Cooperative lane changing and forced
merging model
Moshe Ben-Akiva,
Charisma Choudhury, Tomer Toledo,
Gunwoo Lee, Anita Rao
ITS Program
January 21, 2007
Outline
• Introduction
• Lane changing
– Model structure
– Estimation results
– Validation results
• Acceleration research plan
2
Introduction
3
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
4
Merging Behavior
• Vehicle merging
– Lane changing through
gap acceptance
– Models fail in dense traffic
• Additional merging
mechanisms
Lag
Subject
– Lag vehicle may provide courtesy
– Vehicle may force a lane change
• Merging mechanism affects
– Gap acceptance
– Acceleration decisions
5
Lane Changing
6
Combined Lane Changing Model
MLC to
target lane
Merging
Mechanism
Gap
Acceptance
normal
no
change
courtesy
change
Same
Adjacent
Gap
no
change
forced
change
New
Adjacent
Gap
Same
Adjacent
Gap
no
change
change
New
Adjacent
Gap
7
Combined Lane Changing Model:
Detailed Structure
MLC to
target lane
Target Lane
Normal Gap
Acceptance
adjacent gaps
not acceptable
adjacent gaps
acceptable
Gap
Anticipation
anticipated gap
Initiate
Courtesy
Merging
initiate courtesy
merge
do not initiate
courtesy merge
Initiate
Forced
Merging
Courtesy/
Forced
Gap
Acceptance
change
Same
Adjacent
Gap
no
change
change New
Adjacent
Gap
Same
Adjacent
Gap
initiate forced
merge
do not initiate
forced merge
no
change
change New
no
change
Adjacent
Gap
8
Available Gap
Adjacent gap
Lag
vehicle
Lag gap
Lead gap
Subject
vehicle
Lead
vehicle
Traffic direction
• Adjacent gap changes if either lead or lag
vehicle changes
9
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  n
– Anticipated gap acceptable
• Courtesy merging
• Driver initiates lane change
10
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
11
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
12
NGSIM I-80 Study Area
1650 ft = 502.92m
EB I-80
11.8ft = 3.6m
1
1
2
2
3
3
4
4
5
5
11.8ft = 3.6m
shoulder
6
24ft = 7.3m
7
Powell St.
On-Ramp
Study Area
of Trajectory Data
8
Ashby
Off-Ramp
13
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
– Average speed in Lane 6
15.1 km/hr
16.5 km/hr
– Average d/s density in Lane 6
68.4 veh/km
14
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
15
Estimation Results
• Median critical lag gap variation with relative lag speed
- Effect of type of merge
(m)
gap (m)
lag Gap
critical
Median
Mean Lag
Critical
8
7
6
5
Normal
4
Forced
3
Courtesy
2
1
0
-5
-4
-3
-2
-1
0
1
2
3
4
5
Relative lag speed(m /sec)
16
Estimation Results (2)
• Median critical lag gap variation with remaining distance
- Effect of driver heterogeneity
17
Model Comparison
• Tested against a single
level gap acceptance
model
– No explicit courtesy or
forced merge component
Model
Likelihood
Parameters
Normal only
-1639.69
17
Full model
-1609.65
42
2
LR  60.08   (0.95,25)
 37.65
Reject normal only model at 95% confidence
18
Estimation, Calibration and Validation
Framework
Data collection
Operational
Validation
I80 -trajectory
data
Open sourced
MITSIMLab
Sensor data
collected by CS
Disaggregate testing
Model refinement
Disaggregate
data
Estimation of merging
model
Aggregate
data
Conceptual
Validation
Implementation and
verification
Aggregate calibration
of simulation model
Aggregate validation
Calibrated and
validated simulation
model
19
Calibration and Validation Data
• US 101 trajectory data
– Distinct auxiliary lane
– Higher average speed
Lane 6: 47.1km/hr
Lane 5: 35.2 km/hr
2100 ft (640 m)
1
2
1
2
3
3
4
4
5
5
6
698 ft (213 m)
Ventura On-Ramp
Study Area
of Trajectory Data
Lankershim Off -ramp
• ‘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
20
Validation Results
Comparison of Lane-Specific Counts
RMSE (vehicles/5 mins)
RMSPE
Previous
Model
Combined
Model
Percent
Improvement
20.91
13.22
58.18%
10.81%
7.52%
43.83%
Comparison of Lane-Specific Speeds
RMSE (mph)
RMSPE
Previous
Model
Combined
Model
Percent
Improvement
12.81
8.82
45.17%
29.73%
22.26%
33.58%
21
Validation Results (2)
Comparison of Location of Merges
60
% of Merges
50
40
Observed
30
Combined
Previous
20
10
0
0
50
100
150
200
More
Remaining Distance (m)
22
Acceleration Research Plan
23
Motivation
• Drivers unable to merge immediately
– Target gaps
– Accelerate/decelerate to facilitate merging
Gap
behind
Current
gap
Gap
forward
24
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
25
Extended Model Framework
MLC to
target
lane
Target Lane
Gap
Acceptance
existing gaps
acceptable
existing gaps not
acceptable
Gap
Anticipation
anticipated gap
Anticipated
Gap
Acceptance
anticipated gap
acceptable
Courtesy/
Forced Merging
Lane Action
anticipated gap not
acceptable
initiate forced
merging
initiate change
through courtesy
no
change
change
no
change
change
do not initiate
forced merging
Target Gap
Same
Adjacent
Gap
Acceleration
acc.
Same
Adjacent
Gap
acc.
acc.
New Adjacent Gap
acc.
no
change
change
acc.
gap 1
gap 2
acc.
acc.
...
gap k
acc.
New Adjacent Gap
26
Target Gap Selection
• Conditional on the decision of not initiating a
courtesy/forced merge
• Utility of gap j for individual n at time t
PT
U =β X nt +α j υn +εntj
j
nt
j  adjacent,backward,forward 
β P =coefficient of explanatory variables for gap j
α j =coefficient of individual specific error term for gap j
E
D
C
B
A
27
Target Gap Selection (2)
• Candidate explanatory variables
– Size of gap
– Trend of gap
– Distance traversed to be adjacent to the gap
28
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
29
Proposed Acceleration Model
• The driver responds to different stimuli
depending on merging mechanism and
target gap choice
responsen t   sensitivityn t   stimulusn  t  n 
• Current leader may constrain desired
acceleration
30
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
31
1. Lane Changing Acceleration
• Car-following acceleration or deceleration
based on relative speed of leader in target lane
antlc,i
antlc,i ,acc


antlc,i ,dec

if V leadR  0

n t  n
*

A
otherwise
where,
Vntlead is the relative speed of the leader at time t
 nR is the reaction time,  nR ~ N(  ,  )
R
R
32
1. Lane-changing Acceleration (2)
• Variables affecting acceleration/deceleration
functions
– speed of subject vehicle
– spacing with lead vehicle
33
2. Target Gap Acceleration Models
• General Structure
a. Constrained regime
b. Unconstrained regimes
- based on time headway
antc
an  t   
antuc
if hn t  R  hn*

n

otherwise
where,
hn is the headway with the leader in the current lane
 nR is the reaction time,  nR ~ N(  ,  )
R
R
hn* is the headway threshold, hn* ~ N(  h* , h* )
34
2a. Constrained Regime
• Car-following acceleration
or deceleration based on
relative speed of current front
vehicle
A
*
• Variables
– speed of subject vehicle, spacing with front vehicle,
roadway conditions (e.g. density) etc.
• Same functional form for forward, backward and adjacent
gaps
35
2b. Unconstrained Regime
Distance to desired
position
a. Forward gap acceleration
- function of desired and
current positions, relative
speed with leader etc.
*
A
Backward gap
b. Backward gap acceleration
Forward gap
Distance to desired
position
- function of desired
and current positions,
subject speed etc.
A
36
2b. Unconstrained Regime (2)
c. Adjacent gap acceleration
- function of desired and current positions,
relative speed of lag etc.
Adjacent
gap
Target lane lag
space headway
*
A
37
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.
Adjacent
gap
Target lane lag
space headway
*
A
38
Estimation
•
Maximum likelihood technique
– Joint estimation of all model parameters
•
Data
–
–
NGSIM I-80 trajectory data
May be enriched by US 101 trajectory data
2100 ft (640 m)
1650 ft = 502.92m
1
1
1
2
2
2
2
3
3
3
3
4
4
4
4
5
5
5
5
1
EB I-80
11.8ft = 3.6m
6
11.8ft = 3.6m
shoulder
6
24ft = 7.3m
7
Powell St.
On-Ramp
Study Area
of Trajectory Data
698 ft (213 m)
8 Ashby
Off-Ramp
Ventura On -Ramp
Study Area
of Trajectory Data
Lankershim Off -ramp
39
Calibration/Validation
•
Implemented in MITSIMLab
– Compared against default MITSIMLab models
•
Data
–
US 101 ‘synthetic’ sensor flows and speeds
2100 ft (640 m)
1
2
1
2
3
3
4
4
5
5
6
698 ft (213 m)
Ventura On-Ramp
Study Area
of Trajectory Data
Lankershim Off -ramp
40
Alternative Structure 1
MLC to
target
lane
Target Lane
Gap
Acceptance
existing gaps
acceptable
Anticipated
Gap
Acceptance
existing gaps not
acceptable
anticipated lag
gap acceptable
Courtesy
Merging
anticipated lag gap
not acceptable
initiate change
through courtesy
backward
gap
Target Gap
Lane Action
change
no
change
change
Acceleration
acc.
acc.
acc.
acc.
initiate forced
merging
forward
gap
change
no
change
acc.
acc.
acc.
41
Alternative Structure 2
MLC to
target
lane
Target Lane
Gap
Acceptance
existing gaps
acceptable
Anticipated
Gap
Acceptance
existing gaps not
acceptable
anticipated lag
gap acceptable
Courtesy
Merging
anticipated lag gap
not acceptable
initiate change
through courtesy
Target
Gap
adjacent
gap
backward
gap
Lane
Action
Acceleration
do initiate
forced
merging
initiate forced
merging
Forced
Merging
change
no
change
change
acc.
acc.
acc.
acc.
forward
gap
change
no
change
no
change
acc.
acc.
acc.
acc.
42