Next Generation Simulation Next Generation Simulation

Alexander Skabardonis, Hwasoo Yeo

University of California, Berkeley

Oversaturated Freeway Flow Oversaturated Freeway Flow AlgorithmAlgorithm

NGSIM Team MeetingWashington DC

January 21, 2007

Outline

Problem Statement

Oversaturated freeway flow model • Car-following model • Lane changing model

Estimation of Parameters• Car-following parameters • Lane changing parameters

Implementation• Algorithm implementation• Verification• Validation

Problem Statement

Existing Simulation Approaches• Do not accurately model oversaturated traffic conditions

such as repeated stops and starts, increased lane changes to position onto perceived “moving” lanes, or in the presence of tall vehicles, and large vehicle headways

• Use additional rules and parameters to the basic “desired headway” and “gap-acceptance” based car-following and lane changing models

• Introduce a large number of parameters that generally cannot be readily observed in the field

Project Overview

Objectives:

Develop an improved model for oversaturated freeway flow

Focus on both car-following and lane-changing behaviors during congested conditions

Evaluation of Model for “non-oversaturated” Flow Predict when & how non-oversaturated conditions breakdown

Coordination • Completed and ongoing NGSIM algorithms• Software Developers • Stakeholder participation in expert panels

Car-following: Concept

dtsts

X jamCF

)(

jam

CF

ststsv

)(),(

sjam s

v

speed

spacing

vf

•Vehicle will change speed according to the current spacing

v

sjam

jamLeaderCF stxtx )()( •Alternative Distance form

Car-following base model concept-acceleration case

v, speed

s, spacing

v2

v1

vf

Acceleration

s1 s2

s2

s1

v1

v2 CF

Leader

xCF(t+dt)=xLeader(t+dt- )-sjam

Car-following base model concept-deceleration case

v, speed

s, spacing

v2

v1

vf

Deceleration

s1s2

s2

s1v1

v2

xCF(t+dt)=xLeader(t+dt- )-sjam

Car-following Model

Newell’s simplified CF model

Maximum Acc

Free Flow speed

Safety Constraint

Maximum Dec

Wave travel time

Jam Spacing

Lane Changing Model

Lane changing choice model• Mandatory Lane changing

Entry, exit • Discretionary lane changing

Gap acceptance model

Lane changing mechanism• Lane changing• Lane changing with cooperation • Emergency Lane changing

Lag gap

Lane changing

Vehicle

Lead gap

cooperation vehicles

n-1′

n+1′

n

Lane changing choice model (1)Mandatory lane changing

Applied to turning and exit traffic

Emergency Lane changing

En

Tn

lExit

))(()()( llTExlxtx ExitnnEExitnn

Number of lane changes needed

Exit location Desired location in exit lane

Ln

ExitnEExitnn a

vllTExlxtx

2))(()()(

2

0

Stopping distance

T0

Ventura Blvd

12

34

56

2100ftCahuengaBlvd

'll

Lane changing probability is the function of speed difference

Probability that vehicle n at time t moves from lane l to lane l’

Ф : sensitivity to speed change

otherwise 0

, ''''

'lll

ll

llnt vvv

dt

v

vv

f

otherwise 0

, ''''

'lll

ll

llnt vvv

dt

v

vv

f

Lane changing choice model(2)Discretionary Lane Changing

Gap acceptance conditions

)()()( '1'1jam

nnnn gltxtx

)()()()()()( '1'1'1 tdtvtdgltxtx nnnnjam

nnnn

)()()()()( '1'1'1'1'1 tdtvtdgltxtx nnnnjam

nnnn

jamnnnn gltxtx '1''1 )()(

Lead gap conditionLead gap condition

Lag gap conditionLag gap condition

Lag gap

Lead gap

n-1′

n+1′

n (Minimum gap condition)

(Safety condition)

(Safety condition)

(Minimum gap condition)

Lane Changing Mechanism (1)

LCdowndownLC Jamgaplxxif

Car-following rule for Lane changing pending

Conflict point

downstream vehicle

x=MIN( xCF(Leader) , xCF(Veh Down) )

Leader

Veh downVeh up

upstream vehicle

LC

x= xCF(Leader)

Request Cooperation

Try to pass and find next gap

LCLCLCcoop Jamgaplxxif

Car-following rule for cooperating vehicle

Conflict point

x=MIN( xCF(Leader) , xCF(LC) )

LeaderVeh up

upstream vehicle

LC

Request Cooperation

Coop

End cooperation

Lane Changing Mechanism (2)

Lane Changing conflict

downLC xxif

If there exist conflict in lane changing

downstream vehicle

x=MIN( xCF(Leader) , xCF(Veh Down) )

Leader

Veh up

upstream vehicle

LC1

else x= xCF(Leader)

Request Cooperation

LC2

LC

LC1 will yield to LC2

LC2 will pass LC1

On-Ramp Model – conflict zone

On-Ramp Model

cpncpconflict dxxdif

Conflict Zone

10,2

2

m

a

vMAXd

Lcp

Conflict point

Find a downstream vehicle

cpd

x=MIN( xCF(Leader) , xCF(Veh Down) )

Leader

Veh down

Short Gap Mode (optional) Lane changing cooperation vehicles keep short gap before and

after lane change Applied to Lane Changing or Cooperation vehicles Ends when the leader vehicle starts acceleration

v, speed

s, spacing

Short gap mode

Leader

nn gl 1

nn gl 1

Short gap mode

5500 5550 5600 5650 5700 5750

200

250

300

350

400

time (x 0.1 sec)

dist

ance

(m)

1

2

3

n-1 th n th

n+1th n+2th

Short gap mode

-10.00

10.00

30.00

50.00

70.00

90.00

110.00

130.00

0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00

0

20

40

60

80

100

120

140

0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00

Effects of Short Gap (Relaxation)

Merging area

Parameter Estimation

Car-following Parameters • vf : free-flow speed• gjam : jam gap• : wave travel time • au, al : Maximum acceleration and deceleration

Lane Changing Parameters

• Ф: sensitivity to speed difference • T : slope of lane changing for exit lane change• E: target location in the exit lane for exit lane change • mn: perceived HOV activation time

Find starting times of vehicles exiting HOV

Free Flow Speed

Extract from detector data

0 2 4 6 8 10 12 14 16 18 20 22 2410

20

30

40

50

60

70

80

90

Time of day(hour)

Speed (

MP

H)

US101 vehicle speed

lane1

lane2

lane3lane4

lane5

0 2 4 6 8 10 12 14 16 18 20 22 24240

10

20

30

40

50

60

70

80

90

100

110

120120

Time of day(hour)

Speed(M

PH

)

I80 vehicle speed

lane1

lane2

lane3

lane4

lane5

5min detector data

30sec detector data

Jam gap

g= xn-1-ln-1-xn

Jam gap Minimum gap at jam condition vehicle speed <3km/hr

0 1 2 3 4 5 6 7 8 9 100

0.5

1

1.5

2

2.5

3

gap

speed

0 1 2 3 4 5 6 7 8 90

20

40

60

80

100

120

jam gap

frequency

Wave Travel Time

: time between the action of leader vehicle and the following vehicle

150 200 250 300 350 400 450 500

-2

0

2

4

6

8

10

12

14

time(sec)

Speed(ft/sec)

Acc(ft/sec2)

-1 0 1 2 3 4 5 60

20

40

60

80

100

120

140

160

180

tau(sec)

Wave Speed

Wave speed = sjam / = ( ㅣ +gjam) / US101

Mean=18.07km/hr,11.22miles/hr I-80

Mean=19.59km/hr,12.18miles/hr

-10 0 10 20 30 40 50 60 700

10

20

30

40

50

60

70

80

wave speed (km/hr)

-10 0 10 20 30 40 50 60 700

5

10

15

20

25

30

35

wave speed(km/hr)

Max Acceleration & Deceleration

Extracted from NGSIM trajectories data US101 Passenger cars (n=4163) Mean=4.516(m/s2), std= 0.808 mean= -4.398(m/s2), std=0.827

-9 -8 -7 -6 -5 -4 -3 -2 -1 0 10

1

2

3

4

5

6

7

8

9

10

acceleration(m/s2)

freq

uenc

y

-1 0 1 2 3 4 5 6 7 8 90

1

2

3

4

5

6

7

8

9

10

acceeleration(m/s2)

freq

uenc

y

Sensitivity to speed difference(φ) in

discretionary lane changing

Assume constant φ Probability of LC

otherwise ,0

)(),()(,)()(

)(''

'

' tvtvtvt

v

tvtvt

ln

l

nf

n

nl

lln )(

)(v

t

v

vv f

nn

-20 0 20 40 60 80 100 1200

0.5

1

1.5

2

2.5

3

3.5x 10

4

speed difference(km/hr)

-20 0 20 40 60 80 100 1200

20

40

60

80

100

120

140

speed difference (km/hr)

)(#

)(#)(

v

vLCv

Exit Lane Changing Parameters (E and T)

0 1 2 3 4 5 60

200

400

600

800

1000

1200

1400

1600

target lane

dist

ance

I80 Exit Lane changing Behavoir

0 50 100 150 200 250 300 350 4000

50

100

150

200

250

300

350

400

450

lane changing slope(m/lane)

dist

ance

to

exit(

m)

A

B

Exit location

mean=0.588Std=0.588

mean=0.579Std=0.398

Lognormal2Wave

travel time (sec)

τ

Mean=5.60 Std=5.41

Mean=4.24Std=3.82

Normal3

Mean=3.66 Std=1.15

Mean=3.78Std=0.98

Normal2Jam gap

(m)gjam

11.7011.70116.6510.08119.77average

11.5811.58101.8216.23104.62Lane 5

12.2012.20109.0614.64112.73Lane 4

10.8410.84111.0718.36118.08Lane 3

12.1212.12137.7013.66134.67Lane 2

9.869.86123.6016.06128.77Lane 1

stdstdmeanstdmeanLane

NormalFree flow

speed(kph)

vf

I-80US-101

TEST SITE DistributionClassParameter

mean=0.588Std=0.588

mean=0.579Std=0.398

Lognormal2Wave

travel time (sec)

τ

Mean=5.60 Std=5.41

Mean=4.24Std=3.82

Normal3

Mean=3.66 Std=1.15

Mean=3.78Std=0.98

Normal2Jam gap

(m)gjam

11.7011.70116.6510.08119.77average

11.5811.58101.8216.23104.62Lane 5

12.2012.20109.0614.64112.73Lane 4

10.8410.84111.0718.36118.08Lane 3

12.1212.12137.7013.66134.67Lane 2

9.869.86123.6016.06128.77Lane 1

stdstdmeanstdmeanLane

NormalFree flow

speed(kph)

vf

I-80US-101

TEST SITE DistributionClassParameter

Parameters - Car-following (1)

Mean=-5.05 Std=1.02

Mean=-4.39 Std=0.82

Normal2

Mean=-4.73 Std=1.00

Mean=-4.55 Std=0.88Normal3

Max dec(m/s2)aL

Mean=4.76 Std=0.95

Mean=4.71Std=0.94

Normal3

Mean=5.13 Std=1.04

Mean=4.51 Std=0.81(m)

Normal2Max acc(m/s2)aU

CF

I-80US101

TEST SITEDistributionClassParameter

Mean=-5.05 Std=1.02

Mean=-4.39 Std=0.82

Normal2

Mean=-4.73 Std=1.00

Mean=-4.55 Std=0.88Normal3

Max dec(m/s2)aL

Mean=4.76 Std=0.95

Mean=4.71Std=0.94

Normal3

Mean=5.13 Std=1.04

Mean=4.51 Std=0.81(m)

Normal2Max acc(m/s2)aU

CF

I-80US101

TEST SITEDistributionClassParameter

Parameters - Car-following (2)

[-5min, 0]UniformAllPerceived HOV Activation time

m

Mean=674Std=253.9

Mean=766Stdev=297

NormalAllTarget

distance to exit location (m)

E

Mean=53.312 Std=21.419

Mean=49.506 Std=25.788

NormalAll

Exit lane changing

parameters (m/lane)

T

2.172.02-AllSensitivity to

speed difference (sec)

φ

LC

I-80US101

TEST SITEDistributionClassParameter

[-5min, 0]UniformAllPerceived HOV Activation time

m

Mean=674Std=253.9

Mean=766Stdev=297

NormalAllTarget

distance to exit location (m)

E

Mean=53.312 Std=21.419

Mean=49.506 Std=25.788

NormalAll

Exit lane changing

parameters (m/lane)

T

2.172.02-AllSensitivity to

speed difference (sec)

φ

LC

I-80US101

TEST SITEDistributionClassParameter

Parameters – Lane Changing

Algorithm Implementation (1)

Mode?

Car-following

Car-following Lane

Changing

Lane Changing

CooperatingCooperating

Car-following for Cooperating

Lane Changing

?

Change Mode

Car-following rule

Gap Acceptabl

e?

No

No

YesYes

Change lane

Change Mode to CF

Change mode of the cooperating vehicle to CF

Car-following for lane changing

pending

End

Find cooperating vehicle and set

mode

Car-following

rule

Emergency Lane

Changing?

Yes

NoMaximum deceleration

Algorithm Implementation (2)

AIMSUN SDK Replacing AIMSUN car-following and lane

changing model Programming language: C++

A2VehicleA2VehicleBehavioralModel

A2VehicleBehavioralModelTest A2VehicleTestA2VehicleModelTestCreator

Vehicle behaviorsCar-following and lane changing Logic

dll entry point for new model

Algorithm Verification – US101

Algorithm Verification:Exit Lane Changing

NGSIM data

0

500

1000

1500

2000

2500

0 20 40 60 80 100 120

density(veh/km)

flow

(veh

/hr)

Detector

Simulation

Simulation 2:30PM-3:00PM Detector 7

Model Testing I-80 (1)

Speed

0

10

20

30

40

50

60

14:3

1:00

14:3

2:30

14:3

4:00

14:3

5:30

14:3

7:00

14:3

8:30

14:4

0:00

14:4

1:30

14:4

3:00

14:4

4:30

14:4

6:00

14:4

7:30

14:4

9:00

14:5

0:30

14:5

2:00

14:5

3:30

14:5

5:00

14:5

6:30

14:5

8:00

time

spee

d(k

m/h

r)

Detector

Simulation

Model Testing I-80 (2)

Characteristics of the Proposed Algorithm

Consistent with kinematic wave theory

Parameters Physical meaning observable

Microscopic: wave travel time, jam gap, free flow speed, Max Acc, Dec

Macroscopic: wave travel time, jam density, free flow speed Can be used for model calibration

Mechanism Oriented approach Integrated Algorithm with Car-following and Lane

changing

Next Steps

Complete Model Validation Trajectory data Aggregate data

Software Code & Documentation Final Report

Possible Future Enhancements

Relaxation Process Partially implemented Caused by driver characteristic change

Sampling interval for speed change Jam gap, reaction time

Traffic Hysteresis Partially implemented Caused by asymmetric behavior

Oscillations in speed-spacing Not considered Asymmetry model

Components of the suggested algorithm

Car-following Car-following

Oversaturated Freeway flow algorithm

Oversaturated Freeway flow algorithm

Lane changing Lane changing

Base Car-following Base Car-following LC Choice model LC Choice model

CF model before LCCF model before LC

Gap Acceptance Gap Acceptance

CF model after LCCF model after LC

Cooperation choiceForced LC choice

Cooperation choiceForced LC choice

Coop Car-following Coop Car-following

LC Target choice LC Target choice

Apply LC model Apply LC model

LC Car-following LC Car-following

LC pending Car-following

LC pending Car-following

After LC Car-following

After LC Car-following

Car-following for Conflict

Car-following for Conflict

Emergency LC Car-following `

Emergency LC Car-following `