Arterial Lane Selection Model
Moshe Ben-Akiva,
Charisma Choudhury, Varun Ramanujam,
Tomer Toledo
ITS ProgramJanuary 21, 2007
2
Outline
1. Introduction and dataset2. Estimation
2.1 Lane choice at intersection2.2 Lane changing within section
3. Validation3.1 Methodology3.2 Data3.2 Results
3
1. Introduction and dataset
4
Introduction
• Objective – Develop a lane changing model for urban arterials
• Tasks– Specify lane changing model and estimate using
NGSIM trajectory data – Implement and verify in MITSIMLab– Calibrate and validate using aggregate data
5
Dataset• Site
– Lankershim Blvd. near Universal Studios CA
• Coverage– Four signalized intersections
• Only destinations available for the fourth intersection
1
2
3
4
6
Dataset (cont.)
1 2 3 4
7
Summary statistics*
* Source: NGSIM Lankershim Data Analysis (2006)
• Number of Vehicles: 2443 – 703 turning vehicles
• 32 mins of data at 1/10 th second resolution• Number of Observations: 1,607,321• Number of Lane-changes: 2284 • Average Speed: 12.4 m/sec• Average Travel Time
– Northbound: 67.3 sec– Southbound: 60.3 sec
8
Models
• Lane choice at intersection– Target lane choice– Immediate lane choice
• Lane changing within section– Target lane choice– Gap acceptance– Execution of lane change
9
2.1 Lane choice at intersection
10
? 1? 2? 3? 4
Lane choice at intersection
11
2.1.1 Summary statistics
• 703 turning vehicles– 269 turn to the naturally
connecting lane
– 435 later change to different lanes within
the section
• 29 OD pairs
• Sections traversed– 1 section: 139
– 2 sections: 171
– 3 sections: 393
0%
25%
50%
75%
100%
1 2 3
Left
Right
Straight
Turning Directions of Vehicles in Lankershim, CA
1 2 3 Section traversed
12
2.1.2 Model structure
1 2 3 4
1 2 3 4
Target Lane
Immediate Lane
( | , )nP l
( | , )nP i l
( | , ) ( | , ) ( | , )n
n n nl C
P i P i l P l
13
• Probability of driver n selecting lane l as target lane
2.1.2 Model structure (cont.)
exp( ( ) )( | , )
exp( ( ) )
T
T
n
l lnt n n
n j jnt n n
j C
XP l
X
,
lnt n
n
n
l
where
X attributes of lane l for vehicle n at time t, can be function of
individual specific plan-ahead distance
cofficients
individual specific aggressiveness
coefficient of individual s
pecific random effect for lane l
14
????
????
Driver classes
Myopic driver
(considers immediate section only)
Driver who plans-ahead
(considers more than one section ahead)
15
• Probability of driver n selecting lane i as immediate lane given that the target lane is l
2.1.2 Model structure (cont.)
exp( )( | , )
exp( )
T
T
n
i int n
n k knt n
k C
XP i l
X
,int
i
where
X attributes of lane i for vehicle n at time t
coefficient of individual specific random effect for lane i
16
2.1.2 Model structure (cont.)• Probability of driver n selecting lane i
• Modeling unobserved aggressiveness and planning capability (‘plan-ahead’)
• Probability of class membership estimated with other model parameters
• Aggressiveness– Individual specific random term
( | , ) ( | , ) ( | , )n
n n nl C
P i P i l P l
( ) ( | , ) ( ) ( )n nP i P i p f d
1 1or (1 )
n ~N(0,1)
1
11n
myopic drivers (consider immediate section only) p
drivers who plan more than one section ahead
17
2.1.3 Variables: Target lane choice
• Path plan variables– Distance to intended downstream turn
– Number of lane changes • Lane attributes
– Queue length and queue discharge rate
– Average speeds
• Driving style and capabilities– Individual driver/vehicle characteristics
• planning capability (‘plan-ahead’)
• aggressiveness
18
2.1.3 Variables: Immediate lane choice
• Current position of the driver– Departure from the naturally connecting lane
• Neighborhood variables– Presence of other vehicles and their actions
• Driving style and capabilities– Individual driver/vehicle characteristics
• aggressiveness
• performance capabilities of the vehicle
(e.g. required turning radius)
19
2.1.4 Estimation resultsInitial Log-likelihood -2797.9Final Log-likelihood -2115.8Number of Parameters 20Number of Observations 703Variable Parameter valuet-Stat
Lane 2 constant -0.837 -3.64Lane 3 constant 1.30 7.62Lane 4 constant 3.25 8.16Anticipated delay (second) -0.477 -0.56Lanes away from turning lane (myopic) coefficient-myopic drivers -0.0240 -0.63
constant-myopic drivers 1.43 0.83heterogenity coefficient -myopic drivers 1.53 0.75
Lanes away from turning lane (with plan-ahead) coefficient-drivers who plan-ahead -4.08 -1.98constant-drivers who plan-ahead 2.05 3.01
heterogenity coefficient -drivers who plan-ahead 0.466 0.74Expected maximum utility from immediate lane* 0.915 7.22
Target Lane
1 2* E( ( ))
,
ln
ln
n
i Iln ln ln ln
iln
Expected maximum utility derived from lane l
utility of immediate lane i for individual n given target lane is l
C 1,2,...,i,...,I
EMU max U ,U ,...,U ,...,U
where EMU
U
20
2.1.4 Estimation results (cont.)
Lanes away from connecting lane : coefficient -1.01 -1.19constant 0.691 1.94
heterogenity coefficient 1.96 3.48Target lane dummy 3.16 4.54Lanes away from target lane : coefficient -4.42 -3.00
constant 2.12 2.14heterogenity coefficient 0.0904 0.36
Lateral conflict dummy -1.76 -9.63
Driver population with >1 section plan-ahead (%) 18.3 2.07Driver Class
Immediate Lane
21
2.1.4 Estimation results (cont.)
• Utility associated with target lane l for vehicle n
1
2
1
l
l
n
l
n
n
where
constant for lane l
q anticipated delay function in lane l for myopic drivers
q anticipated delay function in lane l for drivers who plan-ahead
if the driver plans-ahead beyond immedi
1
2
ln
ln
l
ate section
e lanes away from turning lane for myopic drivers
e lanes away from turning lane for drivers who plan-ahead (consider path-plan beyond current section)
EMU expected maximum utility der
ived from selecting lane l as immediate lane
1 2 1
2
0.0240.477 ( )(1 ) ( )( ) ( )(1 )
1.43 1.53
4.08( ) 0.915( )
2.05 0.466
l ll l ln n n n nn n
n
l ln n
n
U q q ev
e EMUv
22
2.1.4 Estimation results (cont.)
• Utility associated with immediate lane i for vehicle n given his target lane is l
1.01( ) 3.16( 0)
0.691 1.96
4.42( ) 1.76
2.12 .0904
1
i i in n n
n
i in n
n
in
in n
in
U c lv
lv
where
c lanes away from connecting lane
l lanes away from target lane l, l C
if maneuver to lane i is obstructed by
adjacent vehicle
23
1 1 1 2 1 2 2
11,2
1 exp( )
/ , /
kl
nt klnt
l l l l l l lnt nt n nt nt nt n
klnt
kint
kint
q kq
q d r q q d r
where
q anticipated delay in lane l considering k sections ahead
d queue length in lane i in section k at time t (vehicles)
r
average queue discharge rate of lane i in section k (vehicles/sec)
Anticipated Delay
• Delay associated with lane l for driver class k:
Effect of anticipated delay on the utility of lane
0.4
0.8
1.2
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Anticipated delay (sec)
Uti
lity
of
lan
e
2.1.5 Interpretation of results
24
2.1.5 Interpretation of results (cont.)
• Next section- Lane 4 does not continue
1234
0
0.25
0.5
0.75
1 2 3 4
Lane
Pro
bab
ilit
y
Plan-ahead = 1 section Plan-ahead > 1 section
Effect of path-plan in target lane choice
25
2.1.5 Interpretation of results (cont.)
Heterogeneity in Immediate Lane Choice(CL=2,TL=1)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1 2 3 4
Immediate Lane
Pro
ba
bili
ty
Normal Driver
Aggressive Driver
• Aggressive Driver-Lower inertia to stay in current lane
26
2.1.6 Model selection
Statistic Base
Model
New
Model
Log likelihood value -2120.4 -2115.8
Number of parameters (K) 19 20
Akaike information criteria (AIC)* -2139.3 -2135.8
Bayesian information criteria (BIC)* -2182.5 -2181.4
*AIC=LL-K, BIC=LL -K/2*ln*(N)
• Compared with a single level lane-choice model
• Significant improvement in goodness-of-fit
27
2.2 Lane-changing within section
28
2.2.1 Summary statistics
– No. of vehicles in sampled dataset : 401 • NB: 160, SB: 241
• 150 vehicles turning vehicles
• 125 vehicles entering through intermediate intersections
– Total no. of lane changes in sample : 249 • 0.621 per vehicle
– Lane changes by turning vehicles:104• 0.693 per vehicle
• Majority (80.8%) of these lane changes occur in the last section before turn
29
2.2.2 Model structure
Lane 2
Lane 1
Target Lane
Execution
Gap Acceptance
Reject Gap
No Change
AcceptGap
Change Right
No Change
No Change
RejectGap
No Change
AcceptGap
Change Left
No Change
RejectGap
No Change
Accept Gap
Change Left
No Change
Lane 2 Lane 3 Lane 4
Lane 1
Lane 2
Lane 3
Lane 4
30
2.2.2 Model structure: Target lane choice
• Probability of driver n selecting target lane i at time t
• The desired lane shift (left, current or right) is implied by the target lane choice
exp( )( | )
exp( )
T
T
TL i int n
nt TL j jnt n
availablelanes j
XP i
X
,int
TL
n
i
where
X attributes of lane i for vehicle n at time t
cofficients
individual specific aggressiveness
coefficient of individual specific random effect for lane i
31
2.2.2 Model structure: Gap acceptance
• Evaluate adjacent lead and lag gaps • Accept gap if
Available gap >= Critical gap
Subjectvehicle
Leadvehicle
Lagvehicle
Adjacent gap
Lead gapLag gap
Traffic direction
32
2.2.2 Model structure: Gap acceptance (cont.)
• Critical gaps in the adjacent lane in the direction of target lane i
• Assuming is normally distributed:
, exp( )
,
{ , }
Tig cr g ig ig ignt nt n nt
ignt
G X
where
X attributes of gap g in the adjacent lane in the direction of target lane i
g lead lag
ignt
, ,
2
, , ,
ln ln
~ (0, ), ~ (
T T
i lead i lead cr i lag i lag crnt n nt nt n nt nt n
iLead Lead iLead iLead iLag Lag iLag iLagnt nt n nt nt n
Lead Lag
iLead iLagnt Lead nt
P d i P G G i P G G i
G X G X =
N N
20, )Lag
33
2.2.3 Model structure: Execution of lane change
• Critical gaps unacceptable– No execution
• Critical gaps acceptable– Decision to change in current time step or not
– Modeled as a binary logit
nt n l l lnt n
lnt
l
l
1P ( l|d ,i, )
1+exp(- X - )
where,
X var iables associated with the lane changing by n at time t
cofficients
coefficient of individual specific random effect for lane i
34
2.2.2 Model structure (cont.)
• Probability of driver n executing lane action l
• Modeling unobserved aggressiveness
• Aggressiveness– Individual specific random term
( | ) ( | , ) ( | , , )nt
nt n nt nt nti C
P P i P d i P l d i
l
( ) ( | ) ( )nt ntP P f d
l l
n ~N(0,1)
35
2.2.3 Variables: Target lane choice
• Path plan variables– Distance to intended downstream turn– Number of lane changes
• Neighborhood variables– Immediate surroundings (e.g. leaders)
• Lane attributes– Speed, density, queue lengths
• Driving effort– Lanes away from current lane, inertia
36
2.2.3 Variables: Gap acceptance
• Critical gaps may depend on– Lead and lag vehicle relative speeds and
spacing
• May differ from freeways– Different speed ranges – Impact of traffic lights – Impatience
37
2.2.3 Variables: Execution of lane change
• May depend on– Speed of the subject vehicle– Remaining distance to the turn– Density
38
2.2.4 Estimation results: Target lane Initial Log-Likelihood -2094.9Final Log-Likelihood -1004Number of Observations 16696Number of Vehicles 400Number of Parameters 21Variable Name Parameter t-stat
Current Lane Dummy 3.02 3.96
Path Plan impact : No. of lane changes to exit lane -1.28 -4.54
Path plan impact : No. of lane changes to exit interacted with distance from exit
-1.36 -3.49
Exponent of dist. to exit in no. of lanes to exit- dist. to exit interaction
0.707 3.35
No. of lane changes from current lane = 1 -0.815 -1.10
No. of lane changes from current lane >= 2 -5.68 -0.27
Queue length ahead in lane (m) -0.349 -4.19
Front vehicle rel. speed negative, interacted with front veh. Gap (m/s per m)
0.0284 0.57
Extra Bay Dummy 0.148 0.54
αCL -0.418 -2.11
39
Variable Name Parameter t-stat
Lead gap constant 2.38 59.25Relative lead speed (m/s) -0.0221 -3.43σlead 0.00741 0.23αlead -1.75 -42.0
Lag gap constant 1.44 28.6Relative lag speed (m/s) 0.263 18.4σlag 0.00851 0.24αlag -1.86 -36.3
Lead Critical Gap
Lag Critical Gap
2.2.4 Estimation results: Gap acceptance
lead,TLntV
lag,TLntV
40
2.2.4 Estimation results: Execution of lane change
ntV
Variable Name Parameter t-statIntercept -3.7 -3.89αlead 0.357 0.32Subject speed 0.647 3.97
41
Utility associated with lane i for vehicle n at time t :i ic i i exit -exp(0.707) i
nt nt nt nt nt nt
i i ic i i int nt n nt nt nt nt
ic cnt nt
V = 3.024 d - 1.28 e - 1.36 e (d ) -0.815 (k = 1)
- 5.68 ( k >= 2) k - 0.418 u d - 0.349 (q )(q <= 3) - 1.05 (q >= 4)
+(d )[0.0284 * min(0, fr ) /(1+exp cnt (fs ))]
2.2.4 Estimation resultsTarget lane choice
| |)
icnt
int
int
int nt
current lane dummy, 1 if lane i is current lane, 0 ow
q queue ahead in lane i
v average speed ahead in lane i
k number of lane changes required from current lane to lane i ( i j
nt
int
exitnt
cnt
n
where j current lane of individual n at time t
e number of lane changes reqd. to take the desired exit/turn from lane i
d remaining distance to exit/turn
fr = front vehicle rel. speed
fs
ct = front vehicle spacing
42
2.2.4 Estimation resultsGap acceptance
lead TL,cr lead,TL leadnt nt n nt
lead 2nt
G = exp(2.38 - 0.022 V - 1.75 v + )
~ N(0,0.0074 )
,gi gi
nt nt nt
nt
gint
where
V V -V
V speed of subject vehicle n at time t
V speed of vehicle associated with gap g of subject n at time t in direction of target lane i
Critical Lead Gap
Critical Lag Gap
)lag TL,cr lag,TL lagnt nt n nt
lag 2nt
G = exp(1.44 + 0.263 V - 1.86 +
~ N(0,0.0085 )
43
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
CL=1 CL=2 CL=3 CL=4
Pro
ba
bil
ity
Lane 1
Lane 2
Lane 3
Lane 4
2.2.5 Interpretation of resultsInertia and path plan effect
Trade-off between current lane inertia and path plan effectDistance to exit = 410 m ( 2 sections), Turning/exit lane = Lane 4*
*Lane 4 is the rightmost lane, Lane 1 is the leftmost lane
44
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
CL=1 CL=2 CL=3 CL=4
Pro
ba
bili
ty
Lane 1
Lane 2
Lane 3Lane 4
Trade-off between current lane inertia and path plan effectDistance to exit = 150 m (1 section), Turning/exit lane = Lane 4*
2.2.5 Interpretation of resultsInertia and path plan effect (cont.)
45
2.2.5 Interpretation of resultsInertia and path plan effect (cont.)
Trade-off between current lane inertia and path plan effectDistance to exit = 75 m, Turning/exit lane = Lane 4*
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
CL=1 CL=2 CL=3 CL=4
Pro
ba
bili
ty
Lane 1
Lane 2
Lane 3
Lane 4
46
2.2.5 Interpretation of resultsHeterogeneity in critical gap
Critical Lag Gap Variation
-4
-3
-2
-1
0
1
2
3
4
5
6
7
relv = -10 relv = 0 relv = 10
Rel. Lag Speed(m/s)
La
g C
riti
ca
l G
ap
(ln
(m
))
niu = 1
niu = 0
niu = -1
47
2.2.6 Model selection
Statistic Base
Model
New
Model
Log likelihood value -1186.9 -1004.1
Number of parameters (K) 17 22
Akaike information criteria (AIC)* -1203.9 -1126.1
Bayesian information criteria (BIC)* -1271.53 -897.14*AIC=LL-K, BIC=LL –(K/2)*ln(N)
• Compared with simplified model
• Significant improvement in goodness-of-fit
RIGHTLEFT CURRENTLane shift
Gapacceptance
CHANGERIGHT
CHANGELEFT
NOCHANGE
NOCHANGE
NOCHANGE
48
3. Validation
49
Overall Model Development Process
Estimation of merging model
Data collection
Aggregate calibration of simulation model
Disaggregate testing
Model refinement
Dis
aggr
egat
e
data
Agg
rega
te
data
Aggregate validation
Calibrated and validated simulation
model
Open sourced MITSIMLab
Tra
ject
ory
data
Sen
sor
Dat
a
Implementation and verification
Operational Validation
Conceptual Validation
50
3.1 Data
• ‘Synthetic’ sensor data generated from trajectory data– Three sensor stations per section
• Total available data: 8:30 -9:00 am– Calibration: 8:30-8:50 am– Validation: 8:50-9:00 am
‘Synthetic’ Sensor Location
51
3.2 Model comparison• Compared against performance of simplified models
– Lane selection at intersection: rule based model
– Lane selection within section: re-estimated lane-shift model
• Measures of performance– Lane specific speeds
– Lane distributions
RIGHTLEFT CURRENTLane shift
Gapacceptance
CHANGERIGHT
CHANGELEFT
NOCHANGE
NOCHANGE
NOCHANGE
52
3.2 Model comparison (cont.)
Base NewRMSE 11.91 10.64RMSPE 1.82 3.78ME 6.89 2.30MPE 0.47 0.36
Comparison of lane specific speeds
22
1 1
1 1
1 1
1 1
sim obsN Nsim obs n nn n obs
n n n
sim obsN Nsim obs n nn n obs
n n n
obsn
simn
M MRMSE M M ,RMSPE
N N M
M MME M M ,MPE
N N M
M observed speeds / 5min
M simulated speeds / 5min
53
3.2 Model comparison (cont.)
Comparison of lane distributions
Lane Distributions
0
10
20
30
40
1 2 3 4
Lane
%
Observed
Base
New
54
Summary• Intersection lane choice
– Effect of path-plan and ‘plan-ahead’
– Driver heterogeneity• latent driver classes• aggressiveness
• Within section lane change– Effect of path-plan
– Modeling execution of lane change
• Significant improvement in goodness-of-fit compared to simplified models estimated with same data• Improved simulation capability
• Measures of performance– Lane specific speeds
– Lane distributions
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