulla RD

Brunswick RD

Victoria ST

Dawson ST

S2Mebourne city

Tullamarine airport









(1)

S1

E B

urnl

eyM

ary

stree

tE

Chu

rch

StCu

bbit

road

OB IB

453m

238m

620m

Gib

don

St O

P

457m

474m

E Y

arra

Blv

dE

Hey

ingt

on

533m

N Y

arra

Blv

d

313m

S0 Batm

an st

reet

785m

S8S9

N Y

arra

Blv

d 421m

S11

S12

St K

evin

s 550m

Gle

nfer

rie ro

ad

585m

603m

Kooy

ong

park

Toor

ak ro

ad

S10

S2S3

S4S5

S6S7

S8

IB

OB







Ht ot⊙ σc(ct)(2)



0

20

40

60

80

100

120

530

00

533

00

536

00

539

00

542

00

545

00

548

00

551

00

554

00

557

00

600

00

603

00

606

00

609

00

612

00

615

00

618

00

621

00

624

00

627

00

630

00

633

00

636

00

639

00

642

00

645

00

648

00

651

00

654

00

657

00

700

00

703

00

706

00

709

00

712

00

715

00

718

00

721

00

724

00

727

00

730

00

733

00

736

00

739

00

742

00

745

00

748

00

751

00

754

00

757

00

Spee

d (k

mh

)

Period




0

10

20

30

40

50

60

900

00

903

00

906

00

909

00

912

00

915

00

918

00

921

00

924

00

927

00

930

00

933

00

936

00

939

00

942

00

945

00

948

00

951

00

954

00

957

00

100

000

100

300

100

600

100

900

101

200

101

500

101

800

102

100

102

400

102

700

103

000

103

300

103

600

103

900

104

200

104

500

104

800

105

100

105

400

105

700

110

000

110

300

110

600

110

900

111

200

111

500

111

800

112

100

112

400

112

700

Flow

(veh

h)

Period


o (t)F (t)

c (t)

I (t)C (t)

+

o

o

o



c (t ndash 1) c (t)

h (t)

σc






MAPE() 1n

1113944

n

i1

|Y minus Y1|

Y⎛⎝ ⎞⎠ times 100


(3)







Input Input

Output Output

Hidden layer

Hidden layerForward

Forward

Backward

Uni-LSTM BiLSTM



























0

20

40

60

80

100

120

140

131

462

794

012

5315

6618

7921

9225

0528

1831

3134

4437

5740

7043

8346

9650

0953

2256

3559

4862

6165

7468

8772

0075

1378

2681

39

Spee

d (k

mh

)

Time (minutes)

(a)

0

5

10

15

20

25

30

35

40

45

50

137

374

511

1714

8918

6122

3326

0529

7733

4937

2140

9344

6548

3752

0955

8159

5363

2566

9770

6974

4178

1381

8585

5789

29

Flow

(veh

h)

Time (minutes)


(b)



0

20

40

60

80

100

120

1 26 51 76 101

126

151

176

201

226

251

276

301

326

351

376

401

426

451

476

501

526

551

576

601

626

651

Spee

d (k

mh

)

Time (minutes)

(a)


0

10

20

30

40

50

60

70

80

90

1 27 53 79 105

131

157

183

209

235

261

287

313

339

365

391

417

443

469

495

521

547

573

599

625

651

Flow

(veh

h)

Time (minutes)

(b)





Save the model







0

20

40

60

80

100

120

1 74 147

220

293

366

439

512

585

658

731

804

877

950

1023

1096

1169

1242

1315

1388

1461

1534

1607

Spee

d (k

mh

)

Time (minutes)


(a)


0

10

20

30

40

50

60

70

80

90

1 77 153

229

305

381

457

533

609

685

761

837

913

989

1065

1141

1217

1293

1369

1445

1521

1597

Flow

(veh

h)

Time (minutes)

(b)




0

20

40

60

80

100

120

1 61 121

181

241

301

361

421

481

541

601

661

721

781

841

901

961

1021

1081

1141

1201

1261

1321

1381

1441

1501

1561

1621

Spee

d (k

mh

)

Time (minutes)

(a)


0

10

20

30

40

50

60

70

80

90

1 63 125

187

249

311

373

435

497

559

621

683

745

807

869

931

993

1055

1117

1179

1241

1303

1365

1427

1489

1551

1613

Flow

(veh

h)

Time (minutes)

(b)



0

20

40

60

80

100

120

1 73 145

217

289

361

433

505

577

649

721

793

865

937

1009

1081

1153

1225

1297

1369

1441

1513

1585

Spee

d (k

mh

)

Time (minutes)

(a)


0102030405060708090

1 70 139

208

277

346

415

484

553

622

691

760

829

898

967

1036

1105

1174

1243

1312

1381

1450

1519

1588

Flow

(veh

h)

Time(Minutes)

(b)



0

20

40

60

80

100

120

1 73 145

217

289

361

433

505

577

649

721

793

865

937

1009

1081

1153

1225

1297

1369

1441

1513

1585

Spee

d (k

mh

)

Time (minutes)

(a)


10

20

30

40

50

60

70

80

1 70 139

208

277

346

415

484

553

622

691

760

829

898

967

1036

1105

1174

1243

1312

1381

1450

1519

1588

Flow

(veh

h)

Time (minutes)

(b)








0

50

100

150

1 79 157

235

313

391

469

547

625

703

781

859

937

1015

1093

1171

1249

1327

1405

1483

1561

Spee

d (k

mh

)

Time (minutes)


(a)


020406080

100

1 70 139

208

277

346

415

484

553

622

691

760

829

898

967

1036

1105

1174

1243

1312

1381

1450

1519

1588

Flow

(veh

h)

Time (minutes)

(b)



0

50

100

150

1 78 155

232

309

386

463

540

617

694

771

848

925

1002

1079

1156

1233

1310

1387

1464

1541

Spee

d (k

mh

)

Time (minutes)

(a)


10

30

50

70

90

1 68 135

202

269

336

403

470

537

604

671

738

805

872

939

1006

1073

1140

1207

1274

1341

1408

1475

1542

Flow

(veh

h)

Time (minutes)

(b)




Data Availability




Acknowledgments


References
























































(1)

S1

E B

urnl

eyM

ary

stree

tE

Chu

rch

StCu

bbit

road

OB IB

453m

238m

620m

Gib

don

St O

P

457m

474m

E Y

arra

Blv

dE

Hey

ingt

on

533m

N Y

arra

Blv

d

313m

S0 Batm

an st

reet

785m

S8S9

N Y

arra

Blv

d 421m

S11

S12

St K

evin

s 550m

Gle

nfer

rie ro

ad

585m

603m

Kooy

ong

park

Toor

ak ro

ad

S10

S2S3

S4S5

S6S7

S8

IB

OB







Ht ot⊙ σc(ct)(2)



0

20

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530

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533

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700

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703

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706

00

709

00

712

00

715

00

718

00

721

00

724

00

727

00

730

00

733

00

736

00

739

00

742

00

745

00

748

00

751

00

754

00

757

00

Spee

d (k

mh

)

Period




0

10

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00

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933

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110

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110

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111

200

111

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111

800

112

100

112

400

112

700

Flow

(veh

h)

Period


o (t)F (t)

c (t)

I (t)C (t)

+

o

o

o



c (t ndash 1) c (t)

h (t)

σc






MAPE() 1n

1113944

n

i1

|Y minus Y1|

Y⎛⎝ ⎞⎠ times 100


(3)







Input Input

Output Output

Hidden layer

Hidden layerForward

Forward

Backward

Uni-LSTM BiLSTM



























0

20

40

60

80

100

120

140

131

462

794

012

5315

6618

7921

9225

0528

1831

3134

4437

5740

7043

8346

9650

0953

2256

3559

4862

6165

7468

8772

0075

1378

2681

39

Spee

d (k

mh

)

Time (minutes)

(a)

0

5

10

15

20

25

30

35

40

45

50

137

374

511

1714

8918

6122

3326

0529

7733

4937

2140

9344

6548

3752

0955

8159

5363

2566

9770

6974

4178

1381

8585

5789

29

Flow

(veh

h)

Time (minutes)


(b)



0

20

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1 26 51 76 101

126

151

176

201

226

251

276

301

326

351

376

401

426

451

476

501

526

551

576

601

626

651

Spee

d (k

mh

)

Time (minutes)

(a)


0

10

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30

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60

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80

90

1 27 53 79 105

131

157

183

209

235

261

287

313

339

365

391

417

443

469

495

521

547

573

599

625

651

Flow

(veh

h)

Time (minutes)

(b)





Save the model







0

20

40

60

80

100

120

1 74 147

220

293

366

439

512

585

658

731

804

877

950

1023

1096

1169

1242

1315

1388

1461

1534

1607

Spee

d (k

mh

)

Time (minutes)


(a)


0

10

20

30

40

50

60

70

80

90

1 77 153

229

305

381

457

533

609

685

761

837

913

989

1065

1141

1217

1293

1369

1445

1521

1597

Flow

(veh

h)

Time (minutes)

(b)




0

20

40

60

80

100

120

1 61 121

181

241

301

361

421

481

541

601

661

721

781

841

901

961

1021

1081

1141

1201

1261

1321

1381

1441

1501

1561

1621

Spee

d (k

mh

)

Time (minutes)

(a)


0

10

20

30

40

50

60

70

80

90

1 63 125

187

249

311

373

435

497

559

621

683

745

807

869

931

993

1055

1117

1179

1241

1303

1365

1427

1489

1551

1613

Flow

(veh

h)

Time (minutes)

(b)



0

20

40

60

80

100

120

1 73 145

217

289

361

433

505

577

649

721

793

865

937

1009

1081

1153

1225

1297

1369

1441

1513

1585

Spee

d (k

mh

)

Time (minutes)

(a)


0102030405060708090

1 70 139

208

277

346

415

484

553

622

691

760

829

898

967

1036

1105

1174

1243

1312

1381

1450

1519

1588

Flow

(veh

h)

Time(Minutes)

(b)



0

20

40

60

80

100

120

1 73 145

217

289

361

433

505

577

649

721

793

865

937

1009

1081

1153

1225

1297

1369

1441

1513

1585

Spee

d (k

mh

)

Time (minutes)

(a)


10

20

30

40

50

60

70

80

1 70 139

208

277

346

415

484

553

622

691

760

829

898

967

1036

1105

1174

1243

1312

1381

1450

1519

1588

Flow

(veh

h)

Time (minutes)

(b)








0

50

100

150

1 79 157

235

313

391

469

547

625

703

781

859

937

1015

1093

1171

1249

1327

1405

1483

1561

Spee

d (k

mh

)

Time (minutes)


(a)


020406080

100

1 70 139

208

277

346

415

484

553

622

691

760

829

898

967

1036

1105

1174

1243

1312

1381

1450

1519

1588

Flow

(veh

h)

Time (minutes)

(b)



0

50

100

150

1 78 155

232

309

386

463

540

617

694

771

848

925

1002

1079

1156

1233

1310

1387

1464

1541

Spee

d (k

mh

)

Time (minutes)

(a)


10

30

50

70

90

1 68 135

202

269

336

403

470

537

604

671

738

805

872

939

1006

1073

1140

1207

1274

1341

1408

1475

1542

Flow

(veh

h)

Time (minutes)

(b)




Data Availability




Acknowledgments


References






















































Ht ot⊙ σc(ct)(2)



0

20

40

60

80

100

120

530

00

533

00

536

00

539

00

542

00

545

00

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00

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00

554

00

557

00

600

00

603

00

606

00

609

00

612

00

615

00

618

00

621

00

624

00

627

00

630

00

633

00

636

00

639

00

642

00

645

00

648

00

651

00

654

00

657

00

700

00

703

00

706

00

709

00

712

00

715

00

718

00

721

00

724

00

727

00

730

00

733

00

736

00

739

00

742

00

745

00

748

00

751

00

754

00

757

00

Spee

d (k

mh

)

Period




0

10

20

30

40

50

60

900

00

903

00

906

00

909

00

912

00

915

00

918

00

921

00

924

00

927

00

930

00

933

00

936

00

939

00

942

00

945

00

948

00

951

00

954

00

957

00

100

000

100

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100

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100

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101

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101

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100

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700

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500

104

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105

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105

700

110

000

110

300

110

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110

900

111

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111

500

111

800

112

100

112

400

112

700

Flow

(veh

h)

Period


o (t)F (t)

c (t)

I (t)C (t)

+

o

o

o



c (t ndash 1) c (t)

h (t)

σc






MAPE() 1n

1113944

n

i1

|Y minus Y1|

Y⎛⎝ ⎞⎠ times 100


(3)







Input Input

Output Output

Hidden layer

Hidden layerForward

Forward

Backward

Uni-LSTM BiLSTM



























0

20

40

60

80

100

120

140

131

462

794

012

5315

6618

7921

9225

0528

1831

3134

4437

5740

7043

8346

9650

0953

2256

3559

4862

6165

7468

8772

0075

1378

2681

39

Spee

d (k

mh

)

Time (minutes)

(a)

0

5

10

15

20

25

30

35

40

45

50

137

374

511

1714

8918

6122

3326

0529

7733

4937

2140

9344

6548

3752

0955

8159

5363

2566

9770

6974

4178

1381

8585

5789

29

Flow

(veh

h)

Time (minutes)


(b)



0

20

40

60

80

100

120

1 26 51 76 101

126

151

176

201

226

251

276

301

326

351

376

401

426

451

476

501

526

551

576

601

626

651

Spee

d (k

mh

)

Time (minutes)

(a)


0

10

20

30

40

50

60

70

80

90

1 27 53 79 105

131

157

183

209

235

261

287

313

339

365

391

417

443

469

495

521

547

573

599

625

651

Flow

(veh

h)

Time (minutes)

(b)





Save the model







0

20

40

60

80

100

120

1 74 147

220

293

366

439

512

585

658

731

804

877

950

1023

1096

1169

1242

1315

1388

1461

1534

1607

Spee

d (k

mh

)

Time (minutes)


(a)


0

10

20

30

40

50

60

70

80

90

1 77 153

229

305

381

457

533

609

685

761

837

913

989

1065

1141

1217

1293

1369

1445

1521

1597

Flow

(veh

h)

Time (minutes)

(b)




0

20

40

60

80

100

120

1 61 121

181

241

301

361

421

481

541

601

661

721

781

841

901

961

1021

1081

1141

1201

1261

1321

1381

1441

1501

1561

1621

Spee

d (k

mh

)

Time (minutes)

(a)


0

10

20

30

40

50

60

70

80

90

1 63 125

187

249

311

373

435

497

559

621

683

745

807

869

931

993

1055

1117

1179

1241

1303

1365

1427

1489

1551

1613

Flow

(veh

h)

Time (minutes)

(b)



0

20

40

60

80

100

120

1 73 145

217

289

361

433

505

577

649

721

793

865

937

1009

1081

1153

1225

1297

1369

1441

1513

1585

Spee

d (k

mh

)

Time (minutes)

(a)


0102030405060708090

1 70 139

208

277

346

415

484

553

622

691

760

829

898

967

1036

1105

1174

1243

1312

1381

1450

1519

1588

Flow

(veh

h)

Time(Minutes)

(b)



0

20

40

60

80

100

120

1 73 145

217

289

361

433

505

577

649

721

793

865

937

1009

1081

1153

1225

1297

1369

1441

1513

1585

Spee

d (k

mh

)

Time (minutes)

(a)


10

20

30

40

50

60

70

80

1 70 139

208

277

346

415

484

553

622

691

760

829

898

967

1036

1105

1174

1243

1312

1381

1450

1519

1588

Flow

(veh

h)

Time (minutes)

(b)








0

50

100

150

1 79 157

235

313

391

469

547

625

703

781

859

937

1015

1093

1171

1249

1327

1405

1483

1561

Spee

d (k

mh

)

Time (minutes)


(a)


020406080

100

1 70 139

208

277

346

415

484

553

622

691

760

829

898

967

1036

1105

1174

1243

1312

1381

1450

1519

1588

Flow

(veh

h)

Time (minutes)

(b)



0

50

100

150

1 78 155

232

309

386

463

540

617

694

771

848

925

1002

1079

1156

1233

1310

1387

1464

1541

Spee

d (k

mh

)

Time (minutes)

(a)


10

30

50

70

90

1 68 135

202

269

336

403

470

537

604

671

738

805

872

939

1006

1073

1140

1207

1274

1341

1408

1475

1542

Flow

(veh

h)

Time (minutes)

(b)




Data Availability




Acknowledgments


References





















































MAPE() 1n

1113944

n

i1

|Y minus Y1|

Y⎛⎝ ⎞⎠ times 100


(3)







Input Input

Output Output

Hidden layer

Hidden layerForward

Forward

Backward

Uni-LSTM BiLSTM



























0

20

40

60

80

100

120

140

131

462

794

012

5315

6618

7921

9225

0528

1831

3134

4437

5740

7043

8346

9650

0953

2256

3559

4862

6165

7468

8772

0075

1378

2681

39

Spee

d (k

mh

)

Time (minutes)

(a)

0

5

10

15

20

25

30

35

40

45

50

137

374

511

1714

8918

6122

3326

0529

7733

4937

2140

9344

6548

3752

0955

8159

5363

2566

9770

6974

4178

1381

8585

5789

29

Flow

(veh

h)

Time (minutes)


(b)



0

20

40

60

80

100

120

1 26 51 76 101

126

151

176

201

226

251

276

301

326

351

376

401

426

451

476

501

526

551

576

601

626

651

Spee

d (k

mh

)

Time (minutes)

(a)


0

10

20

30

40

50

60

70

80

90

1 27 53 79 105

131

157

183

209

235

261

287

313

339

365

391

417

443

469

495

521

547

573

599

625

651

Flow

(veh

h)

Time (minutes)

(b)





Save the model







0

20

40

60

80

100

120

1 74 147

220

293

366

439

512

585

658

731

804

877

950

1023

1096

1169

1242

1315

1388

1461

1534

1607

Spee

d (k

mh

)

Time (minutes)


(a)


0

10

20

30

40

50

60

70

80

90

1 77 153

229

305

381

457

533

609

685

761

837

913

989

1065

1141

1217

1293

1369

1445

1521

1597

Flow

(veh

h)

Time (minutes)

(b)




0

20

40

60

80

100

120

1 61 121

181

241

301

361

421

481

541

601

661

721

781

841

901

961

1021

1081

1141

1201

1261

1321

1381

1441

1501

1561

1621

Spee

d (k

mh

)

Time (minutes)

(a)


0

10

20

30

40

50

60

70

80

90

1 63 125

187

249

311

373

435

497

559

621

683

745

807

869

931

993

1055

1117

1179

1241

1303

1365

1427

1489

1551

1613

Flow

(veh

h)

Time (minutes)

(b)



0

20

40

60

80

100

120

1 73 145

217

289

361

433

505

577

649

721

793

865

937

1009

1081

1153

1225

1297

1369

1441

1513

1585

Spee

d (k

mh

)

Time (minutes)

(a)


0102030405060708090

1 70 139

208

277

346

415

484

553

622

691

760

829

898

967

1036

1105

1174

1243

1312

1381

1450

1519

1588

Flow

(veh

h)

Time(Minutes)

(b)



0

20

40

60

80

100

120

1 73 145

217

289

361

433

505

577

649

721

793

865

937

1009

1081

1153

1225

1297

1369

1441

1513

1585

Spee

d (k

mh

)

Time (minutes)

(a)


10

20

30

40

50

60

70

80

1 70 139

208

277

346

415

484

553

622

691

760

829

898

967

1036

1105

1174

1243

1312

1381

1450

1519

1588

Flow

(veh

h)

Time (minutes)

(b)








0

50

100

150

1 79 157

235

313

391

469

547

625

703

781

859

937

1015

1093

1171

1249

1327

1405

1483

1561

Spee

d (k

mh

)

Time (minutes)


(a)


020406080

100

1 70 139

208

277

346

415

484

553

622

691

760

829

898

967

1036

1105

1174

1243

1312

1381

1450

1519

1588

Flow

(veh

h)

Time (minutes)

(b)



0

50

100

150

1 78 155

232

309

386

463

540

617

694

771

848

925

1002

1079

1156

1233

1310

1387

1464

1541

Spee

d (k

mh

)

Time (minutes)

(a)


10

30

50

70

90

1 68 135

202

269

336

403

470

537

604

671

738

805

872

939

1006

1073

1140

1207

1274

1341

1408

1475

1542

Flow

(veh

h)

Time (minutes)

(b)




Data Availability




Acknowledgments


References






































































0

20

40

60

80

100

120

140

131

462

794

012

5315

6618

7921

9225

0528

1831

3134

4437

5740

7043

8346

9650

0953

2256

3559

4862

6165

7468

8772

0075

1378

2681

39

Spee

d (k

mh

)

Time (minutes)

(a)

0

5

10

15

20

25

30

35

40

45

50

137

374

511

1714

8918

6122

3326

0529

7733

4937

2140

9344

6548

3752

0955

8159

5363

2566

9770

6974

4178

1381

8585

5789

29

Flow

(veh

h)

Time (minutes)


(b)



0

20

40

60

80

100

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1 26 51 76 101

126

151

176

201

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326

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576

601

626

651

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d (k

mh

)

Time (minutes)

(a)


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131

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183

209

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365

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443

469

495

521

547

573

599

625

651

Flow

(veh

h)

Time (minutes)

(b)





Save the model







0

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1 74 147

220

293

366

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512

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Time (minutes)


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(b)




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d (k

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Time (minutes)

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Time(Minutes)

(b)



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d (k

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Time (minutes)

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Flow

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Time (minutes)

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0

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Spee

d (k

mh

)

Time (minutes)


(a)


020406080

100

1 70 139

208

277

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415

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553

622

691

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829

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1105

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Flow

(veh

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Time (minutes)

(b)



0

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Spee

d (k

mh

)

Time (minutes)

(a)


10

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1207

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Flow

(veh

h)

Time (minutes)

(b)




Data Availability




Acknowledgments


References




















































Save the model







0

20

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80

100

120

1 74 147

220

293

366

439

512

585

658

731

804

877

950

1023

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1315

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Spee

d (k

mh

)

Time (minutes)


(a)


0

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1 77 153

229

305

381

457

533

609

685

761

837

913

989

1065

1141

1217

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1445

1521

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Flow

(veh

h)

Time (minutes)

(b)




0

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Spee

d (k

mh

)

Time (minutes)

(a)


0

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1 63 125

187

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311

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621

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745

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993

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Flow

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Time (minutes)

(b)



0

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Spee

d (k

mh

)

Time (minutes)

(a)


0102030405060708090

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Flow

(veh

h)

Time(Minutes)

(b)



0

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Spee

d (k

mh

)

Time (minutes)

(a)


10

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1 70 139

208

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415

484

553

622

691

760

829

898

967

1036

1105

1174

1243

1312

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1588

Flow

(veh

h)

Time (minutes)

(b)








0

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1 79 157

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469

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625

703

781

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1015

1093

1171

1249

1327

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1483

1561

Spee

d (k

mh

)

Time (minutes)


(a)


020406080

100

1 70 139

208

277

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415

484

553

622

691

760

829

898

967

1036

1105

1174

1243

1312

1381

1450

1519

1588

Flow

(veh

h)

Time (minutes)

(b)



0

50

100

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1 78 155

232

309

386

463

540

617

694

771

848

925

1002

1079

1156

1233

1310

1387

1464

1541

Spee

d (k

mh

)

Time (minutes)

(a)


10

30

50

70

90

1 68 135

202

269

336

403

470

537

604

671

738

805

872

939

1006

1073

1140

1207

1274

1341

1408

1475

1542

Flow

(veh

h)

Time (minutes)

(b)




Data Availability




Acknowledgments


References



















































0

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1 61 121

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661

721

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901

961

1021

1081

1141

1201

1261

1321

1381

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1501

1561

1621

Spee

d (k

mh

)

Time (minutes)

(a)


0

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1 63 125

187

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311

373

435

497

559

621

683

745

807

869

931

993

1055

1117

1179

1241

1303

1365

1427

1489

1551

1613

Flow

(veh

h)

Time (minutes)

(b)



0

20

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1 73 145

217

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361

433

505

577

649

721

793

865

937

1009

1081

1153

1225

1297

1369

1441

1513

1585

Spee

d (k

mh

)

Time (minutes)

(a)


0102030405060708090

1 70 139

208

277

346

415

484

553

622

691

760

829

898

967

1036

1105

1174

1243

1312

1381

1450

1519

1588

Flow

(veh

h)

Time(Minutes)

(b)



0

20

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1 73 145

217

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361

433

505

577

649

721

793

865

937

1009

1081

1153

1225

1297

1369

1441

1513

1585

Spee

d (k

mh

)

Time (minutes)

(a)


10

20

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1 70 139

208

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415

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622

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967

1036

1105

1174

1243

1312

1381

1450

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1588

Flow

(veh

h)

Time (minutes)

(b)








0

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1 79 157

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1171

1249

1327

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1483

1561

Spee

d (k

mh

)

Time (minutes)


(a)


020406080

100

1 70 139

208

277

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415

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553

622

691

760

829

898

967

1036

1105

1174

1243

1312

1381

1450

1519

1588

Flow

(veh

h)

Time (minutes)

(b)



0

50

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1 78 155

232

309

386

463

540

617

694

771

848

925

1002

1079

1156

1233

1310

1387

1464

1541

Spee

d (k

mh

)

Time (minutes)

(a)


10

30

50

70

90

1 68 135

202

269

336

403

470

537

604

671

738

805

872

939

1006

1073

1140

1207

1274

1341

1408

1475

1542

Flow

(veh

h)

Time (minutes)

(b)




Data Availability




Acknowledgments


References























































0

50

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1 79 157

235

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469

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625

703

781

859

937

1015

1093

1171

1249

1327

1405

1483

1561

Spee

d (k

mh

)

Time (minutes)


(a)


020406080

100

1 70 139

208

277

346

415

484

553

622

691

760

829

898

967

1036

1105

1174

1243

1312

1381

1450

1519

1588

Flow

(veh

h)

Time (minutes)

(b)



0

50

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1 78 155

232

309

386

463

540

617

694

771

848

925

1002

1079

1156

1233

1310

1387

1464

1541

Spee

d (k

mh

)

Time (minutes)

(a)


10

30

50

70

90

1 68 135

202

269

336

403

470

537

604

671

738

805

872

939

1006

1073

1140

1207

1274

1341

1408

1475

1542

Flow

(veh

h)

Time (minutes)

(b)




Data Availability




Acknowledgments


References



















































Data Availability




Acknowledgments


References


















































unidirectionalandbidirectionallstmmodelsforshort-term ...2021/01/12 · where σ g is the gate...

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