Cross-Comparison and Calibration of Two Microscopic ...

Research ArticleCross-Comparison and Calibration of Two MicroscopicTraffic Simulation Models for Complex Freeway Corridors withDedicated Lanes

Xingan (David) Kan 1 Lin Xiao2 Hao Liu3 Meng Wang 2 Wouter J Schakel2

Xiao-Yun Lu3 Bart van Arem 2 Steven E Shladover3 and Robert A Ferlis4

1Department of Civil and Environmental Engineering Institute of Transportation Studies 109 McLaughlin HallUniversity of California Berkeley CA 94720-1720 USA

2Faculty of Civil Engineering and Geosciences Del University of Technology Stevinweg 1 2628 CN Del Netherlands3Partners for Advanced Transportation Technology (PATH) Institute of Transportation Studies Richmond Field Station Building 452Richmond CA 94804 USA

4Technical Director for Operations RampD US Department of Transportation Federal Highway Administration6300 Georgetown Pike McLean VA 22101 USA

Correspondence should be addressed to Xingan (David) Kan davidkanberkeleyedu

Received 2 October 2018 Revised 12 January 2019 Accepted 3 February 2019 Published 10 March 2019

Academic Editor Fulvio Simonelli

Copyright copy 2019 Xingan (David) Kan et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Realistic microscopic traffic simulation is essential for prospective evaluation of the potential impacts of new traffic controlstrategies Freeway corridors with interacting bottlenecks and dedicated lanes generate complex traffic flow phenomena andcongestion patterns which are difficult to reproduce with existing microscopic simulation models This paper discusses twoalternative driving behavior models that are capable of modeling freeways with multiple bottlenecks and dedicated lanes over anextended period with varying demand levelsThemodels have been calibrated using archived data from a complicated 13-mile longsection of the northbound SR99 freeway near Sacramento California for an 8-hour time period in which the traffic fluctuated fromfree-flow to congested conditions The corridor includes multiple bottlenecks multiple entry and exit ramps and an HOV laneCalibration results show extremely good agreement between field data andmodel predictionsThemodels have been cross-validatedand produced similar macroscopic traffic performanceThemain behavior that should be captured for successful modeling of sucha complex corridor includes the anticipative and cooperative driver behavior near merges lane preference in presence of dedicatedlanes and variations in desired headway along the corridor

1 Introduction

Microscopic traffic simulation is a viable and cost effectiveapproach for prospectively evaluating the potential impactsof traffic control strategies and shifts in demand patternsTo achieve this the microscopic traffic simulation mustrealistically represent the microscopic level driving behavior[1] and generate realistic macroscopic performance

The widely accepted commercial microsimulation pack-ages such as Aimsun VISSIM and PARAMICS have theirunique proprietary car following and lane changing mod-els Under these simulation frameworks users can adjust

and calibrate the values of behavioral parameters such asreaction time and maximum acceleration to best reproducerealistic driving behavior Recent works in model calibrationhave suggested parameter values and proposed optimizationtechniques to calibrate the parameters [2ndash14] While modelcalibration seeks the parameter values that best reproducereal-world conditions the performance of simulation pack-ages is largely constrained by the capability of the embeddedcore driver behavior models Many simulation packagesdo not capture the adaptive anticipative and cooperativedriver behavior at bottlenecks [15] As a result these workshave not been very successful in accurately modeling the

HindawiJournal of Advanced TransportationVolume 2019 Article ID 8618476 14 pageshttpsdoiorg10115520198618476

2 Journal of Advanced Transportation

onset of congestion capacity drop queue propagation andqueue dissipation when interacting bottlenecks are presentin freeway corridors as demonstrated by a simulation studyon a 13-mile corridor in Sacramento California [16 17]

In addition dedicated lanes generatemore complex trafficdynamics on freeway corridors Friction effect has beenobserved on freeways with HOV lanes characterized bythe speed reduction on the HOV lane when the adjacentgeneral purpose lane is congested [18ndash20] Modeling the dif-ferences in lane usage and lane change between HOV andsingle occupancy vehicles is important to reproduce thetraffic conditions around HOV lanes Although different lanechangemodels have been proposed to capture this large scalesimulation and validation of the lane change model haverarely been reported

The aforementioned problems motivate the developmentof alternative driving behavior models for car followingmerging lane changing etc to better represent the complextraffic dynamics of large scale freeway corridors with dedi-cated lanes Such models will allow users to implement theirexternal behavioral models using software development kitsto simulate driving behavior with the commercial simulationplatforms such as Aimsun and VISSIM or develop completeopen simulation tools In addition it is almost impractical todevelop amodel that is able to perfectly reproduce real-worldobservations Cross-comparison between models has shownto be beneficial [21] since it makes the analysis more reliableand the results more defensible giving more confidence tousers about the simulation results Unfortunately there havenot been any well established and cross-validated alternativecar following and lane changingmodels that are applicable forcomplex freeway corridors

In response this paper introduces two such models anddemonstrates the results of their validation against real-world data from a 13-mile freeway corridor during an 8hour period Although originated from different base modelsand developed separately by two teams the two proposedalternatives focus on refined description ofmerging behaviorlane preference and cooperative car following behavior inthe vicinity of merge and diverge sections They are validatedagainst empirical loop detector data and against each otherThe two models show extremely good agreement betweenfield data and model predictions Comparison of the twomodels and validation results give consistent insights into thetraffic flow models for complex corridors that can be gener-alized to other simulation tools Furthermore both modelsperformed better than the proprietary driver behaviormodel

The rest of the paper is organized as follows the nextsection presents an overview of two proposed alternativedriving behavior models The following section documentsthe calibration and cross validation of both models usingarchived data from a complex freeway corridor The finalsection summarizes and highlights the contribution of thispaper

2 Proposed Driver Behavior Models

Microscopic vehicle behavior and interaction with the nearbyvehicles determine overall traffic behavior at the macroscopic

level based upon the following factors maximum acceler-ationdeceleration and driver behaviors such as preferredheadway and response time gap acceptance threshold forlane changing and perception advance time period or dis-tance for lane changing Those parameters directly affectdensity and delays in the simulation and thus the overalltraffic pattern Below we discuss the two alternative modelsand highlight the main features

21 Alternative 1 Driving Behavior Model Based on NGSIMModel The first proposed driving behavior model (PATHmodel) is built upon the basic framework of the NGSIMoversaturated flow model proposed by Yeo et al [16] Someimportant extensions and modifications were made in orderto depict detailed car following and lane changing behaviorthat were not represented in the original model

To determine the trajectory of a vehicle at a microscopiclevel it is necessary and sufficient to iteratively determineits location at each time step which can be realized througha discrete kinematic model if the desired acceleration andcurrent speed are known [22] The latter is known fromthe last step calculation The former is determined by thedynamic interactions with the adjacent vehicles geometricconstraints and the overall traffic conditions The dynamicinteractions include timeclearance gaps for safety andmobil-ity and possible scenarios associated with lane changes [22]Those scenarios are further partitioned into fundamentalscenarios (or movement phases) and transitions betweenthem for continuoussmooth speed trajectories

(i) CF regular car following mode(ii) YCF yielding (cooperative) car following mode(iii) LC lane change mode which includes discretionary

lane change (DLC) and mandatory lane change(MLC)

(iv) ACF after lane changing car following mode (adriver temporarily adopts a short gap following a lanechange maneuver)

(v) BCF before lane changing car following mode (adriver speeds up or slows down to align with anacceptable gap in the target lane)

(vi) RCF receiving car following mode (a driver tem-porarily adopts a short gap after a vehicle from theadjacent lane merges in front)

The discretized kinematic model is detailed in [22] Asdiscussed in [22] Newellrsquos simplified car following modelwith constraints for safety and acceleration [23] is appliedThe Gippsrsquo deceleration component [1 24] is used here toplace a safety margin onNewellrsquos simplified equation Furtherdetails such as permissible speed and cross-lane friction onmultilane freeways are detailed in [22]

The fundamental scenarios associated with lane changing(LC) are outlined in Figure 1 and discussed in detail by Luet al [22]

As detailed in [22] there are two types of lane changesMandatory lane change is intended for merging onto orexiting the freeway Discretionary lane change is intended for

Journal of Advanced Transportation 3

CF

Is current

Is currentNeed YCFNeed LCStart

Acceptgap

No

No

No

No

No

Yes

Yes

Yes

Yes

Yes

RCF

ACFACF

RCF

YCF

BCF

LC

Figure 1 Lane change behavior structure

SynchronizationGap-creation

HeadwayDeceleration

Follow route Gain speed

Lane change desire (d)

No LC FLC CLC

yesyes

yesno

nono

nono

SLC

Keep right

dfree dsync dcoop

Figure 2 Four types of lane change behaviors corresponding to the level of lane change desire [15]

increasing the vehiclersquos speed or accessing the high occupancyvehicle (HOV) laneDetailedmathematical expressions of thegap acceptance models of both types of lane change can befound in Lu et al [22]

Once a decision for lane change has been made thesubject vehicle will adopt BCFmode prior to changing lanesThis involves accelerating or decelerating in order to alignwith the gaps available in the adjacent lanes In additionthe subject vehicle applies YCF mode to cooperate with theleading vehicle in the adjacent lanes that has an intent fora lane change to the current lane of the subject vehicle Thesubject vehicle also adopts RCFmode (reduced headway jamgap and reaction time) after the lane change maneuver iscomplete Similarly the leading vehicle adopts ACF after thelane change maneuver which is similar to RCF and involvesreduced headway jam gap and reaction time Details of thesecar following criteria are described in Lu et al [22]

22 Alternative 2 Driving Behavior Model Based on LMRSand IDM+ Alternative 2 is an extension of the Lane ChangeModel with Relaxation and Synchronization (LMRS) [15]The LMRS is formulated based on lane change desiresand provides a flexible structure to incorporate additionaldesiresincentives due to changes in infrastructure or trafficregulation

Lane change decisions are made based on comparing laneutility formulated by a combination of desiresincentives Theoverall lane change desire is calculated by three incentivesthat include following the route gaining speed and keepingright

119889119894119895 = 119889119894119895119903119900119906119905119890 + 120579119894119895V119900119897119906119899119905119886119903119910 sdot (119889119894119895119904119901119890119890119889 + 119889119894119895119887) (1)

where 119889119894119895 is the overall lane change desire from lane 119894 to lanej 119889119894119895119903119900119906119905119890 119889119894119895119904119901119890119890119889 and 119889119894119895119887 represent the incentives for the routespeed and a bias to the right lane respectively which canbe set to zero for US traffic The route incentive is based onparameters 1199050 and 1199090 that scope the time-space region beforethe mergediverge 120579119894119895V119900119897119906119899119905119886119903119910 is a weighting factor that reflectsthe relative importance of discretionary incentives and is afunction of |119889119903119900119906119905119890| and this reduces the voluntary incentivesas the mandatory incentive is more urgent

Meaningful lane change desires range from -1 to 1 wherenegative values suggest that a lane change is not desiredBased on the total lane change desire different types of lanechange behavior can be distinguished by three thresholdsdfree dsync and dcoop with 0 lt dfree lt dsync lt dcoop lt 1 Asshown in Figure 2 a lane change desire 119889 smaller than dfreemeans that no lane change (No LC) is performed When 119889


(a) Map of SR-99 with detector stations and postmiles identified

99NB -gt

50W

B

WB Florin

Rd

WB Sh

eldon Rd

Elk Grove Blvd

Post-miles 2985 2979 2960 2953 2947 2939 2928 2924 2919 2915 2906 2900 2894 2893 2876 2873

(b) Lane configuration and road geometry

Figure 3 Study site SR-99 freeway south of downtown Sacramento CA

is between dfree and dsync vehicles execute free lane changes(FLC) When 119889 is within the range of [dsync dcoop] the lanechanging vehicle performs synchronized lane changes (SLC)where it aligns its speed with that of the leader in the targetlane but the follower in the target lane does not actively createa gap for the lane changer As the desire 119889 exceeds dcoopcooperative lane changes (CLC) are expected in which thelane changer synchronizes its speed with the potential leaderand the potential follower in the target lane to create a gapWith the increase in lane change desire drivers tend to acceptsmaller headways and larger decelerations

This incentive-based lane changemodel is integrated withamodified version of the Intelligent Driver Model referred asIDM+ [25] implemented in an open traffic simulation plat-form named MOTUS [26] The IDM+ provides the desiredacceleration as the minimum of the acceleration required toreach the desired speed and the acceleration required to reachthe desired headway The interaction between the lateral andlongitudinal vehicle behavior is modeled by expressing theacceptable gap and acceleration level as functions of thelane change desire As shown in Figure 2 larger lane changedesires lead to smaller acceptable headways for the lanechanger and larger decelerations of the potential follower inthe target lane When the lane change desire is above dsync ordcoop drivers apply the same car following model as that ofthe leading vehicle in an adjacent lane to synchronize speeds

and create gaps to accommodate lane changemaneuversThisacceleration is constrained by a minimum value for comfortand safety

When modeling HOV lane operations 119889119894119895119887is set to a

positive constant for HOVs and to negative infinity for singleoccupant vehicles in the HOV lane when the HOV lane isactive A similar approach is used to model right lane biasof truck traffic In addition a lane change bias correlated tothe desired speed is added to reproduce the fact that driverswith higher desired speeds tend to travel on the left lanes offreeways and vice versa [27]

3 Model Calibration and Cross Validation

The driving behavior model for manually driven vehicleswas calibrated for a relatively complex freeway corridor inSacramento California

31 Selected Site State Route (SR) 99 northbound wasselected for model calibration This section of freeway spansfrom the Elk Grove Blvd interchange to the US-50 freewayinterchange south of downtown Sacramento CA As indi-cated by the arrows in Figure 3(a) there are 9 interchangeswith local arterial streets 4 partial cloverleaf interchanges 3full cloverleaf interchanges and 2 diamond interchanges withthe local arterials Furthermore detailed lane configurations


are shown in Figure 3(b)The on-ramp merging and weavingsections located at the Sheldon Rd interchange the FlorinRd interchange as well as the off-ramp at the US-50 freewayinterchange contribute to the morning peak recurrent delayobserved in this corridor This peak period typically beginsat 630 AM and ends around 1000 AM and the morningcongestion pattern exhibits the typical peak period whenthere is high demand for suburb to downtown trips duringthe morning hours Also shown in Figure 3(a) there is a widecoverage of detectors throughout the corridor Detectors withgood data quality are shown in blue thosewith less acceptabledata quality shown in red were not used to collect field datafor calibration and validation Currently the on-ramps aremetered using the local traffic responsive demand-capacityapproach in order to control the flow of on-ramp traffic andmitigate the peak hour congestion Lastly the traffic demandconsists of almost exclusively passenger cars with trucksaccounting for only 2 of the overall demand

32 Calibration Criteria and Procedures Microscopic simu-lation models were built in the AIMSUN [28] and MOTUS[26] platforms using the most up to date road geometry laneconfigurations and speed limits for the selected site Sinceadopting new driver behaviormodels in any simulation pack-age requires significant effort to ensure error-free simulationtheAIMSUNandMOTUS simulation packageswere selectedbased on relative ease of implementation Freeway mainlineand on-ramp data obtained from an 8-hour period (400 AMto 1200 PM) on October 6 2015 were used for the inputsin demand and turning percentages This 8-hour periodencompasses periods prior to during and after the peak Forthis corridor 5-minute interval loop detector data for flowwere obtained from PeMS [29] and used as the demand inputat the most upstream location of the simulation networkand the entry points of the on-ramps and as the turningpercentages at any applicable mainline-off-ramp split Twopassenger car equivalence (PCE) was used to represent eachtruck in the simulation (HCM 2010) Ramp metering ratesand algorithms were obtained from Caltrans District 3 andmodeled in AIMSUN simulation via the AIMSUN API(Application Programming Interface) [28] However rampmetering operation was not explicitly modeled in MOTUSAs an alternative flowmeasured immediately downstream ofthe ramp meter was used as the on-ramp demand input

The first proposed driving behaviormodel (PATHmodel)was simulated in AIMSUN via the MicroSDK (Micro-Software Development Kit) The latter model was simulatedin MOTUS [15 27]

Ten replications of the PATH model and five replicationsof the MOTUS model with different random number seedswere run in order to calibrate the models to the conditionsof October 6 2015 The predicted flows and speeds atselected locations on the freeway were compared with realtraffic measurements at every 5-minute interval to assessthe accuracy of the simulation models in representing theobserved conditions The predicted flow is acceptable if onaverage of all detectors for at least 85 of all 5-minute timeintervals the flow is to satisfy the condition that 119866119864119867(119896) lt 5[30]

The GEH statistic is computed as

119866119864119867(119896) = radic2 [119872 (119896) minus 119862 (119896)]2119872(119896) + 119862 (119896) (2)

where

119872(119896) simulated flow during the k-th time interval(vehhour)119862(119896) flow measured in the field during the k-th timeinterval (vehhour)

In addition we required that the Mean-Absolute-Percentage-Errors (MAPEs) of flows defined by equation(3) must be less than 10

119872119860119875119864 = 1119873 sdot 119879119873sum119899=1

119879sum119905=1

1003816100381610038161003816100381610038161003816100381610038161003816119872119903119890119886119897119899119905 minus119872119904119894119898119899119905119872119903119890119886119897119899119905

1003816100381610038161003816100381610038161003816100381610038161003816 (3)

where 119873 is the number of detectors and 119879 is the numberof time intervals 119872119903119890119886119897119899119905 and 119872119904119894119898119899119905 are the field observed andsimulated data (ie flow) of detector 119899 obtained during timeinterval t respectively

Furthermore we required that the Root-Mean SquareError (RMSEs) of flows defined by equation (4) must be lessthan 15 [13]

119877119872119878119864 = radic 1119873 sdot 119879119873sum119899=1

119879sum119905=1

(119872119903119890119886119897119899119905 minus119872119904119894119898119899119905119872119903119890119886119897119899119905 )2 (4)


Lastly the simulated flow-density relationship and queuepropagation must be visually acceptable [30] This indicatesthat the fundamental diagrams of field observed and sim-ulated flow versus density should resemble similar patternsfor key bottlenecks along the corridor and the contour plotsof the field observed and simulated speeds at all 5-minuteintervals should exhibit similar trends over the length of thecorridor as well as the duration of the study period

Results from the calibrated PATH and MOTUS modelswere later compared with results from the calibrated propri-etary driver behavior model found in AIMSUN The studyin (Wu et al 2014) conducted a calibration of the identicalSR99 corridor using the proprietary driver behavior foundAIMSUN this study used the same calibration criteria butwas limited to calibrating the flow

321 PATHModel Calibration Procedures Realistic values ofvarious driver behavior parameters were considered in themodel calibration The range of the parameter values used inthe calibration process are shown in the following

(i) Reaction time (120591119903) 06 s to 12 s with increment of 01s(ii) Maximum acceleration (119886119872) 12ms2 to 20ms2

with increment of 02ms2


Table 1 Calibrated PATHmodel parameters of the SR99 corridor

ParameterSymbol Mean Standard DeviationReaction time (120591119903) 08 s 02 sMaximum acceleration (119886119872) 20 ms2 05 ms2

Maximum deceleration (119887119891) 40 ms2 05 ms2

Time headway (120591ℎ) 140 02 sCoefficient of lane friction (119888119891) 05 0Speed difference threshold for DLC ((119907119886119899119905 minus 0)max(0119881119889119897119888)) 015 0

(iii) Maximum deceleration (119887119891) 20ms2 to 50ms2with increment of 05ms2

(iv) Time headway (120591ℎ) 100 s to 220 s with increment of020 s

(v) Coefficient of lane friction (119888119891) 05 to 10 withincrement of 01

(vi) Speed difference threshold for DLC ((V119886119899119905 minusV0)max(V0 119881119889119897119888)) 005 to 025 with incrementof 005

Based on the list of parameter values shown above thereare numerous possible sets of parameter value combinationsAll combinations of parameters were attempted and foreach set of parameters 10 replications were simulated todetermine if the particular parameter value combinationyields the macroscopic traffic pattern that is most similarto the macroscopic traffic pattern observed in the field Theparameter values that were realistic and provided the bestfit (based on the calibration criteria) were chosen Moresophisticated parameter search algorithms were avoided inorder to ensure reasonable simulation and computation timefor this complex corridor As shown in Table 1 simulationexperiments suggest that the following parameters (normallydistributed) provide a good fit

However poor visibility near on-ramp merging areasin the upstream 2-mile section of the corridor requiredincreasing the reaction time to 10 s to better reproducethe field observations Furthermore frequent aggressive andlast-minute lane changes observed in the field requiredreducing the reaction time to 04s for the short weavingsection between the upstream 12th Ave on-ramp and thedownstream US-50 off-ramp in order to replicate the highcapacity and relatively uncongested off-ramp bottleneck nearthe US-50 freeway interchange More than half of the SR-99trafficmake lane changes to access theUS-50 off-ramp duringthe morning peak

322 MOTUSModel Calibration Procedures In the MOTUSplatform the calibrated parameters involves both the lanechange model LMRS and the car following model IDM+[15 27]

A systematic search algorithm developed by Schakel et al[15] was used This algorithm iteratively searches for theoptimal parameters set that minimizes the 5-min flow and

speed errors between the simulated data and field data Theerror is defined as follows

120576 = radicsum119873119899=1sum119879119905=1 (12 sdot (119902119903119890119886119897119899119905 minus 119902119904119894119898119899119905 ))2119873 sdot 119867 + 25

sdot radicsum119873119899=1sum119879119905=1 (V119903119890119886119897119899119905 minus V119904119894119898119899119905 )2119873 sdot 119867 + 119898(5)

where119898 is the number of deleted vehicles in the simulationThe algorithm first calibrates the parameters related

to free-flow traffic conditions and then the parameterscorresponding to oversaturatedcongested conditions Theparameters corresponding to the free-flow conditions aresummarized in the following

(i) Averaged free-flow speed (Vdescar) 123 kmh to127 kmh with increment of 05 kmh

(ii) 120590car 8 kmh to 13 kmh with increment of 025 kmh(iii) Averaged free-flow speed (Vdestruck) 80 kmh to

100 kmh with increment of 5 kmh(iv) Sensitivity to speed gain (vgain) 50 kmh to 60 kmh

with increment of 1 kmh(v) Free lane change criteria (dfree) 02 to 04 with

increment of 005(vi) Lane change desire per lane (1199050) 47 s to 53 s with

increment of 1 s(vii) SOV bias (119889119887) 04 to 06 with increment of 005(viii) Low desire-speed bias 02 to 04 with increment of

005(ix) Local high desire-speed bias 02 to 04 with incre-

ment of 005

The parameters corresponding to the oversaturatedcon-gested conditions are summarized in the following

(i) Average maximum headway (Tmax) 11 s to 15 s withincrement of 005 s

(ii) Average minimum headway (Tmin) 05 s to 065 swith increment of 005 s

(iii) Car acceleration (acar) 12ms2 to 14ms2 withincrement of 01ms2


Table 2 Calibrated MOTUS parameters of the SR99 corridor

ParameterSymbol Original values Calibrated valuesSensitivity to speed gain vgain 696 kmh 54 kmhCar acceleration acar 125 ms2 125 ms2

Truck acceleration atruck 04 ms2 08 ms2

Free lane change criteria dfree 0365 025Synchronized lane change criteria dsync 0577 05Cooperative lane change criteria dcoop 0788 075Maximum deceleration b 209 ms2 209 ms2

Average maximum headwayTmax 12 s 14 sAverage minimum headwayTmin 056 s 052 sLane change desire per lane 1199050 43 s 52 sAveraged free-flow speed Vdescar 1237 kmh 125 kmh120590car 12 kmh 875 kmhAveraged free-flow speed Vdestruck 85 kmh 85 kmh120590truck 25 kmh 25 kmhHOV bias dHOV - 045SOV bias db - 05Low desire-speed bias - 025Local high desire-speed bias - 025

(iv) Truck acceleration (atruck) 05ms2 to 1ms2 withincrement of 01ms2

(v) HOV bias (dHOV) 02 s to 06 s with increment of005ms

This algorithm first searches a wide range of possibleparameter values prior to converging to a smaller range ofpossible parameter values For each iteration five replicationswith different random seeds were conducted Lastly the sim-ulated results obtained using the optimal parameter valuesmust satisfy the calibration criteria

As shown in Table 2 differences can be found in param-eter values between the calibrated results and default valuesA smaller speed gain in our results implies that simulated USdrivers are more sensitive to the speed change in target laneand a low value of dfre119890 suggests that drivers are more likelyto change lanes compared to the Dutch traffic representedby the original values Changes of Tmin and Tmax indicatea less centralized distribution of vehicle headway in thesimulated corridor and an increased 1199050 indicates driversrsquo earlypreparation prior to exiting at an off-ramp

Furthermore a local headway ratio was applied at dif-ferent segments of the corridor The local headway ratiowas used to increase or reduce vehicle headways at certainlocations in order to reproduce characteristics that are uniqueto certain sections of the corridor For the segment upstreamof the Calvine Rd interchange the local headway ratio rangesfrom 128 to 135 and it increases to 145-158 at the four-lane segments between the Calvine Rd and the Fruitridge Rdinterchanges For the remaining downstream section (up toUS-50) a smaller value of 06 was used for the local headwayratio tomaintain the high flow observed in the fieldThe localheadway ratios were fine-tuned individually by comparingthe section-based fundamental diagrams

33 Model Cross Validation and Discussion

331 Quantitative Results Tables 3ndash5 summarize the flowcalibration results for the 16 detectors that provided good dataalong the 13-mile stretch of northbound SR-99 The HOVlane data were aggregated with those of the general purposelanes because the HOV lane is equally congested and exhibitsnearly the same congestion pattern (bottleneck location andduration) as the general purpose lanes It can be seen that onaverage the simulated flows satisfied the calibration criteriaHowever the AIMSUNmodel cannot accurately simulate theflow of the downstream weaving bottleneck at US-50 underthe GEHMAPE and RMSE criteriaThis could be attributedto the limitation that modelrsquos lane changing logic does notreflect the unusually aggressive and frequent lane changebehavior Modeling such area may require better developedlane changing gap acceptance criteria that specifically fit suchan off-ramp bottleneck

The MOTUS model met the GEH and RMSE criteriaat all the detectors along the whole corridor Although theoverall MAPE was less than 10 the MAPEs at 4 locations(out of 16 detector stations) were slightly higher than 10These correspond to the Elk Grove bottleneck EB Sheldonbottleneck and the EBMack bottleneck where the simulatedflow was lower than the flow observed in the field

In addition Figure 4 shows a scatter plot of all simulatedand field observed flows obtained throughout the corridorand the entire analysis period Both the PATH model andthe MOTUS model simulated flows that strongly correlatewith the field observed flows the MOTUS model performedslightly better with an R2 value of 09266 instead of an R2value of 08939 achieved by the PATHmodel

Nevertheless both the PATH model and the MOTUSmodel performed better than the proprietary driver behavior


Table 3 Calibration of freeway flows under GEH criterion

Freeway 5-min flows of SR-99 NorthboundCriterion 1 GEH

Detector Location(post-mile)

Target AIMSUN MOTUSMet Target Met Met Target Met

2873 GEH lt 5 for gt 85 of k 100 Yes 9467 Yes














2979 GEH lt 5 for gt 85 of k 7927 No 9867 Yes


Overall GEH lt 5 for gt 85 of k 9408 Yes 9503 Yes

Table 4 Calibration of freeway flows under MAPE criterion

Freeway 5-min flows of SR-99 NorthboundCriterion 2 MAPE


Target AIMSUN MOTUSMAPE Target Met MAPE Target Met

2873 MAPE lt 10 199 Yes 558 Yes

2876 MAPE lt 10 936 Yes 1185 No

2893 MAPE lt 10 917 Yes 1080 No

2894 MAPE lt 10 861 Yes 988 Yes

2900 MAPE lt 10 685 Yes 842 Yes

2907 MAPE lt 10 741 Yes 908 Yes

2915 MAPE lt 10 992 Yes 1056 No

2919 MAPE lt 10 1038 No 1121 No

2924 MAPE lt 10 898 Yes 959 Yes

2928 MAPE lt 10 802 Yes 935 Yes

2940 MAPE lt 10 837 Yes 901 Yes

2947 MAPE lt 10 737 Yes 826 Yes

2953 MAPE lt 10 801 Yes 814 Yes

2960 MAPE lt 10 1052 No 748 Yes

2979 MAPE lt 10 1420 No 723 Yes

2985 MAPE lt 10 1409 No 849 Yes

Overall MAPE lt 10 821 Yes 906 Yes


Table 5 Calibration of freeway flows under RMSE criterion

Freeway 5-min flows of SR-99 NorthboundCriterion 3 RMSE

Detector Location(post-mile) Target AIMSUN MOTUS

RMSE Target Met RMSE Target Met2873 RMSPE lt 15 259 Yes 1254 Yes2876 RMSPE lt 15 1361 Yes 1446 Yes2893 RMSPE lt 15 1198 Yes 1310 Yes2894 RMSPE lt 15 1166 Yes 1196 Yes2900 RMSPE lt 15 965 Yes 1019 Yes2907 RMSPE lt 15 1102 Yes 1041 Yes2915 RMSPE lt 15 1541 No 1255 Yes2919 RMSPE lt 15 1597 No 1325 Yes2924 RMSPE lt 15 1361 Yes 1134 Yes2928 RMSPE lt 15 1278 Yes 1106 Yes2940 RMSPE lt 15 1174 Yes 978 Yes2947 RMSPE lt 15 939 Yes 903 Yes2953 RMSPE lt 15 1005 Yes 884 Yes2960 RMSPE lt 15 1263 Yes 850 Yes2979 RMSPE lt 15 1543 No 863 Yes2985 RMSPE lt 15 1545 No 909 YesOverall RMSPE lt 15 1199 Yes 1135 Yes

Sim

ulat

ed F

low

(vph

)

Field Observed Flow (vph)0 1000 2000 3000 4000

PATHMOTUS

5000 6000 7000 8000 9000 10000

9000

8000

7000

6000

5000

4000

3000

2000

1000

0

10000

２2 = 08939

２2 = 09266

Figure 4 Scatter plot of simulated versus field observed flows

model in AIMSUN As discussed in the calibration studyby Wu et al (2014) the proprietary AIMSUN model canonly accurately reproduce flows for a portion of the corridorThe portion of the corridor upstream of the Calvine Rd on-ramps (postmile 2907) was well calibrated both the GEHcriterion andRMSE criterionused in this studywere satisfiedHowever the portion of the corridor downstream of theCalvine Rd on-ramps (accounting for major of the corridorlength) cannot be well calibrated the best results yielded

the less than satisfactory RMSE values of 15 or higher andresulted in GEHlt5 unsatisfied for more than 85 of the timesteps

332 FlowCharacteristics Comparison Figure 5 summarizesthe simulated versus observed speed contour plots Thecontour plots show the 5-minute average speeds at thedetectors throughout the selected peak period The first andlast hour (low demand and free-flowing) were omitted from


Time0500 0600 0700 0800 0900 1000 1100

Field Data

288

290

292

294

296

298

Post-

mile

0

10

20

30

40

50

60

70

Spee

d (m

ph)

(a) Speed contour plot field observation

Time0500 0600 0700 0800 0900 1000 1100

Simulated Data AIMSUN

288

290

292

294

296

298

Post-

mile

0

10

20

30

40

50

60

70

Spee

d (m

ph)

(b) Speed contour plot AIMSUN simulation

Time0500 0600 0700 0800 0900 1000 1100

Simulated Data MOTUS

288

290

292

294

296

298

Post-

mile

0

10

20

30

40

50

60

70

Spee

d (m

ph)

(c) Speed contour plot MOTUS simulation

Figure 5 Comparison of speed contour plots


Flow vs Density

AIMSUNSimulation

Field SimulationMOTUS

50 100 150 2000Density (vehmi)

0

1000

2000

3000

4000

5000

6000

7000

8000Fl

ow (v

ehh

r)

(a) Sample replication 1

Flow vs Density

AIMSUNSimulation

SimulationFieldMOTUS

0

1000

2000

3000

4000

5000

6000

7000

8000

Flow

(veh

hr)


(b) Sample replication 2

Figure 6 Comparison of field observed and AIMSUN andMOTUS simulated flow versus density relationship at Florin Rd bottleneck (mile294)

the figures Both models reproduced the field observed peakduration and the length of queue fairly accurately with theexception of the most upstream bottleneck at Sheldon Rdwhich the PATHmodel simulated slightly shorter congestionduration and slightly less queue propagation Additionallythe PATH model simulated faster queue dissipation asevident in the shorter peak duration shown in Figure 5(b)This could be attributed to the higher acceleration and decel-eration rate applied in the PATH model The lane changingand gap acceptance criteria required larger acceleration anddeceleration to prevent simulating low bottleneck flows andsevere queue propagation Such approach ensured accuraterepresentation of the relatively aggressive driver behavior atthe beginning of the peak However the same criteria couldnot replicate the slower queue dissipation and longer peakperiod due to the temporal variation of driver behavior fromthe beginning to the end of the peak period This compro-mised the accuracy of peak duration but can be adjustedby applying different parameter values and lane changingand gap acceptance criteria for different time periods of theday

The PATH model was able to replicate the speed profilesof the most downstream bottleneck which is a complexweaving section with more than 50 off-ramp traffic InMOTUS a special local headway was applied here to meetthe traffic throughputs but unfortunately the model could notsimulate the slight speed reduction at this bottleneck

Figure 6 shows the field observed and simulated flow-density relationships of a four-lane mainline section at themost important bottleneck the Florin Rd on-ramps atmile 294 obtained from two sample replications In bothreplications the simulated data provided near-perfect matchin the uncongested state as well as good representation ofthe congested state Both models simulated the free-flowspeed of 67 mileshour However the PATHmodel simulatedslightly lower than observed maximum capacity This could

possibly be explained by the different methods of generatingdiscretionary lane changes the PATH model generates morediscretionary lane changes in free-flow conditions whichultimately affects the bottleneck discharge rate Additionallythe MOTUS model has a right lane bias and prioritizesthe freeway mainline which leads to less efficient mergingand more queuing on the on-ramps This delayed queuedissipation at the freeway bottleneck and resulted in moredata points corresponding to traffic conditions with higherdensities as illustrated by the red data points in Figure 6

4 Discussion

The simulation results show that the two models are capableof simulating traffic flow characteristics of the complexcorridor with varying demand interacting bottlenecks andan HOV lane Although originated from different basemodels and developed separately by two teams the twomodel approaches focus on refined description of merg-ingdiverging behavior lane preference and cooperative carfollowing behavior in the vicinity of merge and divergesections

Comparison of the two models and validation resultsgives consistent insights into the traffic flow models forcomplex corridors that can be generalized to other simulationtools

The anticipative behavior of the merging vehicles hasbeen captured by many models where the merger alignsits speed with that of the potential leader in the target laneon the mainline However this may not suffice to replicatemerging behavior in congested traffic conditions where themerging vehicle needs to enter the mainline at close spacingThis requires the cooperative (car following) behavior ofthe vehicles in the mainline to yield a gap for the mergingvehicle and an adaptive gap acceptance behavior wheredriver behavior of which the merger accepts short gaps to


change lane and gradually relaxes to the comfortable gaps[15 22]

In weaving bottlenecks the diverging behavior also playsan important role in the resulting flow features Existingmodels often result in short-sighted driver behavior nearoff-ramps which deteriorates traffic operations at weavingbottlenecks and leads to more severe congestion than empir-ical observations The two models capture the anticipativebehavior of drivers by adding an anticipation time andanticipation distance before the off-ramp implying the earlypreparation of the exiting maneuvers [15 22] This appearsto be an essential feature in weaving bottlenecks according toour experience

With activation of HOV lanes the lane preference ofHOV and SOV are affected This should be captured by themodel to replicate the HOV lane operations For modelswithout an explicit target lane choice component the discre-tionary lane change bias (in MOTUS) or discretionary lanechange motivation (in the PATHmodel) towardoutward theHOV lane can be a simple way to capture this lane prefer-ence

Last but not least both models adopt local behaviorparameters (local desired headway in MOTUS and localreaction time in the PATH model) for different bottlenecksto reflect the capacity differences due to road geometricslane markings etc Note that for most car following modelsthose parameters affect the resulting capacity and traffic flowstability It thus influences both the onset and dissipation ofcongestion

Overall both the PATH model and the MOTUS modeloutperformed the proprietary driver behavior model inAIMSUN The calibration study by Wu et al (2014) showedthat the proprietary AIMSUN model can only accuratelyreproduce the observed flows in less than half of the identicalcorridor

Despite the successful calibration of the complex free-way both models present some limitations As shown inFigure 5(b) the PATH model has difficulties in reproducingthe duration of queue dissipation with the current parametervalues which are suitable for modeling queue formation andpropagation This implies that the model cannot depict theinconsistent behavior patterns drivers adopt at the beginningand at the end of a congestion period To address thisproblem we can describe key behavior parameters of asubject driver (eg reaction timemaximum acceleration anddeceleration) as a function of the time in congested stateThe driver would act aggressively at the beginning of thecongestion but become sluggish after spending some timein congestion This method should improve the capabilityof the PATH model in reproducing the duration of conges-tions

MOTUSwas originally developed based onDutch trafficwhere keep-right directive and mainline traffic priority areapplied The absence of keep-right directive and mainlinepriority in the US results in more efficient merging traf-fic observed in the field data than in the MOTUS sim-ulation Although effort had been devoted to mitigatingthe problem we still found vehicles queuing on the on-ramp which leads to the late dissipation of queue at Florin

Rd bottleneck compared to field observations as seen inFigure 5(c)

Another point of attention is the most downstream partof the network where nearly half of the traffic performedlane changes to access the off-ramp at the US-50 interchangeMOTUS produced more congested traffic than field obser-vations if a special treatment of a small local headway werenot predefinedThis problemmight come from short-sightedsynchronizing vehicles that do not anticipate acceptable gapsnear the downstream section An alternative is to set locallane change parameters or no synchronization during lowspeeds

Overall although it is worth noting the differencesbetween the simulated data (obtained from bothmodels) andthe field data the goal of this study is not to precisely calibratethe model for this specific data set but to cross-validate andrecommend two generalizable driving behavior models thatcan reasonably reproduce the onset of congestion capacitydrop queue propagation and queue dissipation at a complexcorridor with multiple interacting bottlenecks and managedlanes

5 Concluding Remarks and Future Work

This paper presented two driving behavior model alternativesto the driving behavior models in the widely acceptedmicroscopic simulation packages such as AIMSUN VISSIMand PARAMICS These models are intended to reproducethe traffic dynamics of large scale and complex freewaycorridors for longer durations which can be difficult bysimply relying on the default models in simulation packagessuch as AIMSUN VISSIM and PARAMICS

A case study has been conducted using real-world datafrom an 8 hour period at a complex freeway corridornear Sacramento California where the two proposed driverbehavior models accurately replicated the locations andthroughput of the freeway bottlenecks as well as the spatialand temporal distributions of speeds The models have beencross-validated and performed well with similar accuracyMost importantly bothmodels outperformed the proprietarydriver behavior model commercially available in AIMSUN

Comparison of the two modeling approaches shows thatboth models capture the anticipative diverging behaviorlane preference in presence of dedicated lane cooperativebehavior of mainline vehicles to facilitate merging at shortspacing at merge and diverge sections and adaptive desiredtime headway settings at different road sections along thecorridor The consistent insights into the traffic flow modelsfor complex corridors can be generalized to other simulationtools

In the future the validated models will be improvedand enhanced to simulate and assess the potential benefit ofconnected and automated vehicles for real-world freeways

Data Availability

The data used to support the findings of this study can befound in the Caltrans Performance Measurement System(PeMS) at httppemsdotcagov


Disclosure

This work was presented at the 97th Transportation ResearchBoard (TRB) Annual Meeting The contents of this paperreflect the views of the authors who are responsible forthe facts and the accuracy of the data presented hereinThe contents do not necessarily reflect the official views orpolicies of FHWAThis paper does not constitute a standardspecification or regulation

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work is supported by the Federal Highway Ad-ministrationrsquos Exploratory Advanced Research Program(EARP) under Cooperative Agreement no DTFH61-13-H00013 and the Federal Highway Administration (FHWA)Exploratory Advanced Research Project (Cooperative Agree-ment DTFH61-13-R-00011)

References

[1] B Ciuffo V Punzo and M Montanino ldquoThirty Years of GippsrsquoCar-Following Modelrdquo Transportation Research Record vol2315 no 1 pp 89ndash99 2012

[2] D E Goldberg ldquoGenetic algorithms in search optimizationand machine learningrdquo Choice Reviews Online vol 27 no 02pp 27-0936ndash27-0936 1989

[3] R L Cheu W W Recker and S G Ritchie ldquoCalibration ofINTRAS for simulation of 30-sec loop detector outputrdquo Trans-portation Research Record no 1457 pp 208ndash215 1994

[4] J Hourdakis P GMichalopoulos and J Kottommannil ldquoPrac-tical Procedure for Calibrating Microscopic Traffic SimulationModelsrdquo Transportation Research Record vol 1852 no 1 pp130ndash139 2003

[5] R Dowling A Skabardonis and V Alexiadis Traffic AnalysisToolbox Volume III Guidelines for Applying Traffic Microsim-ulation Modeling Soware Federal Highway AdministrationPublication No FHWA-HRT-04-038 2004

[6] G Gomes A May and R Horowitz ldquoCongested freewaymicrosimulation model using VISSIMrdquo Transportation Re-search Record no 1876 pp 71ndash81 2004

[7] P Ranjitkar T Nakatsuji and M Asano ldquoPerformance eval-uation of microscopic traffic models with test track datardquoTransportation Research Record no 1876 pp 90ndash100 2004

[8] E Brockfeld R D Kuhne and P Wagner ldquoCalibration andvalidation of microscopicmodels of traffic flowrdquoTransportationResearch Record vol 1934 no 1 pp 179ndash187 2005

[9] B Park and H Qi ldquoDevelopment and evaluation of a proce-dure for the calibration of simulation modelsrdquo TransportationResearch Record vol 1934 pp 208ndash217 2005

[10] H M Zhang J Ma and H Dong ldquoDeveloping calibrationtools for microscopic traffic simulation part II Calibrationframework and calibration of localglobal driving behaviorand DR choice model parametersrdquo California PATH ResearchReport University of California at Davis 2006

[11] J Ma H Dong and H M Zhang ldquoCalibration of Microsim-ulation with Heuristic Optimization Methodsrdquo TransportationResearch Record vol 1999 no 1 pp 208ndash217 2007

[12] J Lee B J Park I Won and Yun ldquoA simplified procedurefor calibrating microscopic traffic simulation modelsrdquo in Pro-ceedings of the CD ROM 92nd Transportation Research BoardAnnual Meeting pp 13ndash17 Washington DC USA Jan 2013

[13] XY Lu J Y LeeD J Chen J BaredDDailey andS ShladoverldquoFreeway micro-simulation calibration case study using aim-sun and VISSIM with detailed field datardquo in Proceedings of theCD ROM 93rd Transportation Research Board Annual MeetingWashington DC USA Jan 2014

[14] C P I J vanHinsbergen W J Schakel V L Knoop JW C vanLint and S P Hoogendoorn ldquoA general framework for calibrat-ing and comparing car-following modelsrdquo Transportmetrica ATransport Science vol 11 no 5 pp 420ndash440 2015

[15] W Schakel V Knoop andBVanArem ldquoIntegrated lane changemodel with relaxation and synchronizationrdquo TransportationResearch Record vol 2316 pp 47ndash57 2012

[16] H Yeo A Skabardonis J Halkias J Colyar and V AlexiadisldquoOversaturated freeway flow algorithm for use in Next Genera-tion Simulationrdquo Transportation Research Record no 2088 pp68ndash79 2008

[17] C-J Wu X Y Lu R Horowitz and S Shladover ldquoMicrosimu-lation of congested freeway with multiple vehicle classes usingAIMSUN a case study on SR-99Nrdquo in Proceedings of the TRBAnnual Meeting Washington DC USA Jan 2016

[18] M Menendez An Analysis of HOV Lanes eir Impact onTraffic [PhD thesis] University of California Berkeley 2006

[19] A Guin M Hunter and R Guensler ldquoAnalysis of reduction ineffective capacities of high-occupancy vehicle lanes related totraffic behaviorrdquo Transportation Research Record no 2065 pp47ndash53 2008

[20] C Chen P Varaiya and J Kwon ldquoAn empirical assessmentof traffic operationsrdquo in Proceedings of the 16th InternationalSymposium on Transportation and Traffic eory ElsevierCollege Park Maryland USA 2015

[21] L Bloomberg and J Dale ldquoComparison of VISSIM andCORSIM traffic simulation models on a congested networkrdquoTransportation Research Record no 1727 pp 52ndash60 2000

[22] X Lu X Kan S E Shladover D Wei and R A Ferlis ldquoAnenhanced microscopic traffic simulation model for applicationto connected automated vehiclesrdquo in Proceedings of the Trans-portation Research Board 96th Annual Meeting WashingtonDC USA 2017

[23] G F Newell ldquoA simplified car following theory a lower ordermodelrdquoTransportation Research Part B Methodological vol 36no 3 pp 195ndash205 2002

[24] P G Gipps ldquoA model for the structure of lane-changingdecisionsrdquo Transportation Research Part B Methodological vol20 no 5 pp 403ndash414 1986

[25] W J Schakel B Van Arem and B D Netten ldquoEffects ofcooperative adaptive cruise control on traffic flow stabilityrdquo inProceedings of the 13th International IEEE Conference on Intelli-gent Transportation Systems ITSC 2010 pp 759ndash764 MadeiraIsland Portugal September 2010

[26] Delft University of Technology MOTUS httphomepagetudelftnl05a3n 2015

[27] L Xiao M Wang W J Schakel and B Arem van ldquoModelinghighway lane change behavior under high occupancy lanes with


continuous access and egressrdquo in Proceedings of the Transporta-tion Research Board 96th Annual Meeting Washington DCUSA 2017

[28] TSS-Aimsun httpwwwaimsuncom 2017[29] Caltrans PeMS httppemsdotcagov 2016[30] WSDOT ldquoFreeway System Operational Assessment - Param-

ics Calibration and Validation Guidelines (Draft)rdquo TechnicalReport I-33WisconsinDOTDistrictWisconsinDOTDistrict2 USA June 2002

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018


Active and Passive Electronic Components

VLSI Design



Shock and Vibration


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Journal of

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Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of



Journal ofEngineeringVolume 2018

SensorsJournal of



RotatingMachinery


Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation


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wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom


onset of congestion capacity drop queue propagation andqueue dissipation when interacting bottlenecks are presentin freeway corridors as demonstrated by a simulation studyon a 13-mile corridor in Sacramento California [16 17]

In addition dedicated lanes generatemore complex trafficdynamics on freeway corridors Friction effect has beenobserved on freeways with HOV lanes characterized bythe speed reduction on the HOV lane when the adjacentgeneral purpose lane is congested [18ndash20] Modeling the dif-ferences in lane usage and lane change between HOV andsingle occupancy vehicles is important to reproduce thetraffic conditions around HOV lanes Although different lanechangemodels have been proposed to capture this large scalesimulation and validation of the lane change model haverarely been reported

The aforementioned problems motivate the developmentof alternative driving behavior models for car followingmerging lane changing etc to better represent the complextraffic dynamics of large scale freeway corridors with dedi-cated lanes Such models will allow users to implement theirexternal behavioral models using software development kitsto simulate driving behavior with the commercial simulationplatforms such as Aimsun and VISSIM or develop completeopen simulation tools In addition it is almost impractical todevelop amodel that is able to perfectly reproduce real-worldobservations Cross-comparison between models has shownto be beneficial [21] since it makes the analysis more reliableand the results more defensible giving more confidence tousers about the simulation results Unfortunately there havenot been any well established and cross-validated alternativecar following and lane changingmodels that are applicable forcomplex freeway corridors

In response this paper introduces two such models anddemonstrates the results of their validation against real-world data from a 13-mile freeway corridor during an 8hour period Although originated from different base modelsand developed separately by two teams the two proposedalternatives focus on refined description ofmerging behaviorlane preference and cooperative car following behavior inthe vicinity of merge and diverge sections They are validatedagainst empirical loop detector data and against each otherThe two models show extremely good agreement betweenfield data and model predictions Comparison of the twomodels and validation results give consistent insights into thetraffic flow models for complex corridors that can be gener-alized to other simulation tools Furthermore both modelsperformed better than the proprietary driver behaviormodel

The rest of the paper is organized as follows the nextsection presents an overview of two proposed alternativedriving behavior models The following section documentsthe calibration and cross validation of both models usingarchived data from a complex freeway corridor The finalsection summarizes and highlights the contribution of thispaper

2 Proposed Driver Behavior Models

Microscopic vehicle behavior and interaction with the nearbyvehicles determine overall traffic behavior at the macroscopic

level based upon the following factors maximum acceler-ationdeceleration and driver behaviors such as preferredheadway and response time gap acceptance threshold forlane changing and perception advance time period or dis-tance for lane changing Those parameters directly affectdensity and delays in the simulation and thus the overalltraffic pattern Below we discuss the two alternative modelsand highlight the main features

21 Alternative 1 Driving Behavior Model Based on NGSIMModel The first proposed driving behavior model (PATHmodel) is built upon the basic framework of the NGSIMoversaturated flow model proposed by Yeo et al [16] Someimportant extensions and modifications were made in orderto depict detailed car following and lane changing behaviorthat were not represented in the original model

To determine the trajectory of a vehicle at a microscopiclevel it is necessary and sufficient to iteratively determineits location at each time step which can be realized througha discrete kinematic model if the desired acceleration andcurrent speed are known [22] The latter is known fromthe last step calculation The former is determined by thedynamic interactions with the adjacent vehicles geometricconstraints and the overall traffic conditions The dynamicinteractions include timeclearance gaps for safety andmobil-ity and possible scenarios associated with lane changes [22]Those scenarios are further partitioned into fundamentalscenarios (or movement phases) and transitions betweenthem for continuoussmooth speed trajectories

(i) CF regular car following mode(ii) YCF yielding (cooperative) car following mode(iii) LC lane change mode which includes discretionary

lane change (DLC) and mandatory lane change(MLC)

(iv) ACF after lane changing car following mode (adriver temporarily adopts a short gap following a lanechange maneuver)

(v) BCF before lane changing car following mode (adriver speeds up or slows down to align with anacceptable gap in the target lane)

(vi) RCF receiving car following mode (a driver tem-porarily adopts a short gap after a vehicle from theadjacent lane merges in front)

The discretized kinematic model is detailed in [22] Asdiscussed in [22] Newellrsquos simplified car following modelwith constraints for safety and acceleration [23] is appliedThe Gippsrsquo deceleration component [1 24] is used here toplace a safety margin onNewellrsquos simplified equation Furtherdetails such as permissible speed and cross-lane friction onmultilane freeways are detailed in [22]

The fundamental scenarios associated with lane changing(LC) are outlined in Figure 1 and discussed in detail by Luet al [22]

As detailed in [22] there are two types of lane changesMandatory lane change is intended for merging onto orexiting the freeway Discretionary lane change is intended for


CF

Is current


Acceptgap

No

No

No

No

No

Yes

Yes

Yes

Yes

Yes

RCF

ACFACF

RCF

YCF

BCF

LC



HeadwayDeceleration



No LC FLC CLC

yesyes

yesno

nono

nono

SLC

Keep right

dfree dsync dcoop






119889119894119895 = 119889119894119895119903119900119906119905119890 + 120579119894119895V119900119897119906119899119905119886119903119910 sdot (119889119894119895119904119901119890119890119889 + 119889119894119895119887) (1)





99NB -gt

50W

B

WB Florin

Rd

WB Sh

eldon Rd

Elk Grove Blvd

Post-miles 2985 2979 2960 2953 2947 2939 2928 2924 2919 2915 2906 2900 2894 2893 2876 2873

















119866119864119867(119896) = radic2 [119872 (119896) minus 119862 (119896)]2119872(119896) + 119862 (119896) (2)

where



119872119860119875119864 = 1119873 sdot 119879119873sum119899=1

119879sum119905=1

1003816100381610038161003816100381610038161003816100381610038161003816119872119903119890119886119897119899119905 minus119872119904119894119898119899119905119872119903119890119886119897119899119905

1003816100381610038161003816100381610038161003816100381610038161003816 (3)



119877119872119878119864 = radic 1119873 sdot 119879119873sum119899=1

119879sum119905=1

(119872119903119890119886119897119899119905 minus119872119904119894119898119899119905119872119903119890119886119897119899119905 )2 (4)
































ment of 005















































2873 MAPE lt 10 199 Yes 558 Yes

2876 MAPE lt 10 936 Yes 1185 No

2893 MAPE lt 10 917 Yes 1080 No

2894 MAPE lt 10 861 Yes 988 Yes

2900 MAPE lt 10 685 Yes 842 Yes

2907 MAPE lt 10 741 Yes 908 Yes

2915 MAPE lt 10 992 Yes 1056 No

2919 MAPE lt 10 1038 No 1121 No

2924 MAPE lt 10 898 Yes 959 Yes

2928 MAPE lt 10 802 Yes 935 Yes

2940 MAPE lt 10 837 Yes 901 Yes

2947 MAPE lt 10 737 Yes 826 Yes

2953 MAPE lt 10 801 Yes 814 Yes

2960 MAPE lt 10 1052 No 748 Yes

2979 MAPE lt 10 1420 No 723 Yes

2985 MAPE lt 10 1409 No 849 Yes







Sim

ulat

ed F

low

(vph

)


PATHMOTUS

5000 6000 7000 8000 9000 10000

9000

8000

7000

6000

5000

4000

3000

2000

1000

0

10000

２2 = 08939

２2 = 09266






Time0500 0600 0700 0800 0900 1000 1100

Field Data

288

290

292

294

296

298

Post-

mile

0

10

20

30

40

50

60

70

Spee

d (m

ph)


Time0500 0600 0700 0800 0900 1000 1100


288

290

292

294

296

298

Post-

mile

0

10

20

30

40

50

60

70

Spee

d (m

ph)


Time0500 0600 0700 0800 0900 1000 1100


288

290

292

294

296

298

Post-

mile

0

10

20

30

40

50

60

70

Spee

d (m

ph)




Flow vs Density

AIMSUNSimulation



0

1000

2000

3000

4000

5000

6000

7000

8000Fl

ow (v

ehh

r)


Flow vs Density

AIMSUNSimulation


0

1000

2000

3000

4000

5000

6000

7000

8000

Flow

(veh

hr)








4 Discussion




















Data Availability



Disclosure




Acknowledgments


References


































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



CF

Is current


Acceptgap

No

No

No

No

No

Yes

Yes

Yes

Yes

Yes

RCF

ACFACF

RCF

YCF

BCF

LC



HeadwayDeceleration



No LC FLC CLC

yesyes

yesno

nono

nono

SLC

Keep right

dfree dsync dcoop






119889119894119895 = 119889119894119895119903119900119906119905119890 + 120579119894119895V119900119897119906119899119905119886119903119910 sdot (119889119894119895119904119901119890119890119889 + 119889119894119895119887) (1)





99NB -gt

50W

B

WB Florin

Rd

WB Sh

eldon Rd

Elk Grove Blvd

Post-miles 2985 2979 2960 2953 2947 2939 2928 2924 2919 2915 2906 2900 2894 2893 2876 2873

















119866119864119867(119896) = radic2 [119872 (119896) minus 119862 (119896)]2119872(119896) + 119862 (119896) (2)

where



119872119860119875119864 = 1119873 sdot 119879119873sum119899=1

119879sum119905=1

1003816100381610038161003816100381610038161003816100381610038161003816119872119903119890119886119897119899119905 minus119872119904119894119898119899119905119872119903119890119886119897119899119905

1003816100381610038161003816100381610038161003816100381610038161003816 (3)



119877119872119878119864 = radic 1119873 sdot 119879119873sum119899=1

119879sum119905=1

(119872119903119890119886119897119899119905 minus119872119904119894119898119899119905119872119903119890119886119897119899119905 )2 (4)
































ment of 005















































2873 MAPE lt 10 199 Yes 558 Yes

2876 MAPE lt 10 936 Yes 1185 No

2893 MAPE lt 10 917 Yes 1080 No

2894 MAPE lt 10 861 Yes 988 Yes

2900 MAPE lt 10 685 Yes 842 Yes

2907 MAPE lt 10 741 Yes 908 Yes

2915 MAPE lt 10 992 Yes 1056 No

2919 MAPE lt 10 1038 No 1121 No

2924 MAPE lt 10 898 Yes 959 Yes

2928 MAPE lt 10 802 Yes 935 Yes

2940 MAPE lt 10 837 Yes 901 Yes

2947 MAPE lt 10 737 Yes 826 Yes

2953 MAPE lt 10 801 Yes 814 Yes

2960 MAPE lt 10 1052 No 748 Yes

2979 MAPE lt 10 1420 No 723 Yes

2985 MAPE lt 10 1409 No 849 Yes







Sim

ulat

ed F

low

(vph

)


PATHMOTUS

5000 6000 7000 8000 9000 10000

9000

8000

7000

6000

5000

4000

3000

2000

1000

0

10000

２2 = 08939

２2 = 09266






Time0500 0600 0700 0800 0900 1000 1100

Field Data

288

290

292

294

296

298

Post-

mile

0

10

20

30

40

50

60

70

Spee

d (m

ph)


Time0500 0600 0700 0800 0900 1000 1100


288

290

292

294

296

298

Post-

mile

0

10

20

30

40

50

60

70

Spee

d (m

ph)


Time0500 0600 0700 0800 0900 1000 1100


288

290

292

294

296

298

Post-

mile

0

10

20

30

40

50

60

70

Spee

d (m

ph)




Flow vs Density

AIMSUNSimulation



0

1000

2000

3000

4000

5000

6000

7000

8000Fl

ow (v

ehh

r)


Flow vs Density

AIMSUNSimulation


0

1000

2000

3000

4000

5000

6000

7000

8000

Flow

(veh

hr)








4 Discussion




















Data Availability



Disclosure




Acknowledgments


References


































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




99NB -gt

50W

B

WB Florin

Rd

WB Sh

eldon Rd

Elk Grove Blvd

Post-miles 2985 2979 2960 2953 2947 2939 2928 2924 2919 2915 2906 2900 2894 2893 2876 2873

















119866119864119867(119896) = radic2 [119872 (119896) minus 119862 (119896)]2119872(119896) + 119862 (119896) (2)

where



119872119860119875119864 = 1119873 sdot 119879119873sum119899=1

119879sum119905=1

1003816100381610038161003816100381610038161003816100381610038161003816119872119903119890119886119897119899119905 minus119872119904119894119898119899119905119872119903119890119886119897119899119905

1003816100381610038161003816100381610038161003816100381610038161003816 (3)



119877119872119878119864 = radic 1119873 sdot 119879119873sum119899=1

119879sum119905=1

(119872119903119890119886119897119899119905 minus119872119904119894119898119899119905119872119903119890119886119897119899119905 )2 (4)
































ment of 005















































2873 MAPE lt 10 199 Yes 558 Yes

2876 MAPE lt 10 936 Yes 1185 No

2893 MAPE lt 10 917 Yes 1080 No

2894 MAPE lt 10 861 Yes 988 Yes

2900 MAPE lt 10 685 Yes 842 Yes

2907 MAPE lt 10 741 Yes 908 Yes

2915 MAPE lt 10 992 Yes 1056 No

2919 MAPE lt 10 1038 No 1121 No

2924 MAPE lt 10 898 Yes 959 Yes

2928 MAPE lt 10 802 Yes 935 Yes

2940 MAPE lt 10 837 Yes 901 Yes

2947 MAPE lt 10 737 Yes 826 Yes

2953 MAPE lt 10 801 Yes 814 Yes

2960 MAPE lt 10 1052 No 748 Yes

2979 MAPE lt 10 1420 No 723 Yes

2985 MAPE lt 10 1409 No 849 Yes







Sim

ulat

ed F

low

(vph

)


PATHMOTUS

5000 6000 7000 8000 9000 10000

9000

8000

7000

6000

5000

4000

3000

2000

1000

0

10000

２2 = 08939

２2 = 09266






Time0500 0600 0700 0800 0900 1000 1100

Field Data

288

290

292

294

296

298

Post-

mile

0

10

20

30

40

50

60

70

Spee

d (m

ph)


Time0500 0600 0700 0800 0900 1000 1100


288

290

292

294

296

298

Post-

mile

0

10

20

30

40

50

60

70

Spee

d (m

ph)


Time0500 0600 0700 0800 0900 1000 1100


288

290

292

294

296

298

Post-

mile

0

10

20

30

40

50

60

70

Spee

d (m

ph)




Flow vs Density

AIMSUNSimulation



0

1000

2000

3000

4000

5000

6000

7000

8000Fl

ow (v

ehh

r)


Flow vs Density

AIMSUNSimulation


0

1000

2000

3000

4000

5000

6000

7000

8000

Flow

(veh

hr)








4 Discussion




















Data Availability



Disclosure




Acknowledgments


References


































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia








119866119864119867(119896) = radic2 [119872 (119896) minus 119862 (119896)]2119872(119896) + 119862 (119896) (2)

where



119872119860119875119864 = 1119873 sdot 119879119873sum119899=1

119879sum119905=1

1003816100381610038161003816100381610038161003816100381610038161003816119872119903119890119886119897119899119905 minus119872119904119894119898119899119905119872119903119890119886119897119899119905

1003816100381610038161003816100381610038161003816100381610038161003816 (3)



119877119872119878119864 = radic 1119873 sdot 119879119873sum119899=1

119879sum119905=1

(119872119903119890119886119897119899119905 minus119872119904119894119898119899119905119872119903119890119886119897119899119905 )2 (4)
































ment of 005















































2873 MAPE lt 10 199 Yes 558 Yes

2876 MAPE lt 10 936 Yes 1185 No

2893 MAPE lt 10 917 Yes 1080 No

2894 MAPE lt 10 861 Yes 988 Yes

2900 MAPE lt 10 685 Yes 842 Yes

2907 MAPE lt 10 741 Yes 908 Yes

2915 MAPE lt 10 992 Yes 1056 No

2919 MAPE lt 10 1038 No 1121 No

2924 MAPE lt 10 898 Yes 959 Yes

2928 MAPE lt 10 802 Yes 935 Yes

2940 MAPE lt 10 837 Yes 901 Yes

2947 MAPE lt 10 737 Yes 826 Yes

2953 MAPE lt 10 801 Yes 814 Yes

2960 MAPE lt 10 1052 No 748 Yes

2979 MAPE lt 10 1420 No 723 Yes

2985 MAPE lt 10 1409 No 849 Yes







Sim

ulat

ed F

low

(vph

)


PATHMOTUS

5000 6000 7000 8000 9000 10000

9000

8000

7000

6000

5000

4000

3000

2000

1000

0

10000

２2 = 08939

２2 = 09266






Time0500 0600 0700 0800 0900 1000 1100

Field Data

288

290

292

294

296

298

Post-

mile

0

10

20

30

40

50

60

70

Spee

d (m

ph)


Time0500 0600 0700 0800 0900 1000 1100


288

290

292

294

296

298

Post-

mile

0

10

20

30

40

50

60

70

Spee

d (m

ph)


Time0500 0600 0700 0800 0900 1000 1100


288

290

292

294

296

298

Post-

mile

0

10

20

30

40

50

60

70

Spee

d (m

ph)




Flow vs Density

AIMSUNSimulation



0

1000

2000

3000

4000

5000

6000

7000

8000Fl

ow (v

ehh

r)


Flow vs Density

AIMSUNSimulation


0

1000

2000

3000

4000

5000

6000

7000

8000

Flow

(veh

hr)








4 Discussion




















Data Availability



Disclosure




Acknowledgments


References


































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



























ment of 005















































2873 MAPE lt 10 199 Yes 558 Yes

2876 MAPE lt 10 936 Yes 1185 No

2893 MAPE lt 10 917 Yes 1080 No

2894 MAPE lt 10 861 Yes 988 Yes

2900 MAPE lt 10 685 Yes 842 Yes

2907 MAPE lt 10 741 Yes 908 Yes

2915 MAPE lt 10 992 Yes 1056 No

2919 MAPE lt 10 1038 No 1121 No

2924 MAPE lt 10 898 Yes 959 Yes

2928 MAPE lt 10 802 Yes 935 Yes

2940 MAPE lt 10 837 Yes 901 Yes

2947 MAPE lt 10 737 Yes 826 Yes

2953 MAPE lt 10 801 Yes 814 Yes

2960 MAPE lt 10 1052 No 748 Yes

2979 MAPE lt 10 1420 No 723 Yes

2985 MAPE lt 10 1409 No 849 Yes







Sim

ulat

ed F

low

(vph

)


PATHMOTUS

5000 6000 7000 8000 9000 10000

9000

8000

7000

6000

5000

4000

3000

2000

1000

0

10000

２2 = 08939

２2 = 09266






Time0500 0600 0700 0800 0900 1000 1100

Field Data

288

290

292

294

296

298

Post-

mile

0

10

20

30

40

50

60

70

Spee

d (m

ph)


Time0500 0600 0700 0800 0900 1000 1100


288

290

292

294

296

298

Post-

mile

0

10

20

30

40

50

60

70

Spee

d (m

ph)


Time0500 0600 0700 0800 0900 1000 1100


288

290

292

294

296

298

Post-

mile

0

10

20

30

40

50

60

70

Spee

d (m

ph)




Flow vs Density

AIMSUNSimulation



0

1000

2000

3000

4000

5000

6000

7000

8000Fl

ow (v

ehh

r)


Flow vs Density

AIMSUNSimulation


0

1000

2000

3000

4000

5000

6000

7000

8000

Flow

(veh

hr)








4 Discussion




















Data Availability



Disclosure




Acknowledgments


References


































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia












































2873 MAPE lt 10 199 Yes 558 Yes

2876 MAPE lt 10 936 Yes 1185 No

2893 MAPE lt 10 917 Yes 1080 No

2894 MAPE lt 10 861 Yes 988 Yes

2900 MAPE lt 10 685 Yes 842 Yes

2907 MAPE lt 10 741 Yes 908 Yes

2915 MAPE lt 10 992 Yes 1056 No

2919 MAPE lt 10 1038 No 1121 No

2924 MAPE lt 10 898 Yes 959 Yes

2928 MAPE lt 10 802 Yes 935 Yes

2940 MAPE lt 10 837 Yes 901 Yes

2947 MAPE lt 10 737 Yes 826 Yes

2953 MAPE lt 10 801 Yes 814 Yes

2960 MAPE lt 10 1052 No 748 Yes

2979 MAPE lt 10 1420 No 723 Yes

2985 MAPE lt 10 1409 No 849 Yes







Sim

ulat

ed F

low

(vph

)


PATHMOTUS

5000 6000 7000 8000 9000 10000

9000

8000

7000

6000

5000

4000

3000

2000

1000

0

10000

２2 = 08939

２2 = 09266






Time0500 0600 0700 0800 0900 1000 1100

Field Data

288

290

292

294

296

298

Post-

mile

0

10

20

30

40

50

60

70

Spee

d (m

ph)


Time0500 0600 0700 0800 0900 1000 1100


288

290

292

294

296

298

Post-

mile

0

10

20

30

40

50

60

70

Spee

d (m

ph)


Time0500 0600 0700 0800 0900 1000 1100


288

290

292

294

296

298

Post-

mile

0

10

20

30

40

50

60

70

Spee

d (m

ph)




Flow vs Density

AIMSUNSimulation



0

1000

2000

3000

4000

5000

6000

7000

8000Fl

ow (v

ehh

r)


Flow vs Density

AIMSUNSimulation


0

1000

2000

3000

4000

5000

6000

7000

8000

Flow

(veh

hr)








4 Discussion




















Data Availability



Disclosure




Acknowledgments


References


































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







Sim

ulat

ed F

low

(vph

)


PATHMOTUS

5000 6000 7000 8000 9000 10000

9000

8000

7000

6000

5000

4000

3000

2000

1000

0

10000

２2 = 08939

２2 = 09266






Time0500 0600 0700 0800 0900 1000 1100

Field Data

288

290

292

294

296

298

Post-

mile

0

10

20

30

40

50

60

70

Spee

d (m

ph)


Time0500 0600 0700 0800 0900 1000 1100


288

290

292

294

296

298

Post-

mile

0

10

20

30

40

50

60

70

Spee

d (m

ph)


Time0500 0600 0700 0800 0900 1000 1100


288

290

292

294

296

298

Post-

mile

0

10

20

30

40

50

60

70

Spee

d (m

ph)




Flow vs Density

AIMSUNSimulation



0

1000

2000

3000

4000

5000

6000

7000

8000Fl

ow (v

ehh

r)


Flow vs Density

AIMSUNSimulation


0

1000

2000

3000

4000

5000

6000

7000

8000

Flow

(veh

hr)








4 Discussion




















Data Availability



Disclosure




Acknowledgments


References


































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Time0500 0600 0700 0800 0900 1000 1100

Field Data

288

290

292

294

296

298

Post-

mile

0

10

20

30

40

50

60

70

Spee

d (m

ph)


Time0500 0600 0700 0800 0900 1000 1100


288

290

292

294

296

298

Post-

mile

0

10

20

30

40

50

60

70

Spee

d (m

ph)


Time0500 0600 0700 0800 0900 1000 1100


288

290

292

294

296

298

Post-

mile

0

10

20

30

40

50

60

70

Spee

d (m

ph)




Flow vs Density

AIMSUNSimulation



0

1000

2000

3000

4000

5000

6000

7000

8000Fl

ow (v

ehh

r)


Flow vs Density

AIMSUNSimulation


0

1000

2000

3000

4000

5000

6000

7000

8000

Flow

(veh

hr)








4 Discussion




















Data Availability



Disclosure




Acknowledgments


References


































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Flow vs Density

AIMSUNSimulation



0

1000

2000

3000

4000

5000

6000

7000

8000Fl

ow (v

ehh

r)


Flow vs Density

AIMSUNSimulation


0

1000

2000

3000

4000

5000

6000

7000

8000

Flow

(veh

hr)








4 Discussion




















Data Availability



Disclosure




Acknowledgments


References


































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


















Data Availability



Disclosure




Acknowledgments


References


































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Disclosure




Acknowledgments


References


































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia








RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Cross-Comparison and Calibration of Two Microscopic ...

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Transcript of Cross-Comparison and Calibration of Two Microscopic ...