Real-Time Prediction of Lane-Based Queue Lengths for...

Research ArticleReal-Time Prediction of Lane-Based Queue Lengths forSignalized Intersections

Bing Li12 Wei Cheng 1 and Lishan Li3

1Faculty of Transportation Engineering Kunming University of Science and Technology Kunming Yunnan 650093 China2Key Laboratory of Urban ITS Technology Optimization and Integration Ministry of Public Security Hefei Anhui 230088 China3Infrastructure Construction Department Kunming University of Science and Technology Kunming Yunnan 650093 China

Correspondence should be addressed to Wei Cheng chengwei dingkmusteducn

Received 24 July 2018 Revised 24 October 2018 Accepted 7 November 2018 Published 3 December 2018

Academic Editor Ludovic Leclercq

Copyright copy 2018 Bing Li et al This is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Queue length is one of the most important traffic evaluation indexes for traffic signal control at signalized intersections Mostprevious studies have focused on estimating queue length which cannot be predicted effectively In this paper we applied theLighthillndashWhithamndashRichards shockwave theory and Robertsonrsquos platoon dispersion model to predict the arrival of vehicles inadvance at intervals of 5 seconds This approach fully described the relationship between disparate upstream traffic arrivals (as aresult of vehicles making different turns) and the variation of incremental queue accumulation It also addressed the shortcomingsof the uniform arrival assumption in previous research In addition to predict the queue length of multiple lanes at the same timewe integrated the prediction of the traffic volume proportions in each lane using the Kalman filter We tested this model in a fieldexperiment and the results showed that the model had satisfactory accuracy We also discussed the limitations of the proposedmodel in this paper

1 Introduction

Queue length is the most important index for signal controlevaluation [1] or signal optimization [2ndash6] Over the yearsmany researchers have devoted themselves to the study ofqueue length which can be divided into three categories(ie detection estimation and prediction) according toqueue length acquisition methods The first categorymdashthedirect detection of queue length using equipment such ascamerasmdashis one of the most commonly used methods toobtain queue length in recent research [7ndash9] This methodcan simply and quickly obtain the queue length but it doesnot consider fluctuations in traffic flow and the maximumqueue will not be obtained when the queue length exceedsthe visual range of the camera

The second category queue length estimation is the moststudied by scholars In the literature queue length estimationmethods can generally be classified into two categories [1011] input-output models [2 12ndash14] and shockwave models[10 11 15ndash18] The input-output model analyzes the cumu-lative traffic input-output (arrival-departure curve) of a link

to estimate the queue length This kind of model has simpleconceptual properties It is limited however by the inabilityto capture the spatial queue in actual arterial traffic Atthe same time the traditional input-output analysis cannotdescribe the spatial distribution of queue length in real timenor is this model suitable for the estimation of queue lengthat oversaturated intersections [10]

Recently much attention has been given to the formationand dissipation of queues using traffic shockwave theory Theshockwave model provides a better analysis framework forqueue length estimation [6] With the development of trafficdata acquisition technology the estimation of queue lengthby probe vehicles has also become a common method [19ndash22] Because of the unique mobility of probe vehicle dataand limitations on probe vehicle size the precision of queuelength estimation can be guaranteed only when the penetra-tion rate of probe vehicles is high A penetration rate of 30was recommended by Ban et al [11] and byGoodall Park andSmith [23] According to Hao et al [24] penetration rates ator above 10 are able to provide mean absolute error withinplusmn3 vehicles in queue length estimation In addition most

HindawiJournal of Advanced TransportationVolume 2018 Article ID 5020518 18 pageshttpsdoiorg10115520185020518

2 Journal of Advanced Transportation

researchers take isolated intersections as the research subjectto establish their queue length estimation model [19ndash22] Itis usually assumed that the vehicle arrives from a uniformtraffic distribution [11 19ndash21] Intersections in real roadnetworks often are not isolated however and downstreamvehicle arrival is often closely related to upstream vehiclerelease characteristics flow rate and travel time [25 26]Theuniform distribution of vehicles cannot accurately describethe dispersed characteristics of vehicle arrival nor can itdescribe the real-time attributes of the arrival of vehicles withdisparate characteristics of queue lengthHow to describe thisdisparity is a primary focus of this paper

The third category is the prediction of queue length Withthe improvement of traffic control requirements predictivetraffic signal control has become a developing trend whichrelies on the ability to obtain relevant parameters of trafficcontrol in advance [27ndash31]Therefore the prediction of queuelength is essential for predictive control optimization Theresearch on queue length prediction is scarce Hao and Ban[24] usedmobile data to estimate queue length and noted thatqueue length prediction is the direction of future researchRHODES [32] and Sharma et al [13] predicted vehicle arrivaland release rate using conventional input-output and queuelength estimations Akcelik [12] modified the parameters ofthe Highway Capacity Manual queue estimation model bystatistical analysis and established a queue length predictionmodel This model however cannot describe the spatialdistribution and evolution of queue length nor is it suitablefor prediction of queue length at oversaturated intersectionsGeroliminis and Skabardonis [25] combined platoon disper-sion characteristics and LighthillndashWhithamndashRichards (LWR)theory to predict queue length effectively but the modelconsiders only the maximum queue and it cannot describethe evolution of the queue in real time or analyze the dynamiceffects of different upstream turning flowon the queue lengthIn addition this model cannot simultaneously predict thequeue length of multiple lanes at the same time

To overcome the shortcomings of previous studies inwhich vehicle arrival was assumed to be uniformly dis-tributed and the evolutionary process of queue length couldnot be described we combined the advantages of traffic wavetheory and the platoon dispersion model to analyze vehiclearrival We predicted the queue length in real time andobtained changes in queue length in advance which providedsupport for predictive traffic signal optimization

This study makes the following contributions

(1) We obtained the upstream different turning flows inreal time at intervals of 5 seconds and fully consideredthe discrete characteristics of the vehicle to predictdownstream vehicle arrival which overcame the lim-itation of the uniform arrival assumption in previousresearch on queue length estimation

(2) The proposed model predicted the lane-based queuelength in real timemdashthe prediction included incre-mental queue accumulation (IQA) queue trajectorymaximum queue and residual queue which over-came the shortcomings of previous research thatcould not obtain the evolution trend of queuing in

advance and we determined the specific predictedadvance interval of the queue length depends on thetravel time between upstream intersection and down-stream intersection This was a convenient way tomake an optimal strategy of proactive signal control

(3) The proposed model obtained the influence of thedifferent upstream turning flows on downstream IQAin real time and the relationship between upstreamand downstream intersections was enhanced whichwas helpful for fine signal coordination optimizationdesign

(4) The prediction of the proportions of traffic volume ineach lane provided the basis for prediction of lane-based queue lengths To improve accuracy in predict-ing the lane-based traffic proportion while using theKalman filter we used the information of all lanesat the first three intervals in the prediction of lane119894 In the previous method however the researchersused only the information of lane 119894 at the first threeintervals in the prediction of lane i

The remainder of this paper is organized as follows InSection 2 we introduce the assumptions made and termi-nology used in this paper and provide the simplified queue-forming and queue-discharging process Section 3 presentsmodels to predict the proportion of lane-based traffic volumeand the real-time queue length The model is then testedusing field data in Section 4 Finally Section 5 summarizesthe findings and provides directions for future work

2 Preliminaries

In this section we provide the assumptions for deriving thequeue length prediction model some terminology defini-tions and a simplified queue-forming and queue-dischargingprocess

21 Assumptions Wemake the following assumptions

(1) The vehicle follows the first-in-first-out (FIFO) prin-ciple and there is no obvious overtaking phe-nomenon

(2) The vehicle has the same acceleration and decelera-tion behavior

(3) The influence of buses on traffic flow is disregarded

The necessity for these assumptions is explained in AppendixA

22 Terminology In this paper real-time queue length isdefined as the number of vehicles queuing at any given time

23 Simplified Queue-Forming and Queue-Discharging Pro-cess On the basis of these assumptions the queue-formingand queue-discharging process can be described as shownin Figure 1(b) The triangular fundamental diagram for con-structing this process is shown in Figure 1(a) In these figures0 and 119896119895 are jam volume and jam density 119902119898 and 119896119898 aresaturation volume and optimal density 119902119899119889119897119886119899119890 119894(5ℎ + 119905) and

Journal of Advanced Transportation 3

Flow

Density

wn3

wn3

qm

km kj

(0 kj)

wn1 lane i

qnd lane i (5ℎ+t)

d lane ikn (5ℎ+t)

(a) Fundamental diagram

Downstream intersection

Upstream intersection

Through Left-turn Right-turn

A

B

CD

l

Green signalRed signal

tnL ＧＲ lane i

wn1 lane i

wn4

wn3wn

2

tng lane i tn+1g lane itnr lane i

Lnre lane iLn

ＧＲ lane iLn

r lane i

(b) Shockwave propagation process

Figure 1 (a) Fundamental diagram (b) shockwave propagation process

119896119899119889119897119886119899119890 119894(5ℎ + 119905) are the volume and density of the downstreamarrival flow in 119897119886119899119890 119894 during the nth cycle at intervals of5 seconds as will be described in detail in Section 33 Inaddition1199081198991119897119886119899119890 1198941199081198992 1199081198993 and1199081198994 are the queue-forming wavein 119897119886119899119890 119894 the queue-discharging wave the departure waveand the residual queue-forming wave respectively As shownin Liu et al [10] and Ban et al [11] the speeds of the four wavescan be calculated as follows

1199081198991119897119886119899119890 119894 = 10038161003816100381610038161003816100381610038161003816100381610038160 minus 119902119899119889119897119886119899119890 119894 (5ℎ + 119905)119896119895 minus 119896119899119889119897119886119899119890 119894 (5ℎ + 119905)

1003816100381610038161003816100381610038161003816100381610038161003816= 119902119899119889119897119886119899119890 119894 (5ℎ + 119905)119896119895 minus 119896119899119889119897119886119899119890 119894 (5ℎ + 119905)

(1)

1199081198992 = 1003816100381610038161003816100381610038161003816100381610038161003816119902119898 minus 0119896119898 minus 119896119895

1003816100381610038161003816100381610038161003816100381610038161003816 =119902119898119896119895 minus 119896119898 (2)

1199081198993 = 1003816100381610038161003816100381610038161003816100381610038161003816119902119898 minus 119902119899119889119897119886119899119890 119894 (5ℎ + 119905)119896119898 minus 119896119899119889119897119886119899119890 119894 (5ℎ + 119905)

1003816100381610038161003816100381610038161003816100381610038161003816 =119902119898119896119898 (3)

1199081198994 = 10038161003816100381610038161003816100381610038161003816100381610038160 minus 119902119898119896119898 minus 119896119895

1003816100381610038161003816100381610038161003816100381610038161003816 = 1199081198992 (4)

In Figure 1(b) A B C and D each describe the queueaccumulation of traffic flow in different directions (iethrough and right-turn movement right-turn movementleft-turn and right-turn movement and right-turn move-ment respectively) from the upstream intersection to the


North

Wes

t Nan

ning

Rd

Wes

t Nan

ning

Rd

South Qilin Rd

Wes

t Nan

ning

Rd

South Qilin Rd

South Qilin Rd

South Qilin Rd

Wen

chan

g St

Wen

chan

g St

W

ench

ang

St

512m

Upstream site A

Upstream site A

First vehicle (current)Stop line Stop line

Firstvehicle

(advanced)

Downstream site B

Downstream site B

Upstream site A Downstream site B

South Qilin Rd

(Current state)

(Advanced state)

(Predicted state)

t

tng lane itn0 lane i

Figure 2The initial state for queue length prediction

downstream intersection A key point of this paper is describ-ing the dynamic differences in vehicle arrival during condi-tions of different turning flow at the upstream intersection

3 Real-Time Queue Length Prediction

31 The Initial Moment of Queue Length Prediction Over-saturated traffic conditions evolve with the gradual increaseof traffic demand in undersaturated traffic conditions In anundersaturated traffic condition the queue length of 119897119886119899119890 119894is generally equal to 0 at the end of the effective green timeof 119897119886119899119890 119894 (119905119899119892119897119886119899119890 119894) Therefore we can use 119905119899119892119897119886119899119890 119894 as the startingtime for the queue length calculation As shown in Figure 2119905119899119892119897119886119899119890 119894 is when the first (current) vehicle actually moves Topredict the arrival of vehicles in advance this paper drewupon lessons from the processing methods in Mirchandaniand Head [32] and Geroliminis and Skabardonis [25] taking1199051198990119897119886119899119890 119894 as the advance running moment of the first vehicle1199051198990119897119886119899119890 119894 = 119905119899119892119897119886119899119890 119894 minus 119905 where 119905119899119892119897119886119899119890 119894 is the end (or duration) ofthe green time for the 119899th cycle of lane i and 119905 is the averagetravel time of vehicles from the upstream section (upstreamsite A) to the downstream stopline (downstream site B)Thuswe have 119905 = 119897V where 119897 is the distance between upstream siteA and downstream site B and V is the average speed of the sec-tion 119897 whichmeans that the predicted advance interval of thequeue length depends on 119905 Namely as shown in Figure 2 thequeue length prediction process is such that according to thecurrent state we determined the advance state according tothe travel time and then we predicted the queue length (giv-ing the predicted state) according to the arrival prediction

32 Lane-Based Traffic Proportions Prediction To predict thequeue length of all lanes at the same time we needed to

predict the proportion of lane-based traffic volume AKalmanfilter [33] is a highly efficient recursive (or autoregres-sive) filter that can be used to estimate the state of a dynamicsystem from a series of measurements with moderate noiseBecause of its good state estimation and prediction accuracyas well as its ease of calculation and implementation ithas been applied extensively to traffic flow estimation andprediction [20 34ndash36]

To start the recursive process we set the system variablestime update equations and measurement equations Let119901119899119889119897119886119899119890 119894 be the proportion of downstream lane-based trafficvolume in lane 119894 in the 119899th interval (we took 5 minutes asan interval) Because the traffic flow at the 119899th interval wasclosely related to the traffic flow in the first three intervals weused the information of all the lanes at the first three intervalsin the prediction of lane 119894 The prediction value 119901119899|119899minus1

119889119897119886119899119890 119894 of119901119899119889119897119886119899119890 119894 can be represented as follows

119901119899|119899minus1119889119897119886119899119890 119894= 119872sum119894=1

(ℎ119899minus1119889119897119886119899119890 119894119901119899minus1119889119897119886119899119890 119894 + ℎ119899minus2119889119897119886119899119890 119894119901119899minus2119889119897119886119899119890 119894 + ℎ119899minus3119889119897119886119899119890 119894119901119899minus3119889119897119886119899119890 119894)+ 120596119899minus1119897119886119899119890 119894

(5)

where 119901119899|119899minus1119889119897119886119899119890 119894

is the predicted value of the proportion ofdownstream volume of lane 119894 during the 119899th interval 119872 isthe total number of approach lanes (119872 is 3 in the test site forthe proposed model) 119901119899minus1119889119897119886119899119890 119894 119901119899minus2119889119897119886119899119890 119894 and 119901119899minus3119889119897119886119899119890 119894 representthe observed proportion of lane-based traffic volume at thedownstream in lane 119894 in the (n-1)th interval the (n-2)thinterval and the (n-3)th interval respectively ℎ119899minus1119889119897119886119899119890 119894 ℎ119899minus2119889119897119886119899119890 119894and ℎ119899minus3119889119897119886119899119890 119894 are parameters relating the state at the (n-1)th


(n-2)th and (n-3)th intervals respectively to the state inthe 119899th cycle at the downstream in lane i 120596119899minus1119889119897119886119899119890 119894 is theobservation noise in the (n-1)th cycle downstream in lane119894 and is assumed to be a white noise with zero mean and119877119899minus1119889119897119886119899119890 119894 is the covariance matrix of 120596119899minus1119889119897119886119899119890 119894 in the (n-1)th cycledownstream in lane 119894

To use the Kalman filter to predict state variables thefollowing integrated transformations are carried out

119862119899minus1119889119897119886119899119890 119894 = (119901119899minus1119889119897119886119899119890 1 sdot sdot sdot 119901119899minus1119889119897119886119899119890119872 119901119899minus2119889119897119886119899119890 1 sdot sdot sdot 119901119899minus2119889119897119886119899119890119872119901119899minus3119889119897119886119899119890 1 sdot sdot sdot 119901119899minus3119889119897119886119899119890119872) (6)

119883119899minus1119889119897119886119899119890 119894 = (ℎ119899minus1119889119897119886119899119890 1 sdot sdot sdot ℎ119899minus1119889119897119886119899119890119872 ℎ119899minus2119889119897119886119899119890 1 sdot sdot sdot ℎ119899minus2119889119897119886119899119890119872ℎ119899minus3119889119897119886119899119890 1 sdot sdot sdot ℎ119899minus3119889119897119886119899119890119872)119879 (7)

Combining 119862119899minus1119889119897119886119899119890 119894 and 119883119899minus1119889119897119886119899119890 119894 with the Kalman filter thetraffic volume proportions for our prediction model can beobtained as follows

119883119899minus1119889119897119886119899119890 119894 = 119865119899minus1119889119897119886119899119890 119894119883119899minus2119889119897119886119899119890 119894 + 119906119899minus2119889119897119886119899119890 119894 (8)

119901119899|119899minus1119889119897119886119899119890 119894 = 119862119899minus1119889119897119886119899119890 119894119883119899minus1119889119897119886119899119890 119894 + 120596119899minus1119889119897119886119899119890 119894 (9)

where 119883119899minus1119889119897119886119899119890 119894 is the state vector 119862119899minus1119889119897119886119899119890 119894 is the observationmatrix 119865119899minus1119889119897119886119899119890 119894 is the state transition matrix 119906119899minus2119889119897119886119899119890 119894 is theprocess noise in the (n-2)th cycle downstream in lane 119894 and isassumed to be awhite noisewith zeromean and119876119899minus2119889119897119886119899119890 119894 is thecovariance matrix of 119906119899minus2119889119897119886119899119890 119894 in the (n-2)th cycle downstreamin lane i

According to this analysis we used the following steps topredict traffic flow using the Kalman filter

(1) Set the Initial Parameters We set the initial value of thestate transition matrix 1198651|0

119889119897119886119899119890 119894in the Kalman filter equation

as the unit matrix 119868 and the dimension was 1198722 times 1198722 Weobtained the initial value of the process noise correlationmatrix and the observation noise correlation matrix by therandom function and covariance function in MATLAB1198760119889119897119886119899119890 119894 = cov(rand 119899(11987221198722)) and in this paper theobserved data were in a one-dimensional time series so1198770119889119897119886119899119890 119894 = cov(rand 119899(1 1)) The initial value of state vectorprediction 1198831|0

119889119897119886119899119890 119894was [0] and its error autocorrelation

matrix 1198701|0119897119886119899119890 119894

was the zero matrix To make the filter gainprocess convergence faster we estimated the initial value ofthe state vector estimation 1198830|0

119889119897119886119899119890 119894using the R programming

language to fit the linear relation (by the method of leastsquares) between the value of the 0 interval and the value of itsprevious three intervals and its error autocorrelation matrixwas the zero matrix

(2) Run a Recursive Prediction Based on the Kalman Filter

Step 1 Set the recursion cycle variable 119899 where the numberof recursions is the predicted length Then calculate thefollowing quantities

Step 2 The Kalman gain matrix

119866119899minus1119889119897119886119899119890 119894 = 119870119899minus1|119899minus2119889119897119886119899119890 119894 (119862119899minus1119889119897119886119899119890 119894)119879sdot [119862119899minus1119889119897119886119899119890 119894119870119899minus1|119899minus2119889119897119886119899119890 119894 (119862119899minus1119889119897119886119899119890 119894)119879 + (119877119899minus1119889119897119886119899119890 119894)]minus1

(10)

Step 3 The observation error

119890119899minus1119889119897119886119899119890 119894 = 119901119899minus1119889119897119886119899119890 119894 minus 119862119899minus1119889119897119886119899119890 119894119883119899minus1|119899minus2119889119897119886119899119890 119894 (11)

Step 4 The state vector optimal estimate

119883119899minus1|119899minus1119889119897119886119899119890 119894 = 119865119899minus1|119899minus2119889119897119886119899119890 119894 119883119899minus2|119899minus2119889119897119886119899119890 119894 + 119866119899minus1119889119897119886119899119890 119894119890119899minus1119889119897119886119899119890 119894 (12)

Step 5 The correlation matrix computation of the error ofstate vector 119883119899|119899minus1119889119897119886119899119890 119894

119870119899minus1|119899minus2119889119897119886119899119890 119894 = 119865119899minus1|119899minus2119889119897119886119899119890 119894 119870119899minus2|119899minus2119889119897119886119899119890 119894 (119865119899minus1|119899minus2119889119897119886119899119890 119894 )119879119876119899minus2119889119897119886119899119890 119894 (13)

Step 6 The correlation matrix optimal estimate of the errorof the state vector

119870119899minus1|119899minus1119889119897119886119899119890 119894 = (119868 minus 119866119899minus1119889119897119886119899119890 119894119862119899minus1119889119897119886119899119890 119894)119870119899minus1|119899minus2119889119897119886119899119890 119894 (14)

Step 7 The estimated value of the state vector

119883119899|119899minus1119889119897119886119899119890 119894 = 119865119899|119899minus1119889119897119886119899119890 119894119883119899minus1|119899minus1119889119897119886119899119890 119894 (15)

Step 8 The prediction of the observation value based on theestimated state value

119901119899|119899minus1119889119897119886119899119890 119894 = 119862119899119889119897119886119899119890 119894119883119899|119899minus1119889119897119886119899119890 119894 (16)

Step 9 TheKalman filter estimation of the observation valuebased on the state filter estimation value

119901119899minus1|119899minus1119889119897119886119899119890 119894 = 119862119899minus1119889119897119886119899119890 119894119883119899minus1|119899minus1119889119897119886119899119890 119894 (17)

Step 10 Finally increment 119899 by the loop variable and repeatthe steps until the loop variable is equal to the predictedlength

In the previous steps the quantities are defined as follows

119866119899minus1119889119897119886119899119890 119894 Kalman gain matrix in lane 119894 during the (n-1)th interval119890119899minus1119889119897119886119899119890 119894 observation errors in lane 119894 during the (n-1)thinterval119865119899|119899minus1119889119897119886119899119890 119894

state transition matrix in lane 119894 from the (n-1)th interval to the 119899th interval119870119899minus1|119899minus2119889119897119886119899119890 119894

correlation matrix of the error of 119883119899|119899minus1119889119897119886119899119890 119894

119876119899minus1119889119897119886119899119890 119894 process noise correlation matrix in lane 119894during the (n-1)th interval

119877119899minus1119889119897119886119899119890 119894 observation noise correlation matrix in lane 119894during the (n-1)th interval


33 The Evolutionary Process of the Queue State

331 Analysis of Platoon Dispersion Characteristics Thequeue at a signalized intersection presented the problem ofstochastic vehicle arrival and fixed service rateThe process ofreceiving service was relatively simple when the red light wasturned on the service rate was zero and the vehicle stoppedwhen the green light was turned on the service rate was thesaturated flow rate The number of vehicles leaving the inter-section was related to the duration of the green light so partof the problemwas to determine the variable service rateTheproblem of vehicle arrival was complex however so it wasnecessary to consider the influence of the signal design andplatoon dispersion characteristics [25] The different platoondispersion characteristics determined different arrival timesand the varying arrival rate determined the dynamic changeof the queue length

When the queuing vehicles of the upstream intersectionleave the intersection during the green phase as a resultof the squeeze and segmentation between the vehicles partof one vehicle is divided into a one-by-one platoon whichcauses the vehicle not to reach the next intersection uni-formly Thus the ldquodispersion phenomenonrdquo has occurred inthe platoon travel process [37ndash39] The platoon dispersionmodel can dynamically describe arrival characteristics andpredict downstream vehicle arrival [40] Because the tail ofthe geometric distribution is longer than the correspondingnormal distribution Robertsonrsquos model can better predict theplatoon dispersion for any given mean travel time [41] Inaddition because of the low computational requirements ofRobertsonrsquos model it is easy to apply this model both to thesignal optimization of large road networks [37 42ndash44] and tothe development of other traffic theories [31 45ndash49]

In light of this when the vehicles are controlled by trafficsignals and left in the form of a platoon we used Robertsonrsquosmodel to predict downstream vehicle arrival (as shown inFigure 1 A and C) When the vehicles are controlled bytraffic signals we used the upstream observation value as thedownstream predicted arrival value (as shown in Figure 1B and D) According to Robertsonrsquos model the relationshipbetween the vehicle arrival rates at the downstream sectionand the vehicle passing rates in the upstream section can bedescribed as follows

119902119899119889 (119909 + 119905) = 11 + 1205721199051199021198990 (119909)+ (1 minus 11 + 120572119905) 119902119899119889 (119909 + 119905 minus 1)

(18)

where 119902119899119889(119909 + 119905) is the estimated vehicle arrival rate on adownstream section in the 119899th cycle of the (x + t)th interval1199021198990(119909) is the vehicle passing rate in the upstream section ofthe 119899th cycle of the xth interval 119905 is 08 times the averagetravel time 119905 between the above two sections and 120572 is acoefficient giving the degree of dispersion of the traffic flowin the process of platoon movement known as the discretecoefficient of the traffic flow This value was obtained by Bieet al [45] and is represented as follows

120572

=

0126119890minus((119906119904minus0786)0107)2 + 0793119890minus((119906119904minus0809)1312)2 119873 = 20160119890minus((119906119904minus0741)0146)2 + 0771119890minus((119906119904minus0706)0778)2 119873 = 30141119890minus((119906119904minus0766)0062)2 + 0771119890minus((119906119904minus0701)0553)2 119873 = 40084119890minus((119906119904minus0744)006)2 + 0815119890minus((119906119904minus0742)0416)2 119873 = 5

(19)

119906 = 36001198761198941003816100381610038161003816119879ℎ119894 minus 1198791199051198941003816100381610038161003816 (20)

119904 = 119873119878119886119894 (21)

where 119876119894 is the sum of the number of vehicles in the platooni 119879ℎ119894 represents the moment at which the lead vehicle ofplatoon 119894 passes through the upstream data collection point(eg upstream site A in Figure 2) 119879119905119894 represents the momentat which the tail vehicle of the platoon 119894 passes through theupstream data collection point 119873 is the number of lanes atthe upstream data collection point in the direction of thetraffic movements and 119878119886119894 is the capacity per lane

In addition to predict the queue length of different lanesat the same time the effect of the proportion of lane-basedtraffic should be considered Robertsonrsquos model after addingthe lane-based traffic proportion is as follows

119902119899119889119897119886119899119890 119894 (119909 + 119905) = 11 + 1205721199051199021198990 (119909) 119901119899|119899minus1119889119897119886119899119890 119894+ (1 minus 11 + 120572119905) 119902119899119889119897119886119899119890 119894 (119909 + 119905 minus 1)

(22)

332 Queue Formation Process Part One As shown inFigure 3 this paper divides the queue length formation pro-cess into two parts part one (119871119899119891119875119886119903119905 1119897119886119899119890 119894) includes the queuelength formed from the moment of initial calculation to theend of the red signal meanwhile part two (119871119899119891119875119886119903119905 2119897119886119899119890 119894) lastsfrom the end of the red signal to the time when themaximumqueue length appears First we analyzed part one of the queueformation process

(1) Calculate Queue Length in Intervals of 5 Seconds Fol-lowing Bell [50] and Shen et al [31] we took 5 seconds asthe time interval in the application of Robertsonrsquos model Toexpress the dynamic evolution of traffic waves more clearlywe introduced the cell transmission model (CTM) [51 52]to describe the formation of traffic waves in intervals of5 seconds CTM is a convergent numerical approximationto the LWR model and is widely recognized as a goodcandidate for dynamic traffic simulation Figure 4 depictsthe traffic flow in two adjacent cells of 1199081198991119897119886119899119890 119894(5ℎ + 119905)The values 119902119899119889119897119886119899119890 119894(5ℎ + 119905) and 119896119899119889119897119886119899119890 119894(5ℎ + 119905) denote thevolume and density in cell 119894 at time (5ℎ + 119905) We predictedthe volume of downstream cells according to Robertsonrsquosmodel

Let 119909 = 5ℎ ℎ = 1 2 3 sdot sdot sdot ROUND((119905119899119903119897119886119899119890 119894 + 119905119899+1119892119897119886119899119890 119894)5)where the ROUND function rounds the value in parentheses119905119899119903119897119886119899119890 119894 is the end (or duration) of the 119899th red signal for lanei and 119905119899+1119892119897119886119899119890 119894 is the end (or duration) of the green time for



l

tnL ＧＲ lane i

wn4

wn3wn

1 lane i wn2


Lnre lane i

Lnf Part 1 lane i

Lnf Part 2 lane i

LnＧＲ lane i

Lnr lane i

Figure 3 Two parts of queue length forming process

Upstream site A

Upstream cells

Downstream site B

Downstream Cells (5 seconds)

Wes

t Nan

ning

Rd

South Qilin RdSouth Qilin Rd

Wen

chan

g St

North

Cell lane 1 (qnd lane 1 d lane 1(5ℎ + t) kn (5ℎ + t))



wn1 lane i (5ℎ+t)

(0 kj)

Figure 4 Two adjacent cells of the queue-forming wave (at an interval of 5 seconds)

the (119899 + 1)th cycle of lane 119894 Then the queue-forming wave1199081198991119897119886119899119890 119894(119909 + 119905) is further expressed as follows

1199081198991119897119886119899119890 119894 (5ℎ + 119905) = 119902119899119889119897119886119899119890 119894 (5ℎ + 119905)119896119895 minus 119896119899119889119897119886119899119890 119894 (5ℎ + 119905) (23)

where 119896119899119889119897119886119899119890 119894(5ℎ+119905) can be obtained by dividing 119902119899119889119897119886119899119890 119894(5ℎ+119905)by V [10]The queue length at the interval of 5 seconds for thenth cycle is

1198711198995ℎ119897119886119899119890 119894 = 5119902119899119889119897119886119899119890 119894 (5ℎ + 119905)119896119895 minus 119896119899119889119897119886119899119890 119894 (5ℎ + 119905) (24)

(2) Improve Robertsonrsquos Model in the Queue-Forming ProcessDuring queue formation the two observation sections ofRobertsonrsquosmodel are as follows upstream siteArsquos section andthe downstream section of the queuersquos tail end Upstream siteArsquos section is fixed whereas the downstream section movesbackward with an increase in the queue length in this case119905 changes with the movement of the downstream section

Given the ratio of queue length to section 119897 the travel time119905ℎ of the hth interval is

119905ℎ = 08119905 119897 minus sum119898ℎ=1 1198711198995ℎ119897119886119899119890 119894119897 (25)

where 119905119899119871max119897119886119899119890 119894 is the duration from the initial momentof queue length prediction to the appearance of the max-imum queue length and 119898 is the number of 5-secondintervals before the maximum queue length occurs 1 le119898 le ROUND(119905119899119871 max119897119886119899119890 1198945) Thus the modified Robertsonrsquosmodel can be expressed as follows

119902119899119889119897119886119899119890 119894 (5ℎ + 119905ℎ)= 11 + 120572119905ℎminus1 1199021198990 (5ℎ) 119901119899|119899minus1119889119897119886119899119890 119894+ (1 minus 11 + 120572119905ℎminus1)119902119899119889119897119886119899119890 119894 (5ℎ + 119905ℎminus1 minus 1)

(26)

(3) Determine Queue Length at the End of the Red SignalOn the basis of the duration of the red signal 119871119899119903119897119886119899119890 119894 (the



l

tnL ＧＲ lane i


LnＧＲ lane i

Lnr lane i

Lnre lane i

wn2

wn3 wn

3

wn4

wn1 lane i

(qm km)

Figure 5 Queue length discharging process

queue length of lane 119894 at the end of the 119899th red signal) canbe calculated as follows

119871119899119903119897119886119899119890 119894 = ROUND(1199051198991199031198971198861198991198901198945)sumℎ=1

51199081198991119897119886119899119890 119894 (5ℎ + 119905ℎ)= ROUND(119905119899119903119897119886119899119890 1198945)sum

ℎ=1

5119902119899119889119897119886119899119890 119894 (5ℎ + 119905ℎ)119896119895 minus 119896119899119889119897119886119899119890 119894 (5ℎ + 119905ℎ) (27)

333 Queue Formation Process Part Two As shown inFigure 3 the key to calculating the maximum queue lengthis to determine the intersection of the queue-forming wave1199081198991119897119886119899119890 119894 and the queue-discharging wave 1199081198992 that is todetermine the moment at which the maximum queue lengthoccurs (119905119899119871max119897119886119899119890 119894) We determined this moment from thefollowing equations

119871119899119903119897119886119899119890 119894 + ROUND(119905119899119871max119897119886119899119890 1198945)sumℎ=ROUND(119905119899

119903119897119886119899119890 1198945)

51199081198991119897119886119899119890 119894 (5ℎ + 119905ℎ)= 119871119899max119897119886119899119890 119894

(28)

119871119899max119897119886119899119890 119894 = 1199081198992 (119905119899119871max119897119886119899119890 119894 minus 119905119899119903119897119886119899119890 119894) (29)

where1199081198992 = |(119902119898minus0)(119896119898minus119896119895)| = 119902119898(119896119895minus119896119898)We can derive(30) after simplifying (28) and (29)

ROUND(119905119899119871max119897119886119899119890 1198945)sumℎ=1

51199081198991119897119886119899119890 119894 (5ℎ + 119905)= 1199081198992 (119905119899119871max119897119886119899119890 119894 minus 119905119899119903119897119886119899119890 119894)

(30)

Using these equations 119905119899119871max119897119886119899119890 119894 can be obtained from (30)and 119871119899max119897119886119899119890 119894 can be calculated by substituting it into (29)

334 Residual Queue Length Calculation After the maxi-mum queue length appeared the queue dissipated at the

departure wave1199081198993 as shown in Figure 5 where the density infront of the stopline was 119896119898 Assuming that the tail end of themaximum queue began to move before the end of the greensignal the residual queue length (at intervals of 5 seconds)during the queue-discharging period can be determined bythe following equation

119871119899119889119894119904119897119886119899119890 119894 (5ℎ)= 119896119898(119871119899max119897119886119899119890 119894119896119898 minus ROUND(119905119899+1119892119897119886119899119890 1198945)sum

ℎ=ROUND(119905119899119871max1198971198861198991198901198945)

51199081198993 (5ℎ)) (31)

The time for queue clearance can be easily obtained by theequation 119871119899max119897119886119899119890 1198941199081198993 = 1199051198993 When 1199051198993 le 119905119899+1119892119897119886119899119890 119894 + 119905119899119903119897119886119899119890 119894 minus119905119899119871max119897119886119899119890 119894 there was no queue at the end of the green signalwhen 1199051198993 gt 119905119899+1119892119897119886119899119890 119894 + 119905119899119903119897119886119899119890 119894 minus 119905119899119871max119897119886119899119890 119894 it revealed a residualqueue 119871119899119903119890119897119886119899119890 119894 at the end of the green signal which can becalculated as follows

119871119899119903119890119897119886119899119890 119894= (119871119899max119897119886119899119890 119894 minus (119905119899+1119892119897119886119899119890 119894 + 119905119899119903119897119886119899119890 119894 minus 119905119899119871max119897119886119899119890 119894)1199081198993) 119896119898 (32)

When the residual queue existed the traffic was in anoversaturated state and the queue length could be predictedin real time by the residual queue length 119871119899119903119890119897119886119899119890 119894 and theprevious process which enabled us to design a signal controlstrategy to prevent queue overflow in advance

4 Numerical Experiments

41 Test Sites and Basic Data In the case study we selectedthe intersection of South Qilin Road and Wenchang Street(Qujing China) as the testing site The data collection timewas from 1500 to 1800 on October 31 2017 (Tuesday) inwhich 1500 to 1730 was the off-peak period and 1730 to1800 was the evening peak period Figure 6 shows the laneconfiguration of the intersection of the study area and the


North

Wes

t Nan

ning

Rd

Wes

t Nan

ning

Rd

South Qilin Rd

South Qilin Rd

Wen

chan

g St

W

ench

ang

St

Volume collection Site(at intervals of 5 seconds)

512m

Lane 1Lane 2Lane 3Camera A Camera B

North

Wes

t Nan

ning

Rd

Wen

chan

g St

South Qilin Rd

UpstreamIntersection

DownstreamIntersection

Study Area

(b)

(a)

Figure 6 (a) Aerial photograph of the study area (b) data collection site

layout of the data collection sites The upstream volumewas collected by Camera A and the proportion of lane-based downstream traffic volume was collected by Camera BFurthermore through Camera B we effectively validated theproposedmodel by observing the actual queue length Table 1shows the signal timing parameters at the intersection ofSouthQilinRoad andWenchang StreetThe yellow interval ofeach signal stage lasted 3 seconds there was no red clearanceinterval and right-turn vehicles were not controlled by trafficsignals The letters T and L represent through movement andleft-turn movement and E W N and S represent the east-bound approach the westbound approach the northboundapproach and the southbound approach respectively Table 2shows the fundamental parameters for model validation Weestimated the jam density using the equation 119896119895 = 1000ℎ119895where ℎ119895 is the average vehicle spacing in a stationary queuewhich according to field investigation is 64m

42 Calculation Results and Analysis We used the meanabsolute error (MAE) the mean absolute percentage error(MAPE) and the root mean square error (RMSE) to evaluatethe accuracy of the proposed model The MAE MAPE andRMSE are defined as follows

119872119860119864 = 1119898sum119898

|119874119887119904119890119903V119886119905119894119900119899 minus 119875119903119890119889119894119888119905119894119900119899| (33)

119872119860119875119864 = 1119898sum119898

10038161003816100381610038161003816100381610038161003816119874119887119904119890119903V119886119905119894119900119899 minus 119875119903119890119889119894119888119905119894119900119899119874119887119904119890119903V11988611990511989411990011989910038161003816100381610038161003816100381610038161003816 times 100 (34)

119877119872119878119864 = 1119898radic119898sum119898

(119874119887119904119890119903V119886119905119894119900119899 minus 119875119903119890119889119894119888119905119894119900119899)2 (35)

where119898 is the total number of intervals (a total of 28 intervalsfor prediction of the proportions of traffic volume) or cycles(a total of 48 cycles for queue length prediction) in thisexperiment

421 Prediction of the Proportions of Traffic Volume inEach Lane Figures 7(a)ndash7(c) show comparisons between thepredicted value (all lanes and single lane) and the observedvalue of the traffic volume proportions of lane 1 lane 2and lane 3 respectively The label ldquoall lanesrdquo means thatinformation from all lanes (including lane 1 lane 2 and lane3) in the first three intervals is used in the prediction of lane iwhereas ldquosingle lanerdquo means that only information from lane119894 in the first three intervals is used in the prediction of lane 119894As shown in Table 3 when using information from all lanesthe MAE MAPE and RMSE were lower than when usinginformation from a single lane meaning that it was necessaryto take all lane information into account when predictingtraffic flow proportions The average MAE (all lanes) andRMSE (all lanes) of each lane were close to three whichindicated that the average error of queue length prediction inthe proposedmodel did not exceed three vehicles and showedsatisfactory prediction accuracy In addition the MAE andRMSE of different lanes were close and showed no obviousdeviation which indicated that the calculation results of theproposed model were stable and reliable The overall average


ObservationPrediction (all lanes)Prediction (single lane)

0

005

01

015

02

025

03

154000 155500 161000 162500 164000 165500 171000 172500 174000 175500

Prop

ortio

ns o

f Tra

ffic V

olum

e

Time

Proportions of Traffic Volume Comparison (Lane 1 Left-turn movement)

(a) Proportions of traffic volume (Lane 1 left-turn movement)


03

035

04

045

05

055

154000 155500 161000 162500 164000 165500 171000 172500 174000 175500

Prop

ortio

ns o

f Tra

ffic V

olum

e

Time

Proportions of Traffic Volume Comparison (Lane 2 Through movement)

(b) Proportions of traffic volume (Lane 2 through movement)

03

035

04

045

05

055

154000 155500 161000 162500 164000 165500 171000 172500 174000 175500

Prop

ortio

ns o

f Tra

ffic V

olum

e

Time

Proportions of Traffic Volume Comparison (Lane 3 Through and right-turn movement)


(c) Proportions of traffic volume (Lane 3 through and right-turn move-ment)

Figure 7 Proportions of traffic volume (observed and predicted)

Table 1 The signal timing of the South Qilin Road-Wenchang Street intersection (downstream intersection)

Time interval (min) Time length of signal stage (s) Cycle (s)T and L of N T of N and S T and L of S T and L of E T and L of W

1540ndash1730 31 34 30 37 28 1601730ndash1740 40 45 37 37 43 2001740ndash1900 37 35 39 26 43 180

MAPE (all lanes) was 1033 which showed favorable predic-tion accuracy especially for lane 2 (652) and lane 3 (671)The averageMAPEof lane 1was the largest (1775)Themainreason was that the left-turn volume was lower than that ofthe other lanes and its observed traffic volume was relativelysmall which made the MAPE value increase however its

average MAE (243) showed that the prediction result wassatisfactory Furthermore as shown in Table 3 when usinginformation from a single lane (the previous method withthe Kalman filter) every MAE MAPE and RMSE was largerthan that of the other traditional prediction methods (singleexponential smoothing quadratic exponential smoothing


ObservationPrediction

0

2

4

6

8

10

12

14

16

18

Num

ber o

f Que

uing

Veh

icle

s

Time

Maximum Queue Length Comparison (Lane 1 Left Turn movement) 154652

160252

170132170712171217171732172257172807173442174217174827175427

160817161332161857162407162932163457164017164532165052165622

155212155737

(a) Maximum queue length comparison (Lane 1 left-turn movement)


0

5

10

15

20

25

30

Num

ber o

f Que

uing

Veh

icle

s

Time

Maximum Queue Length Comparison (Lane 2 Through movement)

154712

160317

170147170717171227171752172307172842173502174242174837175427

160832161357161907162422162957163537164027164542165102165627

155227155747

(b) Maximum queue length comparison (Lane 2 through movement)

0

5

10

15

20

25

30

Num

ber o

f Que

uing

Veh

icle

s

Time

Maximum Queue Length Comparison (Lane 3 Through and Right Turn movement)


154707

160317

170147170717171227171747172307172842173502174242174837175427

160832161347161902162422162957163517164027164527165102165612

155227155747

(c) Maximum queue length comparison (Lane 3 through and right-turnmovement)

Figure 8 Maximum queue length comparison

Table 2 Model parameters

Parameters Values Parameters ValuesV (119896119898ℎ) 28 119896119895 (V119890ℎ119896119898) 15625V119891 (119896119898ℎ) 50 119896119898 (V119890ℎ119896119898) 78125

and third-ordermoving average) however when using infor-mation from all lanes (the proposedmethod with the Kalmanfilter) every MAE MAPE and RMSE was the smallestof all the noted methods This further demonstrated theeffectiveness of the proposed method

422 Queue Length Predictions for Each Lane As shown inTable 4 the average MAE and RMSE of each lane was lessthan three which indicated that the average error of queue

length prediction in the proposed model showed satisfactoryprediction accuracy The average MAE of lane 3 was slightlyhigher than that of lane 1 and lane 2 because lane 3 wasthe through and right-turn lane and the right-turn vehicleswere not controlled by the signals Thus some of the right-turn vehicles would leave the intersection during the redsignal resulting in increased error However the overallaverage MAE was 182 less than 2 the overall average RMSEwas 233 less than 3 and the MAE and RMSE of differentlanes were close and showed no obvious deviation whichshowed that the calculation results of the proposed modelwere satisfactoryTheoverall averageMAPEwas 1612 closeto 15 and the average MAPE of lane 1 was the largest(2094) As when predicting the traffic volume proportionsthe main reason for this finding was that the left-turn volumewas the smallest and its observed queue length was relatively


Table 3 MAE MAPE and RMSE of the predictions of traffic volume proportion in each lane

Prediction methods Errors Lane 1 Lane 2 Lane 3 Average

Kalman filter

MAE (vehs)

All lanes (the proposed method) 243 237 225 235Single lane (the previous method) 336 328 274 313

Single exponential smoothing Single lane 315 298 246 286Quadratic exponential smoothing Single lane 278 277 231 262Third-order moving average Single lane 285 289 235 270

Kalman filter

MAPE ()



Kalman filter

RMSE (vehs)



Table 4 MAE MAPE and RMSE of maximum queue length

Errors Lane 1 Lane 2 Lane 3 Average(left-turn movement) (through movement) (through and right-turn movement)

MAE (vehs) 152 183 212 182MAPE () 2094 1128 1614 1612RMSE (vehs) 193 242 265 233

0

5

10

15

20

25

30

172317 172727 173137 173547 173957 174407 174817 175227 175637

Num

ber o

f Que

uing

Veh

icle

s

Time

Queue Trajectories

Lane 1

Lane 2

Lane 3

Figure 9 Queue trajectory

small which made the MAPE value increase However itcan be seen from its average MAE (152) that the predictionresult was better than that of the other lanes Overall Table 4shows that the proposed model performed very well in thecalculated results of all three lanes

Figures 8(a)ndash8(c) compare the predicted value and theobservation value of the maximum queue length of lane 1lane 2 and lane 3 respectively The queue length of the peakperiod (1730ndash1800) was greater than the queue length of the

off-peak period (1540ndash1730) as a whole Moreover becauseof the randomness and diversity of the vehicle arrivals thequeue length may show a sudden change at certain timessuch as the queue length near the moments 164017 and170712 in the off-peak period of lane 1 and the queue lengthnear the moment 163537 in lane 2 which was obviouslylarger than that at other off-peak times Figure 8 shows thatthe proposed model can predict the burst phenomenon ofqueue growth in advance and thus is convenient for theoptimization of predictive signal control

Figure 9 gives the queue length variation which showsthat the proposed model clearly described the process ofqueue formation and discharge The quadrilaterals depictedthe residual queue trajectory points in the queue dischargeprocess (at intervals of 5 seconds) Figures 10(a)ndash10(c) showtrajectories of the upstream section arrivals and the IQA oflane 1 lane 2 and lane 3 respectively Figure 10 shows thatthe queue length prediction at intervals of 5 seconds candynamically reflect the effect of different upstream turningflow releases on IQA (R T and R and L and R representthe right-turn flow the through and right-turn flow and theleft-turn and right-turn flow at the upstream intersectionrespectively) The IQAwas consistent with the dynamic trendof traffic flow The IQA when the upstream through flow wasreleased was obviously larger than the IQA when the othertraffic flows were released (see Table 5) This change couldprovide powerful support for the precise analysis of signalcontrol parameters for example in delay analysis [53]


0

02

04

06

08

1

12

14

0

1

2

3

4

5

6

7

8

9

T an

d R R R R

L an

d R R R R R

T an

d R

T an

d R

T an

d R R R R

L an

d R R R R

T an

d R

T an

d R

T an

d R R R R R

L an

d R R R R

T an

d R

T an

d R

T an

d R R R R

L an

d R

L an

d R

174002

174007 174057 174212 174307 174402 174517 174612 174707 174817 174912

IQA

(veh

5 s)

Valu

me o

f ups

trea

m d

ata

colle

ctio

n sit

e (ve

h5s

)

Time

IQA Trajectories (Lane 1 Left-turn movement)

Valume

IQA

(a) IQA trajectories (Lane 1 left-turn movement)

Valume

IQA

0

05

1

15

2

25

0

1

2

3

4

5

6

7

8

9

T an

d R R R R

L an

d R

L an

d R R R

T an

d R

T an

d R

T an

d R R R R R

L an

d R R R

T an

d R

T an

d R

T an

d R

T an

d R R R R

L an

d R

L an

d R R

T an

d R

T an

d R

T an

d R R R R

L an

d R

L an

d R

174002 174057 174217 174312 174407 174527 174622 174717 174847 174942

IQA

(veh

5 s)

Valu

me o

f ups

trea

m d

ata

colle

ctio

n si

te (v

eh5

s)

Time

IQA Trajectories (Lane 2 Through movement)

(b) IQA trajectories (Lane 2 through movement)

Valume

IQA

0

05

1

15

2

25

3

0

1

2

3

4

5

6

7

8

9

T an

d R R R R

L an

d R

L an

d R R R

T an

d R

T an

d R

T an

d R R R R R

L an

d R R R

T an

d R

T an

d R

T an

d R R R R R

L an

d R R R

T an

d R

T an

d R

T an

d R R R R

L an

d R

174002 174057 174217 174312 174407 174532 174627 174722 174852 174947

IQA

(veh

5 s)

Valu

me o

f ups

trea

m d

ata

colle

ctio

n si

te (v

eh5

s)

Time

IQA Trajectories (Lane 3 Through and right-turn movement)

(c) IQA trajectories (Lane 3 through and right-turn movement)

Figure 10 IQA trajectories

Table 5 Average IQA (veh5 seconds) under the influence of different upstream turning flows (period 1740ndash1750)

Upstream turning flow Lane 1 Lane 2 Lane 3(left-turn movement) (through Movement) (through and right-turn movement)

T and R 064 127 155L and R 020 045 054R 005 013 015

43 Discussion

431 Model Reliability and Sensitivity To further analyzethe stability and reliability of the model and the sensitivityof selecting initial conditions we analyzed the accuracy ofthe model by changing the V in Table 2 (in reality otherparameters are relatively fixed) As discussed in Section 31changing V is actually a change in the initial moment Thesurvey showed that 90 of the vehicles travel within a speedrange of 20 (119896119898ℎ) le V le 40 (119896119898ℎ) (excluding 5 low-speed vehicles and 5 high-speed vehicles respectively) sothe corresponding travel time was 46 s le 119905 le 92 s Inaccordance with the upstream data acquisition interval wechanged the initial moment at an interval of 5 seconds tocalculate the accuracy of queue length estimation As shownin Figure 11 and Table 6 when 60 s le 119905 le 75 s the average

MAE and RMSE of all lanes was less than 3 and the averageMAPE of all lanes was less 20 which showed that the resultsof the model were satisfactory in the range of 20 seconds(four 5-second intervals) when 119905 le 55 s and 119905 ge 80 s thecalculation error of the model increased gradually Thereforeit was evident that the calculation results of the model werestable and reliable in a certain range of initial parameters Atthe same time the calculation also reflected that the selectionof initial parameters had a significant impact on the accuracyof the model How to dynamically select the calculationparameters of the model is the next step to be improved

Inevitably a delay occurred between the observed andpredicted time of the model In the verification of themaximum queue length we predicted the maximum queuelength and its occurrence time by the proposed model andthe calculation error was compared with the actual maximum


Table 6 MAE MAPE and RMSE of maximum queue length for different travel times

Errors Travel time 119905 (s) Lane 1 Lane 2 Lane 3 Average(left-turn movement) (through movement) (through and right-turn movement)

MAE (vehs)

45 300 598 417 43850 233 448 360 34755 197 332 331 28760 202 269 201 22465 152 183 212 18270 171 240 216 20975 207 183 212 20180 226 281 292 26685 194 465 427 36290 268 530 523 440

MAPE ()

45 4068 3482 3000 351750 3170 2653 2616 281355 2702 1980 2405 236260 2732 1522 1580 194565 2094 1128 1614 161270 2358 1270 1895 184175 2850 1476 1560 196280 3077 1646 2158 229485 2659 2724 3070 281890 3630 3092 3744 3489

RMSE (vehs)

45 327 635 461 47450 269 485 416 39055 237 382 380 33360 239 334 243 27265 193 242 265 23370 215 279 307 26775 242 295 270 26980 261 329 342 31185 234 506 471 40490 298 568 565 477

queue length value without considering its occurrence time(which was consistent with the processing method of Liu etal [10]) By comparing the time of maximum queue lengthbetween the predicted value and the observed value we foundthat within 60 s le 119905 le 75 s the average time differencebetween the two was less than three 5-second intervals (15seconds) which indicated that model accuracy would not beaffected when the average error between the observed timeand the predicted time was within three intervals

432 The Real-Time and Proactivity of the Model We tookthe maximum queue prediction value at 154707 of lane 3as an example As shown in Figure 12 during this signalcycle the red time was 129 seconds 1199050119871max119897119886119899119890 119894 minus 1199050119903119897119886119899119890 119894is 12 seconds and according to Section 31 the predictedadvance interval (119905) of the queue length was 65 seconds(V = 28 119896119898ℎ) Furthermore the initial moment of queuelength prediction was 154341 and the red time started at154446 (the initial moment of queue length observation)

In the 154341ndash154446 interval (65 seconds) we obtainedthe historical data of upstream section A to estimate thedownstream arrival and at that time the acquisition time ofthe data of upstream sectionA lagged behind the downstreamarrival estimation time After 154446 the upstream datacould be acquired in real time with 5-second intervalsand the downstream queue could be predicted Translatingthe dotted line at 154341 with 119905(65 s) to the predicted119871119899max119897119886119899119890 119894 clearly showed that the maximum queue length waspredicted in advance of 65 seconds at 154602 which fullydemonstrated the proactivity of the model

5 Conclusion

In this paper we used LWR shockwave theory and Robert-sonrsquos model to establish a real-time prediction model oflane-based queue length which effectively predicted queuelength (including IQA queue trajectory maximum queueand residual queue)This model is convenient for the optimal


40 45 50 55 60 65 70 75 80 85 90 95Travel time (s)

MAE (veh)RMSE (veh)MAPE ()

0

1

2

3

4

5

6ve

h

0

5

10

15

20

25

30

35

40

Figure 11 Average MAE MAPE and RMSE of maximum queuelength at different travel times

design of predictive signal control In the proposed modelvehicle arrival was described with an interval of 5 seconds inRobertsonrsquos model In this way we described the formationand dissipation of queue length in real time and dynami-cally described the influence of different upstream vehiclesarriving from disparate turning lanes on IQA In additionthe model predicted the queue length of multiple lanes atthe same time by predicting the proportion of traffic volumeusing the Kalman filter The computational complexity ofthe model was relatively low and it was convenient forengineering and design

Several directions for future research can be summarizedas follows

(1) Lane-changing phenomenon This paper assumedthat vehicle lane changing had no effect on vehiclearrival characteristics However research has shownthat when the vehicle lane-changing phenomenonwas prominent the vehicle running state was dis-turbed [20 54]Therefore analyzing the effect of lanechanging on queue length prediction is a promisingresearch direction

(2) Arrival effect of heterogeneous traffic flow When thebus occupied a large proportion of the lane the travelcharacteristics of the bus (such as passengers slowerspeed relative to cars and so on) interfered withcar travel and affected the travel time distributionand formation and dissipation of traffic waves [55]Thus another important research direction is to studythe queue length under the arrival characteristics ofheterogeneous traffic flow

(3) Dynamic correction of travel time In this paper thetravel time of Robertsonrsquos model was fixed but thetravel time will be different according to the change ofthe traffic flow Another research direction will be tooptimize and perfect this model while incorporating

the short-term prediction of travel time for probevehicles

Appendix

A Analysis of the Necessity of Assumptions

A1 The Vehicle Follows the First-In-First-Out (FIFO) Prin-ciple and There Is no Obvious Overtaking Phenomenon Inthe queue-discharging process of a cycle a free-flow vehiclecannot depart ahead of any queued vehicle a normallyqueued vehicle cannot depart ahead of any oversaturatedvehicle This can be ensured if the principle of first-in-first-out (FIFO) is satisfied In a real-world situation FIFO can beviolated if overtaking is frequent (eg if multiple lanes exist)[24] which provides no guarantee that IQA changes followthe FIFO principle so the assumption is made to ensure thereasonableness of IQA analysis

A2 The Vehicle Has the Same Acceleration and DecelerationBehavior Differences between drivers and vehicles will causedifferences in vehicle acceleration and deceleration In thiscase the complexity of traffic wave analysis will be increasedand the fundamental diagram (FD) cannot be guaranteedto be a triangle form [55] Because we used triangular FDto analyze the evolution of traffic waves it was necessaryto assume the consistency of acceleration and decelerationbehavior

A3 The Influence of Buses on Traffic Flow Is DisregardedBecause of significant differences in arrival characteristicsbetween cars and buses when the percentage of buses is large(eg above 10 [46]) there will be an obvious influenceon the discrete characteristics of traffic flow [46 56] butRobertsonrsquos model (taking homogeneous traffic flow as theobject of study) cannot describe these characteristics wellTherefore we ignored the influence of buses in this paperIn addition queue estimation in a heterogeneous traffic flowenvironment is another topic of the authorsrsquo current researchwhich will be discussed in a subsequent paper

Data Availability

The survey and analytical data used to support the findings ofthis study are included within the article and the supplemen-tary information files

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China [Grant no 61364019] and the KeyLaboratory of Urban ITS Technology Optimization andIntegration Ministry of Public Security of China [Grant no2017KFKT04]


l


Upstream site A

Downstream site B

Upstream dataacquisition time154446154341 154707

Observation

Prediction

Historicaldata Real-time data

12 s129 s

154602

t0g lane i

t0g lane i

t1g lane i

t1g lane i

t2g lane it0r lane i

t0r lane i

t1r lane i

t1r lane i

t (65 s)

t(65 s)

L0ＧＲ lane i

L0ＧＲ lane i

t0L ＧＲ lane i

Figure 12 Queue length real-time prediction process (Lane 3)

Supplementary Materials

See Tables S1-S6 in the Supplementary Materials for compre-hensive data analysis (Supplementary Materials)

References

[1] K N Balke and H Charara ldquoDevelopment of a traffic signalperformance measurement system (tspms)rdquo Texas Transporta-tion Institute College Station Tx vol 42 no 3 pp 546ndash556 2005

[2] I D Neilson ldquoResearch at the Road Research Laboratory intothe Protection of Car Occupantsrdquo in Proceedings of the 11thStapp Car Crash Conference (1967)

[3] G F Newell ldquoApproximation methods for queues with applica-tion to the fixed-cycle traffic lightrdquo SIAM Review vol 7 no 2pp 223ndash240 1965

[4] T Chang and J Lin ldquoOptimal signal timing for an oversaturatedintersectionrdquo Transportation Research Part B Methodologicalvol 34 no 6 pp 471ndash491 2000

[5] P B Mirchandani and Z Ning ldquoQueuingmodels for analysis oftraffic adaptive signal controlrdquo IEEE Transactions on IntelligentTransportation Systems vol 8 no 1 pp 50ndash59 2007

[6] X Zhan R Li and S V Ukkusuri ldquoLane-based real-time queuelength estimation using license plate recognition datardquo Trans-portation Research Part C Emerging Technologies vol 57 pp 85ndash102 2015

[7] M Zanin S Messelodi andCMModena ldquoAn efficient vehiclequeue detection system based on image processingrdquo in Proceed-ings of the 12th International Conference on Image Analysis andProcessing ICIAP 2003 pp 232ndash237 Italy September 2003

[8] R K Satzoda S Suchitra T Srikanthan and J Y Chia ldquoVision-based vehicle queue detection at traffic junctionsrdquo in Proceed-ings of the 2012 7th IEEEConference on Industrial Electronics andApplications ICIEA 2012 pp 90ndash95 Singapore July 2012

[9] Y Yao K Wang and G Xiong ldquoVision-based vehicle queuelength detection method and embedded platformrdquo Big Dataand Smart Service Systems pp 1ndash13 2016

[10] H X Liu X Wu W Ma and H Hu ldquoReal-time queue lengthestimation for congested signalized intersectionsrdquo Transporta-tion Research Part C Emerging Technologies vol 17 no 4 pp412ndash427 2009

[11] X J Ban PHao and Z Sun ldquoReal time queue length estimationfor signalized intersections using travel times frommobile sen-sorsrdquo Transportation Research Part C Emerging Technologiesvol 19 no 6 pp 1133ndash1156 2011

[12] R Akcelik ldquoProgression factor for queue length and otherqueue-related statisticsrdquo Transportation Research Record no1555 pp 99ndash104 1997

[13] A Sharma D M Bullock and J A Bonneson ldquoInput-outputand hybrid techniques for real-time prediction of delay andmaximumqueue length at signalized intersectionsrdquoTransporta-tion Research Record no 2035 pp 69ndash80 2007

[14] G Vigos M Papageorgiou and Y Wang ldquoReal-time estima-tion of vehicle-count within signalized linksrdquo TransportationResearch Part C Emerging Technologies vol 16 no 1 pp 18ndash352008

[15] M J Lighthill and G B Whitham ldquoOn kinematic waves IIA theory of traffic flow on long crowded roadsrdquo Proceedingsof the Royal Society A Mathematical Physical and EngineeringSciences vol 229 pp 317ndash345 1955

[16] P I Richards ldquoShock waves on the highwayrdquo OperationsResearch vol 4 no 1 pp 42ndash51 1956

[17] G Stephanopoulos P G Michalopoulos and G Stephanopou-los ldquoModelling and analysis of traffic queue dynamics at signal-ized intersectionsrdquoTransportation Research Part A General vol13 no 5 pp 295ndash307 1979

[18] A Skabardonis andN Geroliminis ldquoReal-timemonitoring andcontrol on signalized arterialsrdquo Journal of Intelligent Transporta-tion Systems Technology Planning and Operations vol 12 no2 pp 64ndash74 2008


[19] G Comert ldquoEffect of stop line detection in queue lengthestimation at traffic signals from probe vehicles datardquo EuropeanJournal of Operational Research vol 226 no 1 pp 67ndash76 2013

[20] S Lee S C Wong and Y C Li ldquoReal-time estimation of lane-based queue lengths at isolated signalized junctionsrdquo Trans-portation Research Part C Emerging Technologies vol 56 pp1ndash17 2015

[21] G Comert ldquoQueue length estimation from probe vehiclesat isolated intersections estimators for primary parametersrdquoEuropean Journal of Operational Research vol 252 no 2 pp502ndash521 2016

[22] H Xu J Ding Y Zhang and J Hu ldquoQueue length estimation atisolated intersections based on intelligent vehicle infrastructurecooperation systemsrdquo in Proceedings of the 28th IEEE IntelligentVehicles Symposium IV 2017 pp 655ndash660 IEEE Los AngelesCA USA June 2017

[23] N J Goodall B Park and B L Smith ldquoMicroscopic Estimationof Arterial Vehicle Positions in a Low-Penetration-Rate Con-nected Vehicle Environmentrdquo Journal of Transportation Engi-neering vol 140 no 10 p 04014047 2014

[24] P Hao and X Ban ldquoLong queue estimation for signalizedintersections using mobile datardquo Transportation Research PartB Methodological vol 82 pp 54ndash73 2015

[25] N Geroliminis and A Skabardonis ldquoPrediction of arrivalprofiles and queue lengths along signalized arterials by using amarkov decision processrdquo Transportation Research Record vol1934 no 1 pp 116ndash124 2005

[26] TRB ldquoTransportation Research Boardrdquo Highway CapacityManual National Research Council Washington DC USA2010

[27] L B de Oliveira and E Camponogara ldquoMulti-agent modelpredictive control of signaling split in urban traffic networksrdquoTransportation Research Part C Emerging Technologies vol 18no 1 pp 120ndash139 2010

[28] B Asadi and A Vahidi ldquoPredictive cruise control utilizingupcoming traffic signal information for improving fuel econ-omy and reducing trip timerdquo IEEE Transactions on ControlSystems Technology vol 19 no 3 pp 707ndash714 2011

[29] C Portilla F Valencia J Espinosa A Nunez and B De Schut-ter ldquoModel-based predictive control for bicycling in urbanintersectionsrdquo Transportation Research Part C Emerging Tech-nologies vol 70 pp 27ndash41 2016

[30] S Coogan C Flores and P Varaiya ldquoTraffic predictive controlfrom low-rank structurerdquoTransportation Research Part BMeth-odological vol 97 pp 1ndash22 2017

[31] L Shen R Liu Z Yao W Wu and H Yang ldquoDevelopmentof Dynamic Platoon Dispersion Models for Predictive TrafficSignal Controlrdquo IEEE Transactions on Intelligent TransportationSystems pp 1ndash10

[32] P Mirchandani and L Head ldquoA real-time traffic signal controlsystem architecture algorithms and analysisrdquo TransportationResearch Part C Emerging Technologies vol 9 no 6 pp 415ndash432 2001

[33] R E Kalman ldquoA new approach to linear filtering and predictionproblemsrdquo Journal of Fluids Engineering vol 82 no 1 pp 35ndash451960

[34] J Guo W Huang and B M Williams ldquoAdaptive Kalman filterapproach for stochastic short-term traffic flow rate predictionanduncertainty quantificationrdquoTransportation Research Part CEmerging Technologies vol 43 pp 50ndash64 2014

[35] S Carrese E Cipriani L Mannini and M Nigro ldquoDynamicdemand estimation and prediction for traffic urban networksadopting new data sourcesrdquo Transportation Research Part CEmerging Technologies vol 81 pp 83ndash98 2017

[36] L Lin J C Handley Y Gu L Zhu X Wen and A W SadekldquoQuantifying uncertainty in short-term traffic prediction andits application to optimal staffing plan developmentrdquo Trans-portation Research Part C Emerging Technologies vol 92 pp323ndash348 2018

[37] R A Vincent A I Mitchell and D I Robertson ldquoUser guideto transty version 8rdquo in Proceedings of the User guide to transtyversion 8 1980

[38] P G Michalopoulos and V Pisharody ldquoPlatoon Dynamics onSignal Controlled Arterialsrdquo Transportation Science vol 14 no4 pp 365ndash396 1980

[39] P DellrsquoOlmo and P BMirchandani ldquoRealband an approach forreal-time coordination of traffic flows on networksrdquoTransporta-tion Research Record no 1494 pp 106ndash116 1995

[40] J A Bonneson M P Pratt and M A Vandehey ldquoPredictingarrival flow profiles and platoon dispersion for urban streetsegmentsrdquo Transportation Research Record vol 2173 pp 28ndash352010

[41] A F Rumsey and M G Hartley ldquoSimulation of A Pair ofIntersectionsrdquoTraffic Engineering and Control vol 13 no 11-12pp 522ndash525 1972

[42] D I Robertson ldquoTransyt a traffic network study toolrdquo TechRep Road Research Laboratory 1969

[43] S C Wong W T Wong C M Leung and C O TongldquoGroup-based optimization of a time-dependent TRANSYTtraffic model for area traffic controlrdquo Transportation ResearchPart B Methodological vol 36 no 4 pp 291ndash312 2002

[44] M Farzaneh and H Rakha ldquoProcedures for calibrating TRAN-SYT platoon dispersion modelrdquo Journal of Transportation Engi-neering vol 132 no 7 pp 548ndash554 2006

[45] Y Bie Z Liu D Ma and D Wang ldquoCalibration of platoondispersion parameter considering the impact of the number oflanesrdquo Journal of Transportation Engineering vol 139 no 2 pp200ndash207 2013

[46] Y Wang X Chen L Yu and Y Qi ldquoCalibration of the PlatoonDispersionModel by Considering the Impact of the Percentageof Buses at Signalized Intersectionsrdquo Transportation ResearchRecord vol 2647 no 1 pp 93ndash99 2018

[47] W Wey and R Jayakrishnan ldquoNetwork Traffic Signal Opti-mization Formulation with Embedded Platoon DispersionSimulationrdquo Transportation Research Record vol 1683 pp 150ndash159 1999

[48] L Yu ldquoCalibration of platoon dispersion parameters on thebasis of link travel time statisticsrdquo Transportation ResearchRecord vol 1727 pp 89ndash94 2000

[49] Y Jiang Z Yao X Luo W Wu X Ding and A KhattakldquoHeterogeneous platoon flow dispersion model based on trun-cated mixed simplified phase-type distribution of travel speedrdquoJournal ofAdvancedTransportation vol 50 no 8 pp 2160ndash21732016

[50] M G H Bell ldquoThe estimation of origin-destinationmatrices byconstrained generalised least squaresrdquo Transportation ResearchPart B Methodological vol 25 no 1 pp 13ndash22 1991

[51] C F Daganzo ldquoThe cell transmission model a dynamic repre-sentation of highway traffic consistent with the hydrodynamictheoryrdquoTransportation Research Part B Methodological vol 28no 4 pp 269ndash287 1994


[52] C F Daganzo ldquoThe cell transmission model part II networktrafficrdquo Transportation Research Part B Methodological vol 29no 2 pp 79ndash93 1995

[53] S Lee and S C Wong ldquoGroup-based approach to predictivedelay model based on incremental queue accumulations foradaptive traffic control systemsrdquo Transportation Research PartB Methodological vol 98 pp 1ndash20 2017

[54] J A Laval andC FDaganzo ldquoLane-changing in traffic streamsrdquoTransportation Research Part B Methodological vol 40 no 3pp 251ndash264 2006

[55] Z (Sean) Qian J Li X Li M Zhang and H Wang ldquoModelingheterogeneous traffic flow A pragmatic approachrdquo Transporta-tion Research Part B Methodological vol 99 pp 183ndash204 2017

[56] W Wu L Shen W Jin and R Liu ldquoDensity-based mixedplatoon dispersion modelling with truncated mixed Gaussiandistribution of speedrdquo Transportmetrica B vol 3 no 2 pp 114ndash130 2015

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researchers take isolated intersections as the research subjectto establish their queue length estimation model [19ndash22] Itis usually assumed that the vehicle arrives from a uniformtraffic distribution [11 19ndash21] Intersections in real roadnetworks often are not isolated however and downstreamvehicle arrival is often closely related to upstream vehiclerelease characteristics flow rate and travel time [25 26]Theuniform distribution of vehicles cannot accurately describethe dispersed characteristics of vehicle arrival nor can itdescribe the real-time attributes of the arrival of vehicles withdisparate characteristics of queue lengthHow to describe thisdisparity is a primary focus of this paper

The third category is the prediction of queue length Withthe improvement of traffic control requirements predictivetraffic signal control has become a developing trend whichrelies on the ability to obtain relevant parameters of trafficcontrol in advance [27ndash31]Therefore the prediction of queuelength is essential for predictive control optimization Theresearch on queue length prediction is scarce Hao and Ban[24] usedmobile data to estimate queue length and noted thatqueue length prediction is the direction of future researchRHODES [32] and Sharma et al [13] predicted vehicle arrivaland release rate using conventional input-output and queuelength estimations Akcelik [12] modified the parameters ofthe Highway Capacity Manual queue estimation model bystatistical analysis and established a queue length predictionmodel This model however cannot describe the spatialdistribution and evolution of queue length nor is it suitablefor prediction of queue length at oversaturated intersectionsGeroliminis and Skabardonis [25] combined platoon disper-sion characteristics and LighthillndashWhithamndashRichards (LWR)theory to predict queue length effectively but the modelconsiders only the maximum queue and it cannot describethe evolution of the queue in real time or analyze the dynamiceffects of different upstream turning flowon the queue lengthIn addition this model cannot simultaneously predict thequeue length of multiple lanes at the same time

To overcome the shortcomings of previous studies inwhich vehicle arrival was assumed to be uniformly dis-tributed and the evolutionary process of queue length couldnot be described we combined the advantages of traffic wavetheory and the platoon dispersion model to analyze vehiclearrival We predicted the queue length in real time andobtained changes in queue length in advance which providedsupport for predictive traffic signal optimization

This study makes the following contributions

(1) We obtained the upstream different turning flows inreal time at intervals of 5 seconds and fully consideredthe discrete characteristics of the vehicle to predictdownstream vehicle arrival which overcame the lim-itation of the uniform arrival assumption in previousresearch on queue length estimation

(2) The proposed model predicted the lane-based queuelength in real timemdashthe prediction included incre-mental queue accumulation (IQA) queue trajectorymaximum queue and residual queue which over-came the shortcomings of previous research thatcould not obtain the evolution trend of queuing in

advance and we determined the specific predictedadvance interval of the queue length depends on thetravel time between upstream intersection and down-stream intersection This was a convenient way tomake an optimal strategy of proactive signal control

(3) The proposed model obtained the influence of thedifferent upstream turning flows on downstream IQAin real time and the relationship between upstreamand downstream intersections was enhanced whichwas helpful for fine signal coordination optimizationdesign

(4) The prediction of the proportions of traffic volume ineach lane provided the basis for prediction of lane-based queue lengths To improve accuracy in predict-ing the lane-based traffic proportion while using theKalman filter we used the information of all lanesat the first three intervals in the prediction of lane119894 In the previous method however the researchersused only the information of lane 119894 at the first threeintervals in the prediction of lane i

The remainder of this paper is organized as follows InSection 2 we introduce the assumptions made and termi-nology used in this paper and provide the simplified queue-forming and queue-discharging process Section 3 presentsmodels to predict the proportion of lane-based traffic volumeand the real-time queue length The model is then testedusing field data in Section 4 Finally Section 5 summarizesthe findings and provides directions for future work

2 Preliminaries

In this section we provide the assumptions for deriving thequeue length prediction model some terminology defini-tions and a simplified queue-forming and queue-dischargingprocess

21 Assumptions Wemake the following assumptions

(1) The vehicle follows the first-in-first-out (FIFO) prin-ciple and there is no obvious overtaking phe-nomenon

(2) The vehicle has the same acceleration and decelera-tion behavior

(3) The influence of buses on traffic flow is disregarded

The necessity for these assumptions is explained in AppendixA

22 Terminology In this paper real-time queue length isdefined as the number of vehicles queuing at any given time

23 Simplified Queue-Forming and Queue-Discharging Pro-cess On the basis of these assumptions the queue-formingand queue-discharging process can be described as shownin Figure 1(b) The triangular fundamental diagram for con-structing this process is shown in Figure 1(a) In these figures0 and 119896119895 are jam volume and jam density 119902119898 and 119896119898 aresaturation volume and optimal density 119902119899119889119897119886119899119890 119894(5ℎ + 119905) and


Flow

Density

wn3

wn3

qm

km kj

(0 kj)

wn1 lane i

qnd lane i (5ℎ+t)

d lane ikn (5ℎ+t)





A

B

CD

l


tnL ＧＲ lane i

wn1 lane i

wn4

wn3wn

2


Lnre lane iLn

ＧＲ lane iLn

r lane i




1199081198991119897119886119899119890 119894 = 10038161003816100381610038161003816100381610038161003816100381610038160 minus 119902119899119889119897119886119899119890 119894 (5ℎ + 119905)119896119895 minus 119896119899119889119897119886119899119890 119894 (5ℎ + 119905)

1003816100381610038161003816100381610038161003816100381610038161003816= 119902119899119889119897119886119899119890 119894 (5ℎ + 119905)119896119895 minus 119896119899119889119897119886119899119890 119894 (5ℎ + 119905)

(1)

1199081198992 = 1003816100381610038161003816100381610038161003816100381610038161003816119902119898 minus 0119896119898 minus 119896119895

1003816100381610038161003816100381610038161003816100381610038161003816 =119902119898119896119895 minus 119896119898 (2)

1199081198993 = 1003816100381610038161003816100381610038161003816100381610038161003816119902119898 minus 119902119899119889119897119886119899119890 119894 (5ℎ + 119905)119896119898 minus 119896119899119889119897119886119899119890 119894 (5ℎ + 119905)

1003816100381610038161003816100381610038161003816100381610038161003816 =119902119898119896119898 (3)

1199081198994 = 10038161003816100381610038161003816100381610038161003816100381610038160 minus 119902119898119896119898 minus 119896119895

1003816100381610038161003816100381610038161003816100381610038161003816 = 1199081198992 (4)



North

Wes

t Nan

ning

Rd

Wes

t Nan

ning

Rd

South Qilin Rd

Wes

t Nan

ning

Rd

South Qilin Rd

South Qilin Rd

South Qilin Rd

Wen

chan

g St

Wen

chan

g St

W

ench

ang

St

512m

Upstream site A

Upstream site A


Firstvehicle

(advanced)

Downstream site B

Downstream site B


South Qilin Rd

(Current state)

(Advanced state)

(Predicted state)

t










119901119899|119899minus1119889119897119886119899119890 119894= 119872sum119894=1


(5)

where 119901119899|119899minus1119889119897119886119899119890 119894
















matrix 1198701|0119897119886119899119890 119894








(10)












119901119899|119899minus1119889119897119886119899119890 119894 = 119862119899119889119897119886119899119890 119894119883119899|119899minus1119889119897119886119899119890 119894 (16)















119902119899119889 (119909 + 119905) = 11 + 1205721199051199021198990 (119909)+ (1 minus 11 + 120572119905) 119902119899119889 (119909 + 119905 minus 1)

(18)


120572

=


(19)

119906 = 36001198761198941003816100381610038161003816119879ℎ119894 minus 1198791199051198941003816100381610038161003816 (20)

119904 = 119873119878119886119894 (21)




(22)






l

tnL ＧＲ lane i

wn4

wn3wn

1 lane i wn2


Lnre lane i

Lnf Part 1 lane i

Lnf Part 2 lane i

LnＧＲ lane i

Lnr lane i


Upstream site A

Upstream cells

Downstream site B


Wes

t Nan

ning

Rd


Wen

chan

g St

North




wn1 lane i (5ℎ+t)

(0 kj)



1199081198991119897119886119899119890 119894 (5ℎ + 119905) = 119902119899119889119897119886119899119890 119894 (5ℎ + 119905)119896119895 minus 119896119899119889119897119886119899119890 119894 (5ℎ + 119905) (23)


1198711198995ℎ119897119886119899119890 119894 = 5119902119899119889119897119886119899119890 119894 (5ℎ + 119905)119896119895 minus 119896119899119889119897119886119899119890 119894 (5ℎ + 119905) (24)



119905ℎ = 08119905 119897 minus sum119898ℎ=1 1198711198995ℎ119897119886119899119890 119894119897 (25)



(26)




l

tnL ＧＲ lane i


LnＧＲ lane i

Lnr lane i

Lnre lane i

wn2

wn3 wn

3

wn4

wn1 lane i

(qm km)



119871119899119903119897119886119899119890 119894 = ROUND(1199051198991199031198971198861198991198901198945)sumℎ=1

51199081198991119897119886119899119890 119894 (5ℎ + 119905ℎ)= ROUND(119905119899119903119897119886119899119890 1198945)sum

ℎ=1

5119902119899119889119897119886119899119890 119894 (5ℎ + 119905ℎ)119896119895 minus 119896119899119889119897119886119899119890 119894 (5ℎ + 119905ℎ) (27)



119903119897119886119899119890 1198945)

51199081198991119897119886119899119890 119894 (5ℎ + 119905ℎ)= 119871119899max119897119886119899119890 119894

(28)

119871119899max119897119886119899119890 119894 = 1199081198992 (119905119899119871max119897119886119899119890 119894 minus 119905119899119903119897119886119899119890 119894) (29)


ROUND(119905119899119871max119897119886119899119890 1198945)sumℎ=1

51199081198991119897119886119899119890 119894 (5ℎ + 119905)= 1199081198992 (119905119899119871max119897119886119899119890 119894 minus 119905119899119903119897119886119899119890 119894)

(30)





ℎ=ROUND(119905119899119871max1198971198861198991198901198945)

51199081198993 (5ℎ)) (31)







North

Wes

t Nan

ning

Rd

Wes

t Nan

ning

Rd

South Qilin Rd

South Qilin Rd

Wen

chan

g St

W

ench

ang

St


512m


North

Wes

t Nan

ning

Rd

Wen

chan

g St

South Qilin Rd



Study Area

(b)

(a)




119872119860119864 = 1119898sum119898

|119874119887119904119890119903V119886119905119894119900119899 minus 119875119903119890119889119894119888119905119894119900119899| (33)

119872119860119875119864 = 1119898sum119898

10038161003816100381610038161003816100381610038161003816119874119887119904119890119903V119886119905119894119900119899 minus 119875119903119890119889119894119888119905119894119900119899119874119887119904119890119903V11988611990511989411990011989910038161003816100381610038161003816100381610038161003816 times 100 (34)

119877119872119878119864 = 1119898radic119898sum119898

(119874119887119904119890119903V119886119905119894119900119899 minus 119875119903119890119889119894119888119905119894119900119899)2 (35)





0

005

01

015

02

025

03

154000 155500 161000 162500 164000 165500 171000 172500 174000 175500

Prop

ortio

ns o

f Tra

ffic V

olum

e

Time




03

035

04

045

05

055

154000 155500 161000 162500 164000 165500 171000 172500 174000 175500

Prop

ortio

ns o

f Tra

ffic V

olum

e

Time



03

035

04

045

05

055

154000 155500 161000 162500 164000 165500 171000 172500 174000 175500

Prop

ortio

ns o

f Tra

ffic V

olum

e

Time












0

2

4

6

8

10

12

14

16

18

Num

ber o

f Que

uing

Veh

icle

s

Time


160252

170132170712171217171732172257172807173442174217174827175427

160817161332161857162407162932163457164017164532165052165622

155212155737



0

5

10

15

20

25

30

Num

ber o

f Que

uing

Veh

icle

s

Time


154712

160317

170147170717171227171752172307172842173502174242174837175427

160832161357161907162422162957163537164027164542165102165627

155227155747


0

5

10

15

20

25

30

Num

ber o

f Que

uing

Veh

icle

s

Time



154707

160317

170147170717171227171747172307172842173502174242174837175427

160832161347161902162422162957163517164027164527165102165612

155227155747











Kalman filter

MAE (vehs)



Kalman filter

MAPE ()



Kalman filter

RMSE (vehs)






0

5

10

15

20

25

30

172317 172727 173137 173547 173957 174407 174817 175227 175637

Num

ber o

f Que

uing

Veh

icle

s

Time

Queue Trajectories

Lane 1

Lane 2

Lane 3







0

02

04

06

08

1

12

14

0

1

2

3

4

5

6

7

8

9

T an

d R R R R

L an

d R R R R R

T an

d R

T an

d R

T an

d R R R R

L an

d R R R R

T an

d R

T an

d R

T an

d R R R R R

L an

d R R R R

T an

d R

T an

d R

T an

d R R R R

L an

d R

L an

d R

174002

174007 174057 174212 174307 174402 174517 174612 174707 174817 174912

IQA

(veh

5 s)

Valu

me o

f ups

trea

m d

ata

colle

ctio

n sit

e (ve

h5s

)

Time


Valume

IQA


Valume

IQA

0

05

1

15

2

25

0

1

2

3

4

5

6

7

8

9

T an

d R R R R

L an

d R

L an

d R R R

T an

d R

T an

d R

T an

d R R R R R

L an

d R R R

T an

d R

T an

d R

T an

d R

T an

d R R R R

L an

d R

L an

d R R

T an

d R

T an

d R

T an

d R R R R

L an

d R

L an

d R

174002 174057 174217 174312 174407 174527 174622 174717 174847 174942

IQA

(veh

5 s)

Valu

me o

f ups

trea

m d

ata

colle

ctio

n si

te (v

eh5

s)

Time



Valume

IQA

0

05

1

15

2

25

3

0

1

2

3

4

5

6

7

8

9

T an

d R R R R

L an

d R

L an

d R R R

T an

d R

T an

d R

T an

d R R R R R

L an

d R R R

T an

d R

T an

d R

T an

d R R R R R

L an

d R R R

T an

d R

T an

d R

T an

d R R R R

L an

d R

174002 174057 174217 174312 174407 174532 174627 174722 174852 174947

IQA

(veh

5 s)

Valu

me o

f ups

trea

m d

ata

colle

ctio

n si

te (v

eh5

s)

Time






T and R 064 127 155L and R 020 045 054R 005 013 015

43 Discussion







MAE (vehs)

45 300 598 417 43850 233 448 360 34755 197 332 331 28760 202 269 201 22465 152 183 212 18270 171 240 216 20975 207 183 212 20180 226 281 292 26685 194 465 427 36290 268 530 523 440

MAPE ()

45 4068 3482 3000 351750 3170 2653 2616 281355 2702 1980 2405 236260 2732 1522 1580 194565 2094 1128 1614 161270 2358 1270 1895 184175 2850 1476 1560 196280 3077 1646 2158 229485 2659 2724 3070 281890 3630 3092 3744 3489

RMSE (vehs)

45 327 635 461 47450 269 485 416 39055 237 382 380 33360 239 334 243 27265 193 242 265 23370 215 279 307 26775 242 295 270 26980 261 329 342 31185 234 506 471 40490 298 568 565 477




5 Conclusion



40 45 50 55 60 65 70 75 80 85 90 95Travel time (s)


0

1

2

3

4

5

6ve

h

0

5

10

15

20

25

30

35

40








Appendix





Data Availability




Acknowledgments



l


Upstream site A

Downstream site B


Observation

Prediction


12 s129 s

154602

t0g lane i

t0g lane i

t1g lane i

t1g lane i


t0r lane i

t1r lane i

t1r lane i

t (65 s)

t(65 s)

L0ＧＲ lane i

L0ＧＲ lane i

t0L ＧＲ lane i




References





























































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Flow

Density

wn3

wn3

qm

km kj

(0 kj)

wn1 lane i

qnd lane i (5ℎ+t)

d lane ikn (5ℎ+t)





A

B

CD

l


tnL ＧＲ lane i

wn1 lane i

wn4

wn3wn

2


Lnre lane iLn

ＧＲ lane iLn

r lane i




1199081198991119897119886119899119890 119894 = 10038161003816100381610038161003816100381610038161003816100381610038160 minus 119902119899119889119897119886119899119890 119894 (5ℎ + 119905)119896119895 minus 119896119899119889119897119886119899119890 119894 (5ℎ + 119905)

1003816100381610038161003816100381610038161003816100381610038161003816= 119902119899119889119897119886119899119890 119894 (5ℎ + 119905)119896119895 minus 119896119899119889119897119886119899119890 119894 (5ℎ + 119905)

(1)

1199081198992 = 1003816100381610038161003816100381610038161003816100381610038161003816119902119898 minus 0119896119898 minus 119896119895

1003816100381610038161003816100381610038161003816100381610038161003816 =119902119898119896119895 minus 119896119898 (2)

1199081198993 = 1003816100381610038161003816100381610038161003816100381610038161003816119902119898 minus 119902119899119889119897119886119899119890 119894 (5ℎ + 119905)119896119898 minus 119896119899119889119897119886119899119890 119894 (5ℎ + 119905)

1003816100381610038161003816100381610038161003816100381610038161003816 =119902119898119896119898 (3)

1199081198994 = 10038161003816100381610038161003816100381610038161003816100381610038160 minus 119902119898119896119898 minus 119896119895

1003816100381610038161003816100381610038161003816100381610038161003816 = 1199081198992 (4)



North

Wes

t Nan

ning

Rd

Wes

t Nan

ning

Rd

South Qilin Rd

Wes

t Nan

ning

Rd

South Qilin Rd

South Qilin Rd

South Qilin Rd

Wen

chan

g St

Wen

chan

g St

W

ench

ang

St

512m

Upstream site A

Upstream site A


Firstvehicle

(advanced)

Downstream site B

Downstream site B


South Qilin Rd

(Current state)

(Advanced state)

(Predicted state)

t










119901119899|119899minus1119889119897119886119899119890 119894= 119872sum119894=1


(5)

where 119901119899|119899minus1119889119897119886119899119890 119894
















matrix 1198701|0119897119886119899119890 119894








(10)












119901119899|119899minus1119889119897119886119899119890 119894 = 119862119899119889119897119886119899119890 119894119883119899|119899minus1119889119897119886119899119890 119894 (16)















119902119899119889 (119909 + 119905) = 11 + 1205721199051199021198990 (119909)+ (1 minus 11 + 120572119905) 119902119899119889 (119909 + 119905 minus 1)

(18)


120572

=


(19)

119906 = 36001198761198941003816100381610038161003816119879ℎ119894 minus 1198791199051198941003816100381610038161003816 (20)

119904 = 119873119878119886119894 (21)




(22)






l

tnL ＧＲ lane i

wn4

wn3wn

1 lane i wn2


Lnre lane i

Lnf Part 1 lane i

Lnf Part 2 lane i

LnＧＲ lane i

Lnr lane i


Upstream site A

Upstream cells

Downstream site B


Wes

t Nan

ning

Rd


Wen

chan

g St

North




wn1 lane i (5ℎ+t)

(0 kj)



1199081198991119897119886119899119890 119894 (5ℎ + 119905) = 119902119899119889119897119886119899119890 119894 (5ℎ + 119905)119896119895 minus 119896119899119889119897119886119899119890 119894 (5ℎ + 119905) (23)


1198711198995ℎ119897119886119899119890 119894 = 5119902119899119889119897119886119899119890 119894 (5ℎ + 119905)119896119895 minus 119896119899119889119897119886119899119890 119894 (5ℎ + 119905) (24)



119905ℎ = 08119905 119897 minus sum119898ℎ=1 1198711198995ℎ119897119886119899119890 119894119897 (25)



(26)




l

tnL ＧＲ lane i


LnＧＲ lane i

Lnr lane i

Lnre lane i

wn2

wn3 wn

3

wn4

wn1 lane i

(qm km)



119871119899119903119897119886119899119890 119894 = ROUND(1199051198991199031198971198861198991198901198945)sumℎ=1

51199081198991119897119886119899119890 119894 (5ℎ + 119905ℎ)= ROUND(119905119899119903119897119886119899119890 1198945)sum

ℎ=1

5119902119899119889119897119886119899119890 119894 (5ℎ + 119905ℎ)119896119895 minus 119896119899119889119897119886119899119890 119894 (5ℎ + 119905ℎ) (27)



119903119897119886119899119890 1198945)

51199081198991119897119886119899119890 119894 (5ℎ + 119905ℎ)= 119871119899max119897119886119899119890 119894

(28)

119871119899max119897119886119899119890 119894 = 1199081198992 (119905119899119871max119897119886119899119890 119894 minus 119905119899119903119897119886119899119890 119894) (29)


ROUND(119905119899119871max119897119886119899119890 1198945)sumℎ=1

51199081198991119897119886119899119890 119894 (5ℎ + 119905)= 1199081198992 (119905119899119871max119897119886119899119890 119894 minus 119905119899119903119897119886119899119890 119894)

(30)





ℎ=ROUND(119905119899119871max1198971198861198991198901198945)

51199081198993 (5ℎ)) (31)







North

Wes

t Nan

ning

Rd

Wes

t Nan

ning

Rd

South Qilin Rd

South Qilin Rd

Wen

chan

g St

W

ench

ang

St


512m


North

Wes

t Nan

ning

Rd

Wen

chan

g St

South Qilin Rd



Study Area

(b)

(a)




119872119860119864 = 1119898sum119898

|119874119887119904119890119903V119886119905119894119900119899 minus 119875119903119890119889119894119888119905119894119900119899| (33)

119872119860119875119864 = 1119898sum119898

10038161003816100381610038161003816100381610038161003816119874119887119904119890119903V119886119905119894119900119899 minus 119875119903119890119889119894119888119905119894119900119899119874119887119904119890119903V11988611990511989411990011989910038161003816100381610038161003816100381610038161003816 times 100 (34)

119877119872119878119864 = 1119898radic119898sum119898

(119874119887119904119890119903V119886119905119894119900119899 minus 119875119903119890119889119894119888119905119894119900119899)2 (35)





0

005

01

015

02

025

03

154000 155500 161000 162500 164000 165500 171000 172500 174000 175500

Prop

ortio

ns o

f Tra

ffic V

olum

e

Time




03

035

04

045

05

055

154000 155500 161000 162500 164000 165500 171000 172500 174000 175500

Prop

ortio

ns o

f Tra

ffic V

olum

e

Time



03

035

04

045

05

055

154000 155500 161000 162500 164000 165500 171000 172500 174000 175500

Prop

ortio

ns o

f Tra

ffic V

olum

e

Time












0

2

4

6

8

10

12

14

16

18

Num

ber o

f Que

uing

Veh

icle

s

Time


160252

170132170712171217171732172257172807173442174217174827175427

160817161332161857162407162932163457164017164532165052165622

155212155737



0

5

10

15

20

25

30

Num

ber o

f Que

uing

Veh

icle

s

Time


154712

160317

170147170717171227171752172307172842173502174242174837175427

160832161357161907162422162957163537164027164542165102165627

155227155747


0

5

10

15

20

25

30

Num

ber o

f Que

uing

Veh

icle

s

Time



154707

160317

170147170717171227171747172307172842173502174242174837175427

160832161347161902162422162957163517164027164527165102165612

155227155747











Kalman filter

MAE (vehs)



Kalman filter

MAPE ()



Kalman filter

RMSE (vehs)






0

5

10

15

20

25

30

172317 172727 173137 173547 173957 174407 174817 175227 175637

Num

ber o

f Que

uing

Veh

icle

s

Time

Queue Trajectories

Lane 1

Lane 2

Lane 3







0

02

04

06

08

1

12

14

0

1

2

3

4

5

6

7

8

9

T an

d R R R R

L an

d R R R R R

T an

d R

T an

d R

T an

d R R R R

L an

d R R R R

T an

d R

T an

d R

T an

d R R R R R

L an

d R R R R

T an

d R

T an

d R

T an

d R R R R

L an

d R

L an

d R

174002

174007 174057 174212 174307 174402 174517 174612 174707 174817 174912

IQA

(veh

5 s)

Valu

me o

f ups

trea

m d

ata

colle

ctio

n sit

e (ve

h5s

)

Time


Valume

IQA


Valume

IQA

0

05

1

15

2

25

0

1

2

3

4

5

6

7

8

9

T an

d R R R R

L an

d R

L an

d R R R

T an

d R

T an

d R

T an

d R R R R R

L an

d R R R

T an

d R

T an

d R

T an

d R

T an

d R R R R

L an

d R

L an

d R R

T an

d R

T an

d R

T an

d R R R R

L an

d R

L an

d R

174002 174057 174217 174312 174407 174527 174622 174717 174847 174942

IQA

(veh

5 s)

Valu

me o

f ups

trea

m d

ata

colle

ctio

n si

te (v

eh5

s)

Time



Valume

IQA

0

05

1

15

2

25

3

0

1

2

3

4

5

6

7

8

9

T an

d R R R R

L an

d R

L an

d R R R

T an

d R

T an

d R

T an

d R R R R R

L an

d R R R

T an

d R

T an

d R

T an

d R R R R R

L an

d R R R

T an

d R

T an

d R

T an

d R R R R

L an

d R

174002 174057 174217 174312 174407 174532 174627 174722 174852 174947

IQA

(veh

5 s)

Valu

me o

f ups

trea

m d

ata

colle

ctio

n si

te (v

eh5

s)

Time






T and R 064 127 155L and R 020 045 054R 005 013 015

43 Discussion







MAE (vehs)

45 300 598 417 43850 233 448 360 34755 197 332 331 28760 202 269 201 22465 152 183 212 18270 171 240 216 20975 207 183 212 20180 226 281 292 26685 194 465 427 36290 268 530 523 440

MAPE ()

45 4068 3482 3000 351750 3170 2653 2616 281355 2702 1980 2405 236260 2732 1522 1580 194565 2094 1128 1614 161270 2358 1270 1895 184175 2850 1476 1560 196280 3077 1646 2158 229485 2659 2724 3070 281890 3630 3092 3744 3489

RMSE (vehs)

45 327 635 461 47450 269 485 416 39055 237 382 380 33360 239 334 243 27265 193 242 265 23370 215 279 307 26775 242 295 270 26980 261 329 342 31185 234 506 471 40490 298 568 565 477




5 Conclusion



40 45 50 55 60 65 70 75 80 85 90 95Travel time (s)


0

1

2

3

4

5

6ve

h

0

5

10

15

20

25

30

35

40








Appendix





Data Availability




Acknowledgments



l


Upstream site A

Downstream site B


Observation

Prediction


12 s129 s

154602

t0g lane i

t0g lane i

t1g lane i

t1g lane i


t0r lane i

t1r lane i

t1r lane i

t (65 s)

t(65 s)

L0ＧＲ lane i

L0ＧＲ lane i

t0L ＧＲ lane i




References





























































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



North

Wes

t Nan

ning

Rd

Wes

t Nan

ning

Rd

South Qilin Rd

Wes

t Nan

ning

Rd

South Qilin Rd

South Qilin Rd

South Qilin Rd

Wen

chan

g St

Wen

chan

g St

W

ench

ang

St

512m

Upstream site A

Upstream site A


Firstvehicle

(advanced)

Downstream site B

Downstream site B


South Qilin Rd

(Current state)

(Advanced state)

(Predicted state)

t










119901119899|119899minus1119889119897119886119899119890 119894= 119872sum119894=1


(5)

where 119901119899|119899minus1119889119897119886119899119890 119894
















matrix 1198701|0119897119886119899119890 119894








(10)












119901119899|119899minus1119889119897119886119899119890 119894 = 119862119899119889119897119886119899119890 119894119883119899|119899minus1119889119897119886119899119890 119894 (16)















119902119899119889 (119909 + 119905) = 11 + 1205721199051199021198990 (119909)+ (1 minus 11 + 120572119905) 119902119899119889 (119909 + 119905 minus 1)

(18)


120572

=


(19)

119906 = 36001198761198941003816100381610038161003816119879ℎ119894 minus 1198791199051198941003816100381610038161003816 (20)

119904 = 119873119878119886119894 (21)




(22)






l

tnL ＧＲ lane i

wn4

wn3wn

1 lane i wn2


Lnre lane i

Lnf Part 1 lane i

Lnf Part 2 lane i

LnＧＲ lane i

Lnr lane i


Upstream site A

Upstream cells

Downstream site B


Wes

t Nan

ning

Rd


Wen

chan

g St

North




wn1 lane i (5ℎ+t)

(0 kj)



1199081198991119897119886119899119890 119894 (5ℎ + 119905) = 119902119899119889119897119886119899119890 119894 (5ℎ + 119905)119896119895 minus 119896119899119889119897119886119899119890 119894 (5ℎ + 119905) (23)


1198711198995ℎ119897119886119899119890 119894 = 5119902119899119889119897119886119899119890 119894 (5ℎ + 119905)119896119895 minus 119896119899119889119897119886119899119890 119894 (5ℎ + 119905) (24)



119905ℎ = 08119905 119897 minus sum119898ℎ=1 1198711198995ℎ119897119886119899119890 119894119897 (25)



(26)




l

tnL ＧＲ lane i


LnＧＲ lane i

Lnr lane i

Lnre lane i

wn2

wn3 wn

3

wn4

wn1 lane i

(qm km)



119871119899119903119897119886119899119890 119894 = ROUND(1199051198991199031198971198861198991198901198945)sumℎ=1

51199081198991119897119886119899119890 119894 (5ℎ + 119905ℎ)= ROUND(119905119899119903119897119886119899119890 1198945)sum

ℎ=1

5119902119899119889119897119886119899119890 119894 (5ℎ + 119905ℎ)119896119895 minus 119896119899119889119897119886119899119890 119894 (5ℎ + 119905ℎ) (27)



119903119897119886119899119890 1198945)

51199081198991119897119886119899119890 119894 (5ℎ + 119905ℎ)= 119871119899max119897119886119899119890 119894

(28)

119871119899max119897119886119899119890 119894 = 1199081198992 (119905119899119871max119897119886119899119890 119894 minus 119905119899119903119897119886119899119890 119894) (29)


ROUND(119905119899119871max119897119886119899119890 1198945)sumℎ=1

51199081198991119897119886119899119890 119894 (5ℎ + 119905)= 1199081198992 (119905119899119871max119897119886119899119890 119894 minus 119905119899119903119897119886119899119890 119894)

(30)





ℎ=ROUND(119905119899119871max1198971198861198991198901198945)

51199081198993 (5ℎ)) (31)







North

Wes

t Nan

ning

Rd

Wes

t Nan

ning

Rd

South Qilin Rd

South Qilin Rd

Wen

chan

g St

W

ench

ang

St


512m


North

Wes

t Nan

ning

Rd

Wen

chan

g St

South Qilin Rd



Study Area

(b)

(a)




119872119860119864 = 1119898sum119898

|119874119887119904119890119903V119886119905119894119900119899 minus 119875119903119890119889119894119888119905119894119900119899| (33)

119872119860119875119864 = 1119898sum119898

10038161003816100381610038161003816100381610038161003816119874119887119904119890119903V119886119905119894119900119899 minus 119875119903119890119889119894119888119905119894119900119899119874119887119904119890119903V11988611990511989411990011989910038161003816100381610038161003816100381610038161003816 times 100 (34)

119877119872119878119864 = 1119898radic119898sum119898

(119874119887119904119890119903V119886119905119894119900119899 minus 119875119903119890119889119894119888119905119894119900119899)2 (35)





0

005

01

015

02

025

03

154000 155500 161000 162500 164000 165500 171000 172500 174000 175500

Prop

ortio

ns o

f Tra

ffic V

olum

e

Time




03

035

04

045

05

055

154000 155500 161000 162500 164000 165500 171000 172500 174000 175500

Prop

ortio

ns o

f Tra

ffic V

olum

e

Time



03

035

04

045

05

055

154000 155500 161000 162500 164000 165500 171000 172500 174000 175500

Prop

ortio

ns o

f Tra

ffic V

olum

e

Time












0

2

4

6

8

10

12

14

16

18

Num

ber o

f Que

uing

Veh

icle

s

Time


160252

170132170712171217171732172257172807173442174217174827175427

160817161332161857162407162932163457164017164532165052165622

155212155737



0

5

10

15

20

25

30

Num

ber o

f Que

uing

Veh

icle

s

Time


154712

160317

170147170717171227171752172307172842173502174242174837175427

160832161357161907162422162957163537164027164542165102165627

155227155747


0

5

10

15

20

25

30

Num

ber o

f Que

uing

Veh

icle

s

Time



154707

160317

170147170717171227171747172307172842173502174242174837175427

160832161347161902162422162957163517164027164527165102165612

155227155747











Kalman filter

MAE (vehs)



Kalman filter

MAPE ()



Kalman filter

RMSE (vehs)






0

5

10

15

20

25

30

172317 172727 173137 173547 173957 174407 174817 175227 175637

Num

ber o

f Que

uing

Veh

icle

s

Time

Queue Trajectories

Lane 1

Lane 2

Lane 3







0

02

04

06

08

1

12

14

0

1

2

3

4

5

6

7

8

9

T an

d R R R R

L an

d R R R R R

T an

d R

T an

d R

T an

d R R R R

L an

d R R R R

T an

d R

T an

d R

T an

d R R R R R

L an

d R R R R

T an

d R

T an

d R

T an

d R R R R

L an

d R

L an

d R

174002

174007 174057 174212 174307 174402 174517 174612 174707 174817 174912

IQA

(veh

5 s)

Valu

me o

f ups

trea

m d

ata

colle

ctio

n sit

e (ve

h5s

)

Time


Valume

IQA


Valume

IQA

0

05

1

15

2

25

0

1

2

3

4

5

6

7

8

9

T an

d R R R R

L an

d R

L an

d R R R

T an

d R

T an

d R

T an

d R R R R R

L an

d R R R

T an

d R

T an

d R

T an

d R

T an

d R R R R

L an

d R

L an

d R R

T an

d R

T an

d R

T an

d R R R R

L an

d R

L an

d R

174002 174057 174217 174312 174407 174527 174622 174717 174847 174942

IQA

(veh

5 s)

Valu

me o

f ups

trea

m d

ata

colle

ctio

n si

te (v

eh5

s)

Time



Valume

IQA

0

05

1

15

2

25

3

0

1

2

3

4

5

6

7

8

9

T an

d R R R R

L an

d R

L an

d R R R

T an

d R

T an

d R

T an

d R R R R R

L an

d R R R

T an

d R

T an

d R

T an

d R R R R R

L an

d R R R

T an

d R

T an

d R

T an

d R R R R

L an

d R

174002 174057 174217 174312 174407 174532 174627 174722 174852 174947

IQA

(veh

5 s)

Valu

me o

f ups

trea

m d

ata

colle

ctio

n si

te (v

eh5

s)

Time






T and R 064 127 155L and R 020 045 054R 005 013 015

43 Discussion







MAE (vehs)

45 300 598 417 43850 233 448 360 34755 197 332 331 28760 202 269 201 22465 152 183 212 18270 171 240 216 20975 207 183 212 20180 226 281 292 26685 194 465 427 36290 268 530 523 440

MAPE ()

45 4068 3482 3000 351750 3170 2653 2616 281355 2702 1980 2405 236260 2732 1522 1580 194565 2094 1128 1614 161270 2358 1270 1895 184175 2850 1476 1560 196280 3077 1646 2158 229485 2659 2724 3070 281890 3630 3092 3744 3489

RMSE (vehs)

45 327 635 461 47450 269 485 416 39055 237 382 380 33360 239 334 243 27265 193 242 265 23370 215 279 307 26775 242 295 270 26980 261 329 342 31185 234 506 471 40490 298 568 565 477




5 Conclusion



40 45 50 55 60 65 70 75 80 85 90 95Travel time (s)


0

1

2

3

4

5

6ve

h

0

5

10

15

20

25

30

35

40








Appendix





Data Availability




Acknowledgments



l


Upstream site A

Downstream site B


Observation

Prediction


12 s129 s

154602

t0g lane i

t0g lane i

t1g lane i

t1g lane i


t0r lane i

t1r lane i

t1r lane i

t (65 s)

t(65 s)

L0ＧＲ lane i

L0ＧＲ lane i

t0L ＧＲ lane i




References





























































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia
















matrix 1198701|0119897119886119899119890 119894








(10)












119901119899|119899minus1119889119897119886119899119890 119894 = 119862119899119889119897119886119899119890 119894119883119899|119899minus1119889119897119886119899119890 119894 (16)















119902119899119889 (119909 + 119905) = 11 + 1205721199051199021198990 (119909)+ (1 minus 11 + 120572119905) 119902119899119889 (119909 + 119905 minus 1)

(18)


120572

=


(19)

119906 = 36001198761198941003816100381610038161003816119879ℎ119894 minus 1198791199051198941003816100381610038161003816 (20)

119904 = 119873119878119886119894 (21)




(22)






l

tnL ＧＲ lane i

wn4

wn3wn

1 lane i wn2


Lnre lane i

Lnf Part 1 lane i

Lnf Part 2 lane i

LnＧＲ lane i

Lnr lane i


Upstream site A

Upstream cells

Downstream site B


Wes

t Nan

ning

Rd


Wen

chan

g St

North




wn1 lane i (5ℎ+t)

(0 kj)



1199081198991119897119886119899119890 119894 (5ℎ + 119905) = 119902119899119889119897119886119899119890 119894 (5ℎ + 119905)119896119895 minus 119896119899119889119897119886119899119890 119894 (5ℎ + 119905) (23)


1198711198995ℎ119897119886119899119890 119894 = 5119902119899119889119897119886119899119890 119894 (5ℎ + 119905)119896119895 minus 119896119899119889119897119886119899119890 119894 (5ℎ + 119905) (24)



119905ℎ = 08119905 119897 minus sum119898ℎ=1 1198711198995ℎ119897119886119899119890 119894119897 (25)



(26)




l

tnL ＧＲ lane i


LnＧＲ lane i

Lnr lane i

Lnre lane i

wn2

wn3 wn

3

wn4

wn1 lane i

(qm km)



119871119899119903119897119886119899119890 119894 = ROUND(1199051198991199031198971198861198991198901198945)sumℎ=1

51199081198991119897119886119899119890 119894 (5ℎ + 119905ℎ)= ROUND(119905119899119903119897119886119899119890 1198945)sum

ℎ=1

5119902119899119889119897119886119899119890 119894 (5ℎ + 119905ℎ)119896119895 minus 119896119899119889119897119886119899119890 119894 (5ℎ + 119905ℎ) (27)



119903119897119886119899119890 1198945)

51199081198991119897119886119899119890 119894 (5ℎ + 119905ℎ)= 119871119899max119897119886119899119890 119894

(28)

119871119899max119897119886119899119890 119894 = 1199081198992 (119905119899119871max119897119886119899119890 119894 minus 119905119899119903119897119886119899119890 119894) (29)


ROUND(119905119899119871max119897119886119899119890 1198945)sumℎ=1

51199081198991119897119886119899119890 119894 (5ℎ + 119905)= 1199081198992 (119905119899119871max119897119886119899119890 119894 minus 119905119899119903119897119886119899119890 119894)

(30)





ℎ=ROUND(119905119899119871max1198971198861198991198901198945)

51199081198993 (5ℎ)) (31)







North

Wes

t Nan

ning

Rd

Wes

t Nan

ning

Rd

South Qilin Rd

South Qilin Rd

Wen

chan

g St

W

ench

ang

St


512m


North

Wes

t Nan

ning

Rd

Wen

chan

g St

South Qilin Rd



Study Area

(b)

(a)




119872119860119864 = 1119898sum119898

|119874119887119904119890119903V119886119905119894119900119899 minus 119875119903119890119889119894119888119905119894119900119899| (33)

119872119860119875119864 = 1119898sum119898

10038161003816100381610038161003816100381610038161003816119874119887119904119890119903V119886119905119894119900119899 minus 119875119903119890119889119894119888119905119894119900119899119874119887119904119890119903V11988611990511989411990011989910038161003816100381610038161003816100381610038161003816 times 100 (34)

119877119872119878119864 = 1119898radic119898sum119898

(119874119887119904119890119903V119886119905119894119900119899 minus 119875119903119890119889119894119888119905119894119900119899)2 (35)





0

005

01

015

02

025

03

154000 155500 161000 162500 164000 165500 171000 172500 174000 175500

Prop

ortio

ns o

f Tra

ffic V

olum

e

Time




03

035

04

045

05

055

154000 155500 161000 162500 164000 165500 171000 172500 174000 175500

Prop

ortio

ns o

f Tra

ffic V

olum

e

Time



03

035

04

045

05

055

154000 155500 161000 162500 164000 165500 171000 172500 174000 175500

Prop

ortio

ns o

f Tra

ffic V

olum

e

Time












0

2

4

6

8

10

12

14

16

18

Num

ber o

f Que

uing

Veh

icle

s

Time


160252

170132170712171217171732172257172807173442174217174827175427

160817161332161857162407162932163457164017164532165052165622

155212155737



0

5

10

15

20

25

30

Num

ber o

f Que

uing

Veh

icle

s

Time


154712

160317

170147170717171227171752172307172842173502174242174837175427

160832161357161907162422162957163537164027164542165102165627

155227155747


0

5

10

15

20

25

30

Num

ber o

f Que

uing

Veh

icle

s

Time



154707

160317

170147170717171227171747172307172842173502174242174837175427

160832161347161902162422162957163517164027164527165102165612

155227155747











Kalman filter

MAE (vehs)



Kalman filter

MAPE ()



Kalman filter

RMSE (vehs)






0

5

10

15

20

25

30

172317 172727 173137 173547 173957 174407 174817 175227 175637

Num

ber o

f Que

uing

Veh

icle

s

Time

Queue Trajectories

Lane 1

Lane 2

Lane 3







0

02

04

06

08

1

12

14

0

1

2

3

4

5

6

7

8

9

T an

d R R R R

L an

d R R R R R

T an

d R

T an

d R

T an

d R R R R

L an

d R R R R

T an

d R

T an

d R

T an

d R R R R R

L an

d R R R R

T an

d R

T an

d R

T an

d R R R R

L an

d R

L an

d R

174002

174007 174057 174212 174307 174402 174517 174612 174707 174817 174912

IQA

(veh

5 s)

Valu

me o

f ups

trea

m d

ata

colle

ctio

n sit

e (ve

h5s

)

Time


Valume

IQA


Valume

IQA

0

05

1

15

2

25

0

1

2

3

4

5

6

7

8

9

T an

d R R R R

L an

d R

L an

d R R R

T an

d R

T an

d R

T an

d R R R R R

L an

d R R R

T an

d R

T an

d R

T an

d R

T an

d R R R R

L an

d R

L an

d R R

T an

d R

T an

d R

T an

d R R R R

L an

d R

L an

d R

174002 174057 174217 174312 174407 174527 174622 174717 174847 174942

IQA

(veh

5 s)

Valu

me o

f ups

trea

m d

ata

colle

ctio

n si

te (v

eh5

s)

Time



Valume

IQA

0

05

1

15

2

25

3

0

1

2

3

4

5

6

7

8

9

T an

d R R R R

L an

d R

L an

d R R R

T an

d R

T an

d R

T an

d R R R R R

L an

d R R R

T an

d R

T an

d R

T an

d R R R R R

L an

d R R R

T an

d R

T an

d R

T an

d R R R R

L an

d R

174002 174057 174217 174312 174407 174532 174627 174722 174852 174947

IQA

(veh

5 s)

Valu

me o

f ups

trea

m d

ata

colle

ctio

n si

te (v

eh5

s)

Time






T and R 064 127 155L and R 020 045 054R 005 013 015

43 Discussion







MAE (vehs)

45 300 598 417 43850 233 448 360 34755 197 332 331 28760 202 269 201 22465 152 183 212 18270 171 240 216 20975 207 183 212 20180 226 281 292 26685 194 465 427 36290 268 530 523 440

MAPE ()

45 4068 3482 3000 351750 3170 2653 2616 281355 2702 1980 2405 236260 2732 1522 1580 194565 2094 1128 1614 161270 2358 1270 1895 184175 2850 1476 1560 196280 3077 1646 2158 229485 2659 2724 3070 281890 3630 3092 3744 3489

RMSE (vehs)

45 327 635 461 47450 269 485 416 39055 237 382 380 33360 239 334 243 27265 193 242 265 23370 215 279 307 26775 242 295 270 26980 261 329 342 31185 234 506 471 40490 298 568 565 477




5 Conclusion



40 45 50 55 60 65 70 75 80 85 90 95Travel time (s)


0

1

2

3

4

5

6ve

h

0

5

10

15

20

25

30

35

40








Appendix





Data Availability




Acknowledgments



l


Upstream site A

Downstream site B


Observation

Prediction


12 s129 s

154602

t0g lane i

t0g lane i

t1g lane i

t1g lane i


t0r lane i

t1r lane i

t1r lane i

t (65 s)

t(65 s)

L0ＧＲ lane i

L0ＧＲ lane i

t0L ＧＲ lane i




References





























































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







119902119899119889 (119909 + 119905) = 11 + 1205721199051199021198990 (119909)+ (1 minus 11 + 120572119905) 119902119899119889 (119909 + 119905 minus 1)

(18)


120572

=


(19)

119906 = 36001198761198941003816100381610038161003816119879ℎ119894 minus 1198791199051198941003816100381610038161003816 (20)

119904 = 119873119878119886119894 (21)




(22)






l

tnL ＧＲ lane i

wn4

wn3wn

1 lane i wn2


Lnre lane i

Lnf Part 1 lane i

Lnf Part 2 lane i

LnＧＲ lane i

Lnr lane i


Upstream site A

Upstream cells

Downstream site B


Wes

t Nan

ning

Rd


Wen

chan

g St

North




wn1 lane i (5ℎ+t)

(0 kj)



1199081198991119897119886119899119890 119894 (5ℎ + 119905) = 119902119899119889119897119886119899119890 119894 (5ℎ + 119905)119896119895 minus 119896119899119889119897119886119899119890 119894 (5ℎ + 119905) (23)


1198711198995ℎ119897119886119899119890 119894 = 5119902119899119889119897119886119899119890 119894 (5ℎ + 119905)119896119895 minus 119896119899119889119897119886119899119890 119894 (5ℎ + 119905) (24)



119905ℎ = 08119905 119897 minus sum119898ℎ=1 1198711198995ℎ119897119886119899119890 119894119897 (25)



(26)




l

tnL ＧＲ lane i


LnＧＲ lane i

Lnr lane i

Lnre lane i

wn2

wn3 wn

3

wn4

wn1 lane i

(qm km)



119871119899119903119897119886119899119890 119894 = ROUND(1199051198991199031198971198861198991198901198945)sumℎ=1

51199081198991119897119886119899119890 119894 (5ℎ + 119905ℎ)= ROUND(119905119899119903119897119886119899119890 1198945)sum

ℎ=1

5119902119899119889119897119886119899119890 119894 (5ℎ + 119905ℎ)119896119895 minus 119896119899119889119897119886119899119890 119894 (5ℎ + 119905ℎ) (27)



119903119897119886119899119890 1198945)

51199081198991119897119886119899119890 119894 (5ℎ + 119905ℎ)= 119871119899max119897119886119899119890 119894

(28)

119871119899max119897119886119899119890 119894 = 1199081198992 (119905119899119871max119897119886119899119890 119894 minus 119905119899119903119897119886119899119890 119894) (29)


ROUND(119905119899119871max119897119886119899119890 1198945)sumℎ=1

51199081198991119897119886119899119890 119894 (5ℎ + 119905)= 1199081198992 (119905119899119871max119897119886119899119890 119894 minus 119905119899119903119897119886119899119890 119894)

(30)





ℎ=ROUND(119905119899119871max1198971198861198991198901198945)

51199081198993 (5ℎ)) (31)







North

Wes

t Nan

ning

Rd

Wes

t Nan

ning

Rd

South Qilin Rd

South Qilin Rd

Wen

chan

g St

W

ench

ang

St


512m


North

Wes

t Nan

ning

Rd

Wen

chan

g St

South Qilin Rd



Study Area

(b)

(a)




119872119860119864 = 1119898sum119898

|119874119887119904119890119903V119886119905119894119900119899 minus 119875119903119890119889119894119888119905119894119900119899| (33)

119872119860119875119864 = 1119898sum119898

10038161003816100381610038161003816100381610038161003816119874119887119904119890119903V119886119905119894119900119899 minus 119875119903119890119889119894119888119905119894119900119899119874119887119904119890119903V11988611990511989411990011989910038161003816100381610038161003816100381610038161003816 times 100 (34)

119877119872119878119864 = 1119898radic119898sum119898

(119874119887119904119890119903V119886119905119894119900119899 minus 119875119903119890119889119894119888119905119894119900119899)2 (35)





0

005

01

015

02

025

03

154000 155500 161000 162500 164000 165500 171000 172500 174000 175500

Prop

ortio

ns o

f Tra

ffic V

olum

e

Time




03

035

04

045

05

055

154000 155500 161000 162500 164000 165500 171000 172500 174000 175500

Prop

ortio

ns o

f Tra

ffic V

olum

e

Time



03

035

04

045

05

055

154000 155500 161000 162500 164000 165500 171000 172500 174000 175500

Prop

ortio

ns o

f Tra

ffic V

olum

e

Time












0

2

4

6

8

10

12

14

16

18

Num

ber o

f Que

uing

Veh

icle

s

Time


160252

170132170712171217171732172257172807173442174217174827175427

160817161332161857162407162932163457164017164532165052165622

155212155737



0

5

10

15

20

25

30

Num

ber o

f Que

uing

Veh

icle

s

Time


154712

160317

170147170717171227171752172307172842173502174242174837175427

160832161357161907162422162957163537164027164542165102165627

155227155747


0

5

10

15

20

25

30

Num

ber o

f Que

uing

Veh

icle

s

Time



154707

160317

170147170717171227171747172307172842173502174242174837175427

160832161347161902162422162957163517164027164527165102165612

155227155747











Kalman filter

MAE (vehs)



Kalman filter

MAPE ()



Kalman filter

RMSE (vehs)






0

5

10

15

20

25

30

172317 172727 173137 173547 173957 174407 174817 175227 175637

Num

ber o

f Que

uing

Veh

icle

s

Time

Queue Trajectories

Lane 1

Lane 2

Lane 3







0

02

04

06

08

1

12

14

0

1

2

3

4

5

6

7

8

9

T an

d R R R R

L an

d R R R R R

T an

d R

T an

d R

T an

d R R R R

L an

d R R R R

T an

d R

T an

d R

T an

d R R R R R

L an

d R R R R

T an

d R

T an

d R

T an

d R R R R

L an

d R

L an

d R

174002

174007 174057 174212 174307 174402 174517 174612 174707 174817 174912

IQA

(veh

5 s)

Valu

me o

f ups

trea

m d

ata

colle

ctio

n sit

e (ve

h5s

)

Time


Valume

IQA


Valume

IQA

0

05

1

15

2

25

0

1

2

3

4

5

6

7

8

9

T an

d R R R R

L an

d R

L an

d R R R

T an

d R

T an

d R

T an

d R R R R R

L an

d R R R

T an

d R

T an

d R

T an

d R

T an

d R R R R

L an

d R

L an

d R R

T an

d R

T an

d R

T an

d R R R R

L an

d R

L an

d R

174002 174057 174217 174312 174407 174527 174622 174717 174847 174942

IQA

(veh

5 s)

Valu

me o

f ups

trea

m d

ata

colle

ctio

n si

te (v

eh5

s)

Time



Valume

IQA

0

05

1

15

2

25

3

0

1

2

3

4

5

6

7

8

9

T an

d R R R R

L an

d R

L an

d R R R

T an

d R

T an

d R

T an

d R R R R R

L an

d R R R

T an

d R

T an

d R

T an

d R R R R R

L an

d R R R

T an

d R

T an

d R

T an

d R R R R

L an

d R

174002 174057 174217 174312 174407 174532 174627 174722 174852 174947

IQA

(veh

5 s)

Valu

me o

f ups

trea

m d

ata

colle

ctio

n si

te (v

eh5

s)

Time






T and R 064 127 155L and R 020 045 054R 005 013 015

43 Discussion







MAE (vehs)

45 300 598 417 43850 233 448 360 34755 197 332 331 28760 202 269 201 22465 152 183 212 18270 171 240 216 20975 207 183 212 20180 226 281 292 26685 194 465 427 36290 268 530 523 440

MAPE ()

45 4068 3482 3000 351750 3170 2653 2616 281355 2702 1980 2405 236260 2732 1522 1580 194565 2094 1128 1614 161270 2358 1270 1895 184175 2850 1476 1560 196280 3077 1646 2158 229485 2659 2724 3070 281890 3630 3092 3744 3489

RMSE (vehs)

45 327 635 461 47450 269 485 416 39055 237 382 380 33360 239 334 243 27265 193 242 265 23370 215 279 307 26775 242 295 270 26980 261 329 342 31185 234 506 471 40490 298 568 565 477




5 Conclusion



40 45 50 55 60 65 70 75 80 85 90 95Travel time (s)


0

1

2

3

4

5

6ve

h

0

5

10

15

20

25

30

35

40








Appendix





Data Availability




Acknowledgments



l


Upstream site A

Downstream site B


Observation

Prediction


12 s129 s

154602

t0g lane i

t0g lane i

t1g lane i

t1g lane i


t0r lane i

t1r lane i

t1r lane i

t (65 s)

t(65 s)

L0ＧＲ lane i

L0ＧＲ lane i

t0L ＧＲ lane i




References





























































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




l

tnL ＧＲ lane i

wn4

wn3wn

1 lane i wn2


Lnre lane i

Lnf Part 1 lane i

Lnf Part 2 lane i

LnＧＲ lane i

Lnr lane i


Upstream site A

Upstream cells

Downstream site B


Wes

t Nan

ning

Rd


Wen

chan

g St

North




wn1 lane i (5ℎ+t)

(0 kj)



1199081198991119897119886119899119890 119894 (5ℎ + 119905) = 119902119899119889119897119886119899119890 119894 (5ℎ + 119905)119896119895 minus 119896119899119889119897119886119899119890 119894 (5ℎ + 119905) (23)


1198711198995ℎ119897119886119899119890 119894 = 5119902119899119889119897119886119899119890 119894 (5ℎ + 119905)119896119895 minus 119896119899119889119897119886119899119890 119894 (5ℎ + 119905) (24)



119905ℎ = 08119905 119897 minus sum119898ℎ=1 1198711198995ℎ119897119886119899119890 119894119897 (25)



(26)




l

tnL ＧＲ lane i


LnＧＲ lane i

Lnr lane i

Lnre lane i

wn2

wn3 wn

3

wn4

wn1 lane i

(qm km)



119871119899119903119897119886119899119890 119894 = ROUND(1199051198991199031198971198861198991198901198945)sumℎ=1

51199081198991119897119886119899119890 119894 (5ℎ + 119905ℎ)= ROUND(119905119899119903119897119886119899119890 1198945)sum

ℎ=1

5119902119899119889119897119886119899119890 119894 (5ℎ + 119905ℎ)119896119895 minus 119896119899119889119897119886119899119890 119894 (5ℎ + 119905ℎ) (27)



119903119897119886119899119890 1198945)

51199081198991119897119886119899119890 119894 (5ℎ + 119905ℎ)= 119871119899max119897119886119899119890 119894

(28)

119871119899max119897119886119899119890 119894 = 1199081198992 (119905119899119871max119897119886119899119890 119894 minus 119905119899119903119897119886119899119890 119894) (29)


ROUND(119905119899119871max119897119886119899119890 1198945)sumℎ=1

51199081198991119897119886119899119890 119894 (5ℎ + 119905)= 1199081198992 (119905119899119871max119897119886119899119890 119894 minus 119905119899119903119897119886119899119890 119894)

(30)





ℎ=ROUND(119905119899119871max1198971198861198991198901198945)

51199081198993 (5ℎ)) (31)







North

Wes

t Nan

ning

Rd

Wes

t Nan

ning

Rd

South Qilin Rd

South Qilin Rd

Wen

chan

g St

W

ench

ang

St


512m


North

Wes

t Nan

ning

Rd

Wen

chan

g St

South Qilin Rd



Study Area

(b)

(a)




119872119860119864 = 1119898sum119898

|119874119887119904119890119903V119886119905119894119900119899 minus 119875119903119890119889119894119888119905119894119900119899| (33)

119872119860119875119864 = 1119898sum119898

10038161003816100381610038161003816100381610038161003816119874119887119904119890119903V119886119905119894119900119899 minus 119875119903119890119889119894119888119905119894119900119899119874119887119904119890119903V11988611990511989411990011989910038161003816100381610038161003816100381610038161003816 times 100 (34)

119877119872119878119864 = 1119898radic119898sum119898

(119874119887119904119890119903V119886119905119894119900119899 minus 119875119903119890119889119894119888119905119894119900119899)2 (35)





0

005

01

015

02

025

03

154000 155500 161000 162500 164000 165500 171000 172500 174000 175500

Prop

ortio

ns o

f Tra

ffic V

olum

e

Time




03

035

04

045

05

055

154000 155500 161000 162500 164000 165500 171000 172500 174000 175500

Prop

ortio

ns o

f Tra

ffic V

olum

e

Time



03

035

04

045

05

055

154000 155500 161000 162500 164000 165500 171000 172500 174000 175500

Prop

ortio

ns o

f Tra

ffic V

olum

e

Time












0

2

4

6

8

10

12

14

16

18

Num

ber o

f Que

uing

Veh

icle

s

Time


160252

170132170712171217171732172257172807173442174217174827175427

160817161332161857162407162932163457164017164532165052165622

155212155737



0

5

10

15

20

25

30

Num

ber o

f Que

uing

Veh

icle

s

Time


154712

160317

170147170717171227171752172307172842173502174242174837175427

160832161357161907162422162957163537164027164542165102165627

155227155747


0

5

10

15

20

25

30

Num

ber o

f Que

uing

Veh

icle

s

Time



154707

160317

170147170717171227171747172307172842173502174242174837175427

160832161347161902162422162957163517164027164527165102165612

155227155747











Kalman filter

MAE (vehs)



Kalman filter

MAPE ()



Kalman filter

RMSE (vehs)






0

5

10

15

20

25

30

172317 172727 173137 173547 173957 174407 174817 175227 175637

Num

ber o

f Que

uing

Veh

icle

s

Time

Queue Trajectories

Lane 1

Lane 2

Lane 3







0

02

04

06

08

1

12

14

0

1

2

3

4

5

6

7

8

9

T an

d R R R R

L an

d R R R R R

T an

d R

T an

d R

T an

d R R R R

L an

d R R R R

T an

d R

T an

d R

T an

d R R R R R

L an

d R R R R

T an

d R

T an

d R

T an

d R R R R

L an

d R

L an

d R

174002

174007 174057 174212 174307 174402 174517 174612 174707 174817 174912

IQA

(veh

5 s)

Valu

me o

f ups

trea

m d

ata

colle

ctio

n sit

e (ve

h5s

)

Time


Valume

IQA


Valume

IQA

0

05

1

15

2

25

0

1

2

3

4

5

6

7

8

9

T an

d R R R R

L an

d R

L an

d R R R

T an

d R

T an

d R

T an

d R R R R R

L an

d R R R

T an

d R

T an

d R

T an

d R

T an

d R R R R

L an

d R

L an

d R R

T an

d R

T an

d R

T an

d R R R R

L an

d R

L an

d R

174002 174057 174217 174312 174407 174527 174622 174717 174847 174942

IQA

(veh

5 s)

Valu

me o

f ups

trea

m d

ata

colle

ctio

n si

te (v

eh5

s)

Time



Valume

IQA

0

05

1

15

2

25

3

0

1

2

3

4

5

6

7

8

9

T an

d R R R R

L an

d R

L an

d R R R

T an

d R

T an

d R

T an

d R R R R R

L an

d R R R

T an

d R

T an

d R

T an

d R R R R R

L an

d R R R

T an

d R

T an

d R

T an

d R R R R

L an

d R

174002 174057 174217 174312 174407 174532 174627 174722 174852 174947

IQA

(veh

5 s)

Valu

me o

f ups

trea

m d

ata

colle

ctio

n si

te (v

eh5

s)

Time






T and R 064 127 155L and R 020 045 054R 005 013 015

43 Discussion







MAE (vehs)

45 300 598 417 43850 233 448 360 34755 197 332 331 28760 202 269 201 22465 152 183 212 18270 171 240 216 20975 207 183 212 20180 226 281 292 26685 194 465 427 36290 268 530 523 440

MAPE ()

45 4068 3482 3000 351750 3170 2653 2616 281355 2702 1980 2405 236260 2732 1522 1580 194565 2094 1128 1614 161270 2358 1270 1895 184175 2850 1476 1560 196280 3077 1646 2158 229485 2659 2724 3070 281890 3630 3092 3744 3489

RMSE (vehs)

45 327 635 461 47450 269 485 416 39055 237 382 380 33360 239 334 243 27265 193 242 265 23370 215 279 307 26775 242 295 270 26980 261 329 342 31185 234 506 471 40490 298 568 565 477




5 Conclusion



40 45 50 55 60 65 70 75 80 85 90 95Travel time (s)


0

1

2

3

4

5

6ve

h

0

5

10

15

20

25

30

35

40








Appendix





Data Availability




Acknowledgments



l


Upstream site A

Downstream site B


Observation

Prediction


12 s129 s

154602

t0g lane i

t0g lane i

t1g lane i

t1g lane i


t0r lane i

t1r lane i

t1r lane i

t (65 s)

t(65 s)

L0ＧＲ lane i

L0ＧＲ lane i

t0L ＧＲ lane i




References





























































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




l

tnL ＧＲ lane i


LnＧＲ lane i

Lnr lane i

Lnre lane i

wn2

wn3 wn

3

wn4

wn1 lane i

(qm km)



119871119899119903119897119886119899119890 119894 = ROUND(1199051198991199031198971198861198991198901198945)sumℎ=1

51199081198991119897119886119899119890 119894 (5ℎ + 119905ℎ)= ROUND(119905119899119903119897119886119899119890 1198945)sum

ℎ=1

5119902119899119889119897119886119899119890 119894 (5ℎ + 119905ℎ)119896119895 minus 119896119899119889119897119886119899119890 119894 (5ℎ + 119905ℎ) (27)



119903119897119886119899119890 1198945)

51199081198991119897119886119899119890 119894 (5ℎ + 119905ℎ)= 119871119899max119897119886119899119890 119894

(28)

119871119899max119897119886119899119890 119894 = 1199081198992 (119905119899119871max119897119886119899119890 119894 minus 119905119899119903119897119886119899119890 119894) (29)


ROUND(119905119899119871max119897119886119899119890 1198945)sumℎ=1

51199081198991119897119886119899119890 119894 (5ℎ + 119905)= 1199081198992 (119905119899119871max119897119886119899119890 119894 minus 119905119899119903119897119886119899119890 119894)

(30)





ℎ=ROUND(119905119899119871max1198971198861198991198901198945)

51199081198993 (5ℎ)) (31)







North

Wes

t Nan

ning

Rd

Wes

t Nan

ning

Rd

South Qilin Rd

South Qilin Rd

Wen

chan

g St

W

ench

ang

St


512m


North

Wes

t Nan

ning

Rd

Wen

chan

g St

South Qilin Rd



Study Area

(b)

(a)




119872119860119864 = 1119898sum119898

|119874119887119904119890119903V119886119905119894119900119899 minus 119875119903119890119889119894119888119905119894119900119899| (33)

119872119860119875119864 = 1119898sum119898

10038161003816100381610038161003816100381610038161003816119874119887119904119890119903V119886119905119894119900119899 minus 119875119903119890119889119894119888119905119894119900119899119874119887119904119890119903V11988611990511989411990011989910038161003816100381610038161003816100381610038161003816 times 100 (34)

119877119872119878119864 = 1119898radic119898sum119898

(119874119887119904119890119903V119886119905119894119900119899 minus 119875119903119890119889119894119888119905119894119900119899)2 (35)





0

005

01

015

02

025

03

154000 155500 161000 162500 164000 165500 171000 172500 174000 175500

Prop

ortio

ns o

f Tra

ffic V

olum

e

Time




03

035

04

045

05

055

154000 155500 161000 162500 164000 165500 171000 172500 174000 175500

Prop

ortio

ns o

f Tra

ffic V

olum

e

Time



03

035

04

045

05

055

154000 155500 161000 162500 164000 165500 171000 172500 174000 175500

Prop

ortio

ns o

f Tra

ffic V

olum

e

Time












0

2

4

6

8

10

12

14

16

18

Num

ber o

f Que

uing

Veh

icle

s

Time


160252

170132170712171217171732172257172807173442174217174827175427

160817161332161857162407162932163457164017164532165052165622

155212155737



0

5

10

15

20

25

30

Num

ber o

f Que

uing

Veh

icle

s

Time


154712

160317

170147170717171227171752172307172842173502174242174837175427

160832161357161907162422162957163537164027164542165102165627

155227155747


0

5

10

15

20

25

30

Num

ber o

f Que

uing

Veh

icle

s

Time



154707

160317

170147170717171227171747172307172842173502174242174837175427

160832161347161902162422162957163517164027164527165102165612

155227155747











Kalman filter

MAE (vehs)



Kalman filter

MAPE ()



Kalman filter

RMSE (vehs)






0

5

10

15

20

25

30

172317 172727 173137 173547 173957 174407 174817 175227 175637

Num

ber o

f Que

uing

Veh

icle

s

Time

Queue Trajectories

Lane 1

Lane 2

Lane 3







0

02

04

06

08

1

12

14

0

1

2

3

4

5

6

7

8

9

T an

d R R R R

L an

d R R R R R

T an

d R

T an

d R

T an

d R R R R

L an

d R R R R

T an

d R

T an

d R

T an

d R R R R R

L an

d R R R R

T an

d R

T an

d R

T an

d R R R R

L an

d R

L an

d R

174002

174007 174057 174212 174307 174402 174517 174612 174707 174817 174912

IQA

(veh

5 s)

Valu

me o

f ups

trea

m d

ata

colle

ctio

n sit

e (ve

h5s

)

Time


Valume

IQA


Valume

IQA

0

05

1

15

2

25

0

1

2

3

4

5

6

7

8

9

T an

d R R R R

L an

d R

L an

d R R R

T an

d R

T an

d R

T an

d R R R R R

L an

d R R R

T an

d R

T an

d R

T an

d R

T an

d R R R R

L an

d R

L an

d R R

T an

d R

T an

d R

T an

d R R R R

L an

d R

L an

d R

174002 174057 174217 174312 174407 174527 174622 174717 174847 174942

IQA

(veh

5 s)

Valu

me o

f ups

trea

m d

ata

colle

ctio

n si

te (v

eh5

s)

Time



Valume

IQA

0

05

1

15

2

25

3

0

1

2

3

4

5

6

7

8

9

T an

d R R R R

L an

d R

L an

d R R R

T an

d R

T an

d R

T an

d R R R R R

L an

d R R R

T an

d R

T an

d R

T an

d R R R R R

L an

d R R R

T an

d R

T an

d R

T an

d R R R R

L an

d R

174002 174057 174217 174312 174407 174532 174627 174722 174852 174947

IQA

(veh

5 s)

Valu

me o

f ups

trea

m d

ata

colle

ctio

n si

te (v

eh5

s)

Time






T and R 064 127 155L and R 020 045 054R 005 013 015

43 Discussion







MAE (vehs)

45 300 598 417 43850 233 448 360 34755 197 332 331 28760 202 269 201 22465 152 183 212 18270 171 240 216 20975 207 183 212 20180 226 281 292 26685 194 465 427 36290 268 530 523 440

MAPE ()

45 4068 3482 3000 351750 3170 2653 2616 281355 2702 1980 2405 236260 2732 1522 1580 194565 2094 1128 1614 161270 2358 1270 1895 184175 2850 1476 1560 196280 3077 1646 2158 229485 2659 2724 3070 281890 3630 3092 3744 3489

RMSE (vehs)

45 327 635 461 47450 269 485 416 39055 237 382 380 33360 239 334 243 27265 193 242 265 23370 215 279 307 26775 242 295 270 26980 261 329 342 31185 234 506 471 40490 298 568 565 477




5 Conclusion



40 45 50 55 60 65 70 75 80 85 90 95Travel time (s)


0

1

2

3

4

5

6ve

h

0

5

10

15

20

25

30

35

40








Appendix





Data Availability




Acknowledgments



l


Upstream site A

Downstream site B


Observation

Prediction


12 s129 s

154602

t0g lane i

t0g lane i

t1g lane i

t1g lane i


t0r lane i

t1r lane i

t1r lane i

t (65 s)

t(65 s)

L0ＧＲ lane i

L0ＧＲ lane i

t0L ＧＲ lane i




References





























































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



North

Wes

t Nan

ning

Rd

Wes

t Nan

ning

Rd

South Qilin Rd

South Qilin Rd

Wen

chan

g St

W

ench

ang

St


512m


North

Wes

t Nan

ning

Rd

Wen

chan

g St

South Qilin Rd



Study Area

(b)

(a)




119872119860119864 = 1119898sum119898

|119874119887119904119890119903V119886119905119894119900119899 minus 119875119903119890119889119894119888119905119894119900119899| (33)

119872119860119875119864 = 1119898sum119898

10038161003816100381610038161003816100381610038161003816119874119887119904119890119903V119886119905119894119900119899 minus 119875119903119890119889119894119888119905119894119900119899119874119887119904119890119903V11988611990511989411990011989910038161003816100381610038161003816100381610038161003816 times 100 (34)

119877119872119878119864 = 1119898radic119898sum119898

(119874119887119904119890119903V119886119905119894119900119899 minus 119875119903119890119889119894119888119905119894119900119899)2 (35)





0

005

01

015

02

025

03

154000 155500 161000 162500 164000 165500 171000 172500 174000 175500

Prop

ortio

ns o

f Tra

ffic V

olum

e

Time




03

035

04

045

05

055

154000 155500 161000 162500 164000 165500 171000 172500 174000 175500

Prop

ortio

ns o

f Tra

ffic V

olum

e

Time



03

035

04

045

05

055

154000 155500 161000 162500 164000 165500 171000 172500 174000 175500

Prop

ortio

ns o

f Tra

ffic V

olum

e

Time












0

2

4

6

8

10

12

14

16

18

Num

ber o

f Que

uing

Veh

icle

s

Time


160252

170132170712171217171732172257172807173442174217174827175427

160817161332161857162407162932163457164017164532165052165622

155212155737



0

5

10

15

20

25

30

Num

ber o

f Que

uing

Veh

icle

s

Time


154712

160317

170147170717171227171752172307172842173502174242174837175427

160832161357161907162422162957163537164027164542165102165627

155227155747


0

5

10

15

20

25

30

Num

ber o

f Que

uing

Veh

icle

s

Time



154707

160317

170147170717171227171747172307172842173502174242174837175427

160832161347161902162422162957163517164027164527165102165612

155227155747











Kalman filter

MAE (vehs)



Kalman filter

MAPE ()



Kalman filter

RMSE (vehs)






0

5

10

15

20

25

30

172317 172727 173137 173547 173957 174407 174817 175227 175637

Num

ber o

f Que

uing

Veh

icle

s

Time

Queue Trajectories

Lane 1

Lane 2

Lane 3







0

02

04

06

08

1

12

14

0

1

2

3

4

5

6

7

8

9

T an

d R R R R

L an

d R R R R R

T an

d R

T an

d R

T an

d R R R R

L an

d R R R R

T an

d R

T an

d R

T an

d R R R R R

L an

d R R R R

T an

d R

T an

d R

T an

d R R R R

L an

d R

L an

d R

174002

174007 174057 174212 174307 174402 174517 174612 174707 174817 174912

IQA

(veh

5 s)

Valu

me o

f ups

trea

m d

ata

colle

ctio

n sit

e (ve

h5s

)

Time


Valume

IQA


Valume

IQA

0

05

1

15

2

25

0

1

2

3

4

5

6

7

8

9

T an

d R R R R

L an

d R

L an

d R R R

T an

d R

T an

d R

T an

d R R R R R

L an

d R R R

T an

d R

T an

d R

T an

d R

T an

d R R R R

L an

d R

L an

d R R

T an

d R

T an

d R

T an

d R R R R

L an

d R

L an

d R

174002 174057 174217 174312 174407 174527 174622 174717 174847 174942

IQA

(veh

5 s)

Valu

me o

f ups

trea

m d

ata

colle

ctio

n si

te (v

eh5

s)

Time



Valume

IQA

0

05

1

15

2

25

3

0

1

2

3

4

5

6

7

8

9

T an

d R R R R

L an

d R

L an

d R R R

T an

d R

T an

d R

T an

d R R R R R

L an

d R R R

T an

d R

T an

d R

T an

d R R R R R

L an

d R R R

T an

d R

T an

d R

T an

d R R R R

L an

d R

174002 174057 174217 174312 174407 174532 174627 174722 174852 174947

IQA

(veh

5 s)

Valu

me o

f ups

trea

m d

ata

colle

ctio

n si

te (v

eh5

s)

Time






T and R 064 127 155L and R 020 045 054R 005 013 015

43 Discussion







MAE (vehs)

45 300 598 417 43850 233 448 360 34755 197 332 331 28760 202 269 201 22465 152 183 212 18270 171 240 216 20975 207 183 212 20180 226 281 292 26685 194 465 427 36290 268 530 523 440

MAPE ()

45 4068 3482 3000 351750 3170 2653 2616 281355 2702 1980 2405 236260 2732 1522 1580 194565 2094 1128 1614 161270 2358 1270 1895 184175 2850 1476 1560 196280 3077 1646 2158 229485 2659 2724 3070 281890 3630 3092 3744 3489

RMSE (vehs)

45 327 635 461 47450 269 485 416 39055 237 382 380 33360 239 334 243 27265 193 242 265 23370 215 279 307 26775 242 295 270 26980 261 329 342 31185 234 506 471 40490 298 568 565 477




5 Conclusion



40 45 50 55 60 65 70 75 80 85 90 95Travel time (s)


0

1

2

3

4

5

6ve

h

0

5

10

15

20

25

30

35

40








Appendix





Data Availability




Acknowledgments



l


Upstream site A

Downstream site B


Observation

Prediction


12 s129 s

154602

t0g lane i

t0g lane i

t1g lane i

t1g lane i


t0r lane i

t1r lane i

t1r lane i

t (65 s)

t(65 s)

L0ＧＲ lane i

L0ＧＲ lane i

t0L ＧＲ lane i




References





























































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




0

005

01

015

02

025

03

154000 155500 161000 162500 164000 165500 171000 172500 174000 175500

Prop

ortio

ns o

f Tra

ffic V

olum

e

Time




03

035

04

045

05

055

154000 155500 161000 162500 164000 165500 171000 172500 174000 175500

Prop

ortio

ns o

f Tra

ffic V

olum

e

Time



03

035

04

045

05

055

154000 155500 161000 162500 164000 165500 171000 172500 174000 175500

Prop

ortio

ns o

f Tra

ffic V

olum

e

Time












0

2

4

6

8

10

12

14

16

18

Num

ber o

f Que

uing

Veh

icle

s

Time


160252

170132170712171217171732172257172807173442174217174827175427

160817161332161857162407162932163457164017164532165052165622

155212155737



0

5

10

15

20

25

30

Num

ber o

f Que

uing

Veh

icle

s

Time


154712

160317

170147170717171227171752172307172842173502174242174837175427

160832161357161907162422162957163537164027164542165102165627

155227155747


0

5

10

15

20

25

30

Num

ber o

f Que

uing

Veh

icle

s

Time



154707

160317

170147170717171227171747172307172842173502174242174837175427

160832161347161902162422162957163517164027164527165102165612

155227155747











Kalman filter

MAE (vehs)



Kalman filter

MAPE ()



Kalman filter

RMSE (vehs)






0

5

10

15

20

25

30

172317 172727 173137 173547 173957 174407 174817 175227 175637

Num

ber o

f Que

uing

Veh

icle

s

Time

Queue Trajectories

Lane 1

Lane 2

Lane 3







0

02

04

06

08

1

12

14

0

1

2

3

4

5

6

7

8

9

T an

d R R R R

L an

d R R R R R

T an

d R

T an

d R

T an

d R R R R

L an

d R R R R

T an

d R

T an

d R

T an

d R R R R R

L an

d R R R R

T an

d R

T an

d R

T an

d R R R R

L an

d R

L an

d R

174002

174007 174057 174212 174307 174402 174517 174612 174707 174817 174912

IQA

(veh

5 s)

Valu

me o

f ups

trea

m d

ata

colle

ctio

n sit

e (ve

h5s

)

Time


Valume

IQA


Valume

IQA

0

05

1

15

2

25

0

1

2

3

4

5

6

7

8

9

T an

d R R R R

L an

d R

L an

d R R R

T an

d R

T an

d R

T an

d R R R R R

L an

d R R R

T an

d R

T an

d R

T an

d R

T an

d R R R R

L an

d R

L an

d R R

T an

d R

T an

d R

T an

d R R R R

L an

d R

L an

d R

174002 174057 174217 174312 174407 174527 174622 174717 174847 174942

IQA

(veh

5 s)

Valu

me o

f ups

trea

m d

ata

colle

ctio

n si

te (v

eh5

s)

Time



Valume

IQA

0

05

1

15

2

25

3

0

1

2

3

4

5

6

7

8

9

T an

d R R R R

L an

d R

L an

d R R R

T an

d R

T an

d R

T an

d R R R R R

L an

d R R R

T an

d R

T an

d R

T an

d R R R R R

L an

d R R R

T an

d R

T an

d R

T an

d R R R R

L an

d R

174002 174057 174217 174312 174407 174532 174627 174722 174852 174947

IQA

(veh

5 s)

Valu

me o

f ups

trea

m d

ata

colle

ctio

n si

te (v

eh5

s)

Time






T and R 064 127 155L and R 020 045 054R 005 013 015

43 Discussion







MAE (vehs)

45 300 598 417 43850 233 448 360 34755 197 332 331 28760 202 269 201 22465 152 183 212 18270 171 240 216 20975 207 183 212 20180 226 281 292 26685 194 465 427 36290 268 530 523 440

MAPE ()

45 4068 3482 3000 351750 3170 2653 2616 281355 2702 1980 2405 236260 2732 1522 1580 194565 2094 1128 1614 161270 2358 1270 1895 184175 2850 1476 1560 196280 3077 1646 2158 229485 2659 2724 3070 281890 3630 3092 3744 3489

RMSE (vehs)

45 327 635 461 47450 269 485 416 39055 237 382 380 33360 239 334 243 27265 193 242 265 23370 215 279 307 26775 242 295 270 26980 261 329 342 31185 234 506 471 40490 298 568 565 477




5 Conclusion



40 45 50 55 60 65 70 75 80 85 90 95Travel time (s)


0

1

2

3

4

5

6ve

h

0

5

10

15

20

25

30

35

40








Appendix





Data Availability




Acknowledgments



l


Upstream site A

Downstream site B


Observation

Prediction


12 s129 s

154602

t0g lane i

t0g lane i

t1g lane i

t1g lane i


t0r lane i

t1r lane i

t1r lane i

t (65 s)

t(65 s)

L0ＧＲ lane i

L0ＧＲ lane i

t0L ＧＲ lane i




References





























































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




0

2

4

6

8

10

12

14

16

18

Num

ber o

f Que

uing

Veh

icle

s

Time


160252

170132170712171217171732172257172807173442174217174827175427

160817161332161857162407162932163457164017164532165052165622

155212155737



0

5

10

15

20

25

30

Num

ber o

f Que

uing

Veh

icle

s

Time


154712

160317

170147170717171227171752172307172842173502174242174837175427

160832161357161907162422162957163537164027164542165102165627

155227155747


0

5

10

15

20

25

30

Num

ber o

f Que

uing

Veh

icle

s

Time



154707

160317

170147170717171227171747172307172842173502174242174837175427

160832161347161902162422162957163517164027164527165102165612

155227155747











Kalman filter

MAE (vehs)



Kalman filter

MAPE ()



Kalman filter

RMSE (vehs)






0

5

10

15

20

25

30

172317 172727 173137 173547 173957 174407 174817 175227 175637

Num

ber o

f Que

uing

Veh

icle

s

Time

Queue Trajectories

Lane 1

Lane 2

Lane 3







0

02

04

06

08

1

12

14

0

1

2

3

4

5

6

7

8

9

T an

d R R R R

L an

d R R R R R

T an

d R

T an

d R

T an

d R R R R

L an

d R R R R

T an

d R

T an

d R

T an

d R R R R R

L an

d R R R R

T an

d R

T an

d R

T an

d R R R R

L an

d R

L an

d R

174002

174007 174057 174212 174307 174402 174517 174612 174707 174817 174912

IQA

(veh

5 s)

Valu

me o

f ups

trea

m d

ata

colle

ctio

n sit

e (ve

h5s

)

Time


Valume

IQA


Valume

IQA

0

05

1

15

2

25

0

1

2

3

4

5

6

7

8

9

T an

d R R R R

L an

d R

L an

d R R R

T an

d R

T an

d R

T an

d R R R R R

L an

d R R R

T an

d R

T an

d R

T an

d R

T an

d R R R R

L an

d R

L an

d R R

T an

d R

T an

d R

T an

d R R R R

L an

d R

L an

d R

174002 174057 174217 174312 174407 174527 174622 174717 174847 174942

IQA

(veh

5 s)

Valu

me o

f ups

trea

m d

ata

colle

ctio

n si

te (v

eh5

s)

Time



Valume

IQA

0

05

1

15

2

25

3

0

1

2

3

4

5

6

7

8

9

T an

d R R R R

L an

d R

L an

d R R R

T an

d R

T an

d R

T an

d R R R R R

L an

d R R R

T an

d R

T an

d R

T an

d R R R R R

L an

d R R R

T an

d R

T an

d R

T an

d R R R R

L an

d R

174002 174057 174217 174312 174407 174532 174627 174722 174852 174947

IQA

(veh

5 s)

Valu

me o

f ups

trea

m d

ata

colle

ctio

n si

te (v

eh5

s)

Time






T and R 064 127 155L and R 020 045 054R 005 013 015

43 Discussion







MAE (vehs)

45 300 598 417 43850 233 448 360 34755 197 332 331 28760 202 269 201 22465 152 183 212 18270 171 240 216 20975 207 183 212 20180 226 281 292 26685 194 465 427 36290 268 530 523 440

MAPE ()

45 4068 3482 3000 351750 3170 2653 2616 281355 2702 1980 2405 236260 2732 1522 1580 194565 2094 1128 1614 161270 2358 1270 1895 184175 2850 1476 1560 196280 3077 1646 2158 229485 2659 2724 3070 281890 3630 3092 3744 3489

RMSE (vehs)

45 327 635 461 47450 269 485 416 39055 237 382 380 33360 239 334 243 27265 193 242 265 23370 215 279 307 26775 242 295 270 26980 261 329 342 31185 234 506 471 40490 298 568 565 477




5 Conclusion



40 45 50 55 60 65 70 75 80 85 90 95Travel time (s)


0

1

2

3

4

5

6ve

h

0

5

10

15

20

25

30

35

40








Appendix





Data Availability




Acknowledgments



l


Upstream site A

Downstream site B


Observation

Prediction


12 s129 s

154602

t0g lane i

t0g lane i

t1g lane i

t1g lane i


t0r lane i

t1r lane i

t1r lane i

t (65 s)

t(65 s)

L0ＧＲ lane i

L0ＧＲ lane i

t0L ＧＲ lane i




References





























































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





Kalman filter

MAE (vehs)



Kalman filter

MAPE ()



Kalman filter

RMSE (vehs)






0

5

10

15

20

25

30

172317 172727 173137 173547 173957 174407 174817 175227 175637

Num

ber o

f Que

uing

Veh

icle

s

Time

Queue Trajectories

Lane 1

Lane 2

Lane 3







0

02

04

06

08

1

12

14

0

1

2

3

4

5

6

7

8

9

T an

d R R R R

L an

d R R R R R

T an

d R

T an

d R

T an

d R R R R

L an

d R R R R

T an

d R

T an

d R

T an

d R R R R R

L an

d R R R R

T an

d R

T an

d R

T an

d R R R R

L an

d R

L an

d R

174002

174007 174057 174212 174307 174402 174517 174612 174707 174817 174912

IQA

(veh

5 s)

Valu

me o

f ups

trea

m d

ata

colle

ctio

n sit

e (ve

h5s

)

Time


Valume

IQA


Valume

IQA

0

05

1

15

2

25

0

1

2

3

4

5

6

7

8

9

T an

d R R R R

L an

d R

L an

d R R R

T an

d R

T an

d R

T an

d R R R R R

L an

d R R R

T an

d R

T an

d R

T an

d R

T an

d R R R R

L an

d R

L an

d R R

T an

d R

T an

d R

T an

d R R R R

L an

d R

L an

d R

174002 174057 174217 174312 174407 174527 174622 174717 174847 174942

IQA

(veh

5 s)

Valu

me o

f ups

trea

m d

ata

colle

ctio

n si

te (v

eh5

s)

Time



Valume

IQA

0

05

1

15

2

25

3

0

1

2

3

4

5

6

7

8

9

T an

d R R R R

L an

d R

L an

d R R R

T an

d R

T an

d R

T an

d R R R R R

L an

d R R R

T an

d R

T an

d R

T an

d R R R R R

L an

d R R R

T an

d R

T an

d R

T an

d R R R R

L an

d R

174002 174057 174217 174312 174407 174532 174627 174722 174852 174947

IQA

(veh

5 s)

Valu

me o

f ups

trea

m d

ata

colle

ctio

n si

te (v

eh5

s)

Time






T and R 064 127 155L and R 020 045 054R 005 013 015

43 Discussion







MAE (vehs)

45 300 598 417 43850 233 448 360 34755 197 332 331 28760 202 269 201 22465 152 183 212 18270 171 240 216 20975 207 183 212 20180 226 281 292 26685 194 465 427 36290 268 530 523 440

MAPE ()

45 4068 3482 3000 351750 3170 2653 2616 281355 2702 1980 2405 236260 2732 1522 1580 194565 2094 1128 1614 161270 2358 1270 1895 184175 2850 1476 1560 196280 3077 1646 2158 229485 2659 2724 3070 281890 3630 3092 3744 3489

RMSE (vehs)

45 327 635 461 47450 269 485 416 39055 237 382 380 33360 239 334 243 27265 193 242 265 23370 215 279 307 26775 242 295 270 26980 261 329 342 31185 234 506 471 40490 298 568 565 477




5 Conclusion



40 45 50 55 60 65 70 75 80 85 90 95Travel time (s)


0

1

2

3

4

5

6ve

h

0

5

10

15

20

25

30

35

40








Appendix





Data Availability




Acknowledgments



l


Upstream site A

Downstream site B


Observation

Prediction


12 s129 s

154602

t0g lane i

t0g lane i

t1g lane i

t1g lane i


t0r lane i

t1r lane i

t1r lane i

t (65 s)

t(65 s)

L0ＧＲ lane i

L0ＧＲ lane i

t0L ＧＲ lane i




References





























































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



0

02

04

06

08

1

12

14

0

1

2

3

4

5

6

7

8

9

T an

d R R R R

L an

d R R R R R

T an

d R

T an

d R

T an

d R R R R

L an

d R R R R

T an

d R

T an

d R

T an

d R R R R R

L an

d R R R R

T an

d R

T an

d R

T an

d R R R R

L an

d R

L an

d R

174002

174007 174057 174212 174307 174402 174517 174612 174707 174817 174912

IQA

(veh

5 s)

Valu

me o

f ups

trea

m d

ata

colle

ctio

n sit

e (ve

h5s

)

Time


Valume

IQA


Valume

IQA

0

05

1

15

2

25

0

1

2

3

4

5

6

7

8

9

T an

d R R R R

L an

d R

L an

d R R R

T an

d R

T an

d R

T an

d R R R R R

L an

d R R R

T an

d R

T an

d R

T an

d R

T an

d R R R R

L an

d R

L an

d R R

T an

d R

T an

d R

T an

d R R R R

L an

d R

L an

d R

174002 174057 174217 174312 174407 174527 174622 174717 174847 174942

IQA

(veh

5 s)

Valu

me o

f ups

trea

m d

ata

colle

ctio

n si

te (v

eh5

s)

Time



Valume

IQA

0

05

1

15

2

25

3

0

1

2

3

4

5

6

7

8

9

T an

d R R R R

L an

d R

L an

d R R R

T an

d R

T an

d R

T an

d R R R R R

L an

d R R R

T an

d R

T an

d R

T an

d R R R R R

L an

d R R R

T an

d R

T an

d R

T an

d R R R R

L an

d R

174002 174057 174217 174312 174407 174532 174627 174722 174852 174947

IQA

(veh

5 s)

Valu

me o

f ups

trea

m d

ata

colle

ctio

n si

te (v

eh5

s)

Time






T and R 064 127 155L and R 020 045 054R 005 013 015

43 Discussion







MAE (vehs)

45 300 598 417 43850 233 448 360 34755 197 332 331 28760 202 269 201 22465 152 183 212 18270 171 240 216 20975 207 183 212 20180 226 281 292 26685 194 465 427 36290 268 530 523 440

MAPE ()

45 4068 3482 3000 351750 3170 2653 2616 281355 2702 1980 2405 236260 2732 1522 1580 194565 2094 1128 1614 161270 2358 1270 1895 184175 2850 1476 1560 196280 3077 1646 2158 229485 2659 2724 3070 281890 3630 3092 3744 3489

RMSE (vehs)

45 327 635 461 47450 269 485 416 39055 237 382 380 33360 239 334 243 27265 193 242 265 23370 215 279 307 26775 242 295 270 26980 261 329 342 31185 234 506 471 40490 298 568 565 477




5 Conclusion



40 45 50 55 60 65 70 75 80 85 90 95Travel time (s)


0

1

2

3

4

5

6ve

h

0

5

10

15

20

25

30

35

40








Appendix





Data Availability




Acknowledgments



l


Upstream site A

Downstream site B


Observation

Prediction


12 s129 s

154602

t0g lane i

t0g lane i

t1g lane i

t1g lane i


t0r lane i

t1r lane i

t1r lane i

t (65 s)

t(65 s)

L0ＧＲ lane i

L0ＧＲ lane i

t0L ＧＲ lane i




References





























































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





MAE (vehs)

45 300 598 417 43850 233 448 360 34755 197 332 331 28760 202 269 201 22465 152 183 212 18270 171 240 216 20975 207 183 212 20180 226 281 292 26685 194 465 427 36290 268 530 523 440

MAPE ()

45 4068 3482 3000 351750 3170 2653 2616 281355 2702 1980 2405 236260 2732 1522 1580 194565 2094 1128 1614 161270 2358 1270 1895 184175 2850 1476 1560 196280 3077 1646 2158 229485 2659 2724 3070 281890 3630 3092 3744 3489

RMSE (vehs)

45 327 635 461 47450 269 485 416 39055 237 382 380 33360 239 334 243 27265 193 242 265 23370 215 279 307 26775 242 295 270 26980 261 329 342 31185 234 506 471 40490 298 568 565 477




5 Conclusion



40 45 50 55 60 65 70 75 80 85 90 95Travel time (s)


0

1

2

3

4

5

6ve

h

0

5

10

15

20

25

30

35

40








Appendix





Data Availability




Acknowledgments



l


Upstream site A

Downstream site B


Observation

Prediction


12 s129 s

154602

t0g lane i

t0g lane i

t1g lane i

t1g lane i


t0r lane i

t1r lane i

t1r lane i

t (65 s)

t(65 s)

L0ＧＲ lane i

L0ＧＲ lane i

t0L ＧＲ lane i




References





























































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



40 45 50 55 60 65 70 75 80 85 90 95Travel time (s)


0

1

2

3

4

5

6ve

h

0

5

10

15

20

25

30

35

40








Appendix





Data Availability




Acknowledgments



l


Upstream site A

Downstream site B


Observation

Prediction


12 s129 s

154602

t0g lane i

t0g lane i

t1g lane i

t1g lane i


t0r lane i

t1r lane i

t1r lane i

t (65 s)

t(65 s)

L0ＧＲ lane i

L0ＧＲ lane i

t0L ＧＲ lane i




References





























































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



l


Upstream site A

Downstream site B


Observation

Prediction


12 s129 s

154602

t0g lane i

t0g lane i

t1g lane i

t1g lane i


t0r lane i

t1r lane i

t1r lane i

t (65 s)

t(65 s)

L0ＧＲ lane i

L0ＧＲ lane i

t0L ＧＲ lane i




References





























































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia












































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia










RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


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