Cooperative lane changing and forced merging model

Moshe Ben-Akiva,

Charisma Choudhury, Tomer Toledo,

Gunwoo Lee, Anita Rao

ITS ProgramJanuary 21, 2007

2

Outline

• Introduction

• Lane changing– Model structure– Estimation results – Validation results

• Acceleration research plan

3

Introduction

4

Background• Objective

– Develop and test a model for freeway merges that explicitly incorporates cooperative behavior and forced merging

• Tasks– Specify merging model– Estimate the model with I-80 trajectory data – Implementation– Aggregate calibration and validation

• Extension– Integrate acceleration decisions

5

Merging Behavior• Vehicle merging

– Lane changing throughgap acceptance

– Models fail in dense traffic

• Additional merging mechanisms– Lag vehicle may provide courtesy– Vehicle may force a lane change

• Merging mechanism affects– Gap acceptance– Acceleration decisions

Lag

Subject

6

Lane Changing

7

Combined Lane Changing Model

normal courtesy

change no

change change

forced

change

Merging Mechanism

Gap Acceptance

nochange

nochange Same

AdjacentGap

Same AdjacentGap

MLC to target lane

New AdjacentGap

New AdjacentGap

8

Combined Lane Changing Model: Detailed Structure

Target Lane

InitiateCourtesy Merging

Courtesy/Forced Gap Acceptance

MLC to target lane

adjacent gaps acceptable

adjacent gaps not acceptable

initiate courtesymerge

change no

change change

initiate forced merge

nochange

nochange

change

InitiateForcedMerging

Normal Gap Acceptance

anticipated gapGap Anticipation

Same AdjacentGap

NewAdjacentGap

Same Adjacent

Gap

NewAdjacentGap

do not initiate courtesy merge

do not initiate forced merge

9

Available Gap

• Adjacent gap changes if either lead or lag vehicle changes

Subjectvehicle

Leadvehicle

Lagvehicle

Adjacent gap

Lead gapLag gap

Traffic direction

10

Choice of Merging Mechanism

• Normal gaps evaluated first

• Normal gaps not acceptable– Driver anticipates future gap

• Reflects the courtesy or discourtesy of the through vehicle

• Latent time horizon

– Anticipated gap acceptable • Courtesy merging

• Driver initiates lane change

n

11

Choice of Merging Mechanism (2)• Anticipated gap not acceptable

– Driver considers initiating forced merging• Unacceptable gaps may delay the courtesy/forced

lane change– Driver remains in initiated courtesy/forced

merging state

12

Execution of the Merge

• Driver evaluates lead and lag gaps

• Changes lanes if both gaps are acceptable

• Acceptable gap– available gap >= critical gap

• Smaller critical gaps for courtesy and forced lane changes

13

NGSIM I-80 Study Area

1

6

5

4

3

2

87

1650 ft = 502.92m

3

4

5

Powell St.On-Ramp

AshbyOff-Ramp

EB I-80

1

2

Study Areaof Trajectory Data

11.8ft = 3.6m

24ft = 7.3m

11.8ft = 3.6mshoulder

14

Estimation Data Set• 45 minute data

• 540 merging vehicles

• X and Y coordinates every 1/10th sec

• Estimation based on 17352 observations

• Summary statistics– Average speed of merging vehicles 15.1 km/hr

– Average speed in Lane 6 16.5 km/hr

– Average d/s density in Lane 6 68.4 veh/km

15

Estimation Results• Variables affecting critical gap

– Average speed of the mainline– Speeds of the lead and lag vehicle– Acceleration of the lag vehicle– Remaining distance to MLC point

• Functional form and variables influencing the critical gaps assumed to be the same

• Intercepts differ for normal, courtesy and gap acceptance

16

Estimation Results

0

1

2

3

4

5

6

7

8

-5 -4 -3 -2 -1 0 1 2 3 4 5

Relative lag speed(m/sec)

Mea

n L

ag C

riti

cal G

ap (

m)

Normal

Forced

Courtesy

• Median critical lag gap variation with relative lag speed - Effect of type of merge

Med

ian

cri

tica

l lag

gap

(m

)

17

Estimation Results (2)• Median critical lag gap variation with remaining distance - Effect of driver heterogeneity

18

Model Comparison• Tested against a single

level gap acceptance model– No explicit courtesy or

forced merge component

2(0.95,25)60.08 37.65LR

Model Likelihood Parameters

Normal only -1639.69 17

Full model -1609.65 42

Reject normal only model at 95% confidence

19

Estimation, Calibration and Validation Framework

Estimation of merging model

Data collection

Aggregate calibration of simulation model

Disaggregate testing

Model refinement

Dis

aggr

egat

e da

taA

ggre

gate

da

ta

Aggregate validation

Calibrated and validated simulation

model

Open sourced MITSIMLab

I-

80

traj

ecto

ry

data

Sen

sor

data

co

llect

ed b

y C

S

Implementation and verification

Operational Validation

Conceptual Validation

20

Calibration and Validation Data

1

6

5

4

3

2

2100 ft (640 m)

3

4

5

Ventura On-Ramp

1

2

Study Areaof Trajectory Data

Lankershim Off-ramp

698 ft (213 m)

• US 101 trajectory data – Distinct auxiliary lane – Higher average speed

Lane 6: 47.1km/hr Lane 5: 35.2 km/hr

• ‘Synthetic’ sensor data created from trajectory data to

replicate aggregate counts and speeds• Transferability test to identify most sensitive parameters• Compared against default MITSIMLab models

21

Validation Results

Previous Model

Combined Model

PercentImprovement

RMSE (vehicles/5 mins) 20.91 13.22 58.18%

RMSPE 10.81% 7.52% 43.83%

Comparison of Lane-Specific Counts

Comparison of Lane-Specific Speeds

Previous Model

Combined Model

PercentImprovement

RMSE (mph) 12.81 8.82 45.17%

RMSPE 29.73% 22.26% 33.58%

22

Validation Results (2)

0

10

20

30

40

50

60

0 50 100 150 200 More

Remaining Distance (m)

% o

f M

erg

es Observed

Combined

Previous

Comparison of Location of Merges

23

Acceleration Research Plan

24

Motivation

• Drivers unable to merge immediately– Target gaps– Accelerate/decelerate to facilitate merging

Gapbehind

Gapforward

Currentgap

25

Extended Model

• Incorporate– Target gap selection – Acceleration to facilitate merging

• Challenge– Only acceleration observed

• Unobserved target gap choice

• Unobserved acceleration stimuli

– Modeled as latent variables

26

Extended Model Framework

Target Lane

AnticipatedGap Acceptance

Lane Action

MLC to target lane

existing gaps acceptable

existing gaps not acceptable

anticipated gap acceptable

anticipated gap not acceptable

change

initiate change through courtesy

nochange

change

initiate forced merging

nochange

nochange

change

do not initiate forced merging

Courtesy/Forced Merging

Gap Acceptance

anticipated gapGap Anticipation

gap 1 gap 2 gap k

acc. acc.

...

acc.

Target Gap

Acceleration acc. acc. acc.acc. acc.

Same Adjacent

Gap

Same Adjacent

Gap

New Adjacent Gap New Adjacent Gap

27

Target Gap Selection

• Conditional on the decision of not initiating a courtesy/forced merge

• Utility of gap j for individual n at time t

Tj P j jnt nt n nt

P

j

U =β X +α υ +ε

j adjacent,backward,forward

β =coefficient of explanatory variables for gap j

α =coefficient of individual specific error term for gap j

A

E D BC

28

Target Gap Selection (2)

• Candidate explanatory variables– Size of gap– Trend of gap– Distance traversed to be adjacent to the gap

29

Background

• Our previous research in modeling acceleration– Subramanian (1996)

• Integrated car-following and free-flow model

– Ahmed (1999)• Non-linear stimulus and different reaction time for

sensitivity and stimulus

– Toledo (2003)• Acceleration models for stay in lane, lane change and

target gap

30

Proposed Acceleration Model

• The driver responds to different stimuli depending on merging mechanism and target gap choice

• Current leader may constrain desired acceleration

n n n nresponse t sensitivity t stimulus t

31

Proposed Acceleration Model (2)

1. Lane changing acceleration– Existing gaps are acceptable, car-following the

new leader

2. Target gap acceleration– Improve position w.r.t. to lead and lag vehicles of

target gap

3. Initiated courtesy/forced merging– Improve position in current lane w.r.t. lag vehicle

in target lane

32

• Car-following acceleration or deceleration based on relative speed of leader in target lane

1. Lane Changing Acceleration

0

Rn t n

lc ,i ,acc leadnt

lc ,int

lc ,i ,decnt

a if Va

a otherwise

A

*

R R

leadnt

R Rn n

where,

V is the relative speed of the leader at time t

is the reaction time, ~ N( , )

33

1. Lane-changing Acceleration (2)

• Variables affecting acceleration/deceleration functions– speed of subject vehicle

– spacing with lead vehicle

34

2. Target Gap Acceleration Models

• General Structurea. Constrained regime

b. Unconstrained regimes

- based on time headway

Rn

c *nt nn t

nucnt

a if h ha t

a otherwise

R R

* *

n

R Rn n

* *n n h h

where,

h is the headway with the leader in the current lane

is the reaction time, ~ N( , )

h is the headway threshold, h ~ N( , )

35

2a. Constrained Regime

• Car-following acceleration or deceleration based on relative speed of current front vehicle

• Variables– speed of subject vehicle, spacing with front vehicle,

roadway conditions (e.g. density) etc.

• Same functional form for forward, backward and adjacent gaps

A *

36

2b. Unconstrained Regime

a. Forward gap acceleration - function of desired and

current positions, relative

speed with leader etc.

b. Backward gap acceleration - function of desired

and current positions,

subject speed etc.

A

*

Forward gap

Distance to desired position

A

Backward gapDistance to desired

position

37

2b. Unconstrained Regime (2)

c. Adjacent gap acceleration - function of desired and current positions,

relative speed of lag etc.

A

*

Adjacent gap

Target lane lagspace headway

38

3. Initiated Courtesy/Forced Merging

• Similar to adjacent gap acceleration• Functional form and parameters may differ• Variables

– desired and current positions, relative speed of lag etc.

A

*

Adjacent gap

Target lane lagspace headway

39

• Maximum likelihood technique– Joint estimation of all model parameters

• Data– NGSIM I-80 trajectory data

– May be enriched by US 101 trajectory data

Estimation

1

6

5

4

3

2

87

1650 ft = 502.92m

3

4

5

Powell St.On-Ramp

AshbyOff-Ramp

EB I-80

1

2

Study Areaof Trajectory Data

11.8ft = 3.6m

24ft = 7.3m

11.8ft = 3.6mshoulder

1

6

5

4

3

2

2100 ft (640 m)

3

4

5

Ventura On-Ramp

1

2

Study Areaof Trajectory Data

Lankershim Off-ramp

698 ft (213 m)

40

• Implemented in MITSIMLab– Compared against default MITSIMLab models

• Data– US 101 ‘synthetic’ sensor flows and speeds

Calibration/Validation

1

6

5

4

3

2

2100 ft (640 m)

3

4

5

Ventura On-Ramp

1

2

Study Areaof Trajectory Data

Lankershim Off-ramp

698 ft (213 m)

41

Alternative Structure 1

Target Lane

AnticipatedGap Acceptance

Lane Action

MLC to target lane

existing gaps acceptable

existing gaps not acceptable

anticipated lag gap acceptable

anticipated lag gap not acceptable

change

initiate change through courtesy

nochange

change

initiate forced merging

change

Courtesy Merging

Gap Acceptance

forward gap

acc.acc.

Target Gap

Acceleration acc. acc. acc.acc.

backward gap

acc.

nochange

42

Alternative Structure 2

Target Lane

AnticipatedGap Acceptance

LaneAction

MLC to target lane

existing gaps acceptable

existing gaps not acceptable

anticipated lag gap acceptable

anticipated lag gap not acceptable

change

initiate change through courtesy

nochange

change

initiate forced merging

nochange

change

CourtesyMerging

Gap Acceptance

forward gap

acc.acc.Acceleration acc.

acc. acc.acc.

backward gap

acc.

adjacent gap

nochange

acc.

do initiate forced

mergingForcedMerging

TargetGap