In the name of God
Car-following Model of Vehicle
Traffic
A. Khosravi
Definition: Car-following model is a microscopic simulation model of
vehicle traffic which describes one-by-one following process of
vehicle on the same lane.
Different Models
GHR
-
CA
Cellular Automaton
CT
Cell Transition
GIPS
-
OV
Optimal Velocity
aQUEUE
a Queuing Model
MITSIM
MITSim-Model
Fuzzy
-
…
…
Car-following: Pipes 1958
Gazis-Herman-Rothery(GHR) model (1958)
[Re sponse]n [Stimulus]
Types of model vary since the definition of stimulus vary.
Stimulus
1) Speed of vehicle
2) Relative Speed
3) Spacing between the n & n-1 vehicle
GHR model specifies the stimulus as the relative velocity of the
vehicle that is:
Every vehicle tends to move as the same speed of
its front vehicle.
Formulation:
an (t )  cv(t  T )
acceleration of vehicle
n implemented at time t
Relative speed of the vehicle n to its front vehicle
at earlier time of t-T
T: driver reaction time
c: sensitivity coefficient
Above equation is very different from real situation. In order to make
the model more realistic:
v(t  T )
an (t )  c
x(t  T )
x
Relative spacing to two vehicle
In 1960, Eide modified model again. He thought the velocity of the
vehicle itself influences the behavior of driver, too. So the GHR
model can be more generally expressed as:
v(t  T )
an (t )  cv
x l (t  T )
m
n
Vn the speed of the n th vehicle
m,l are the constant must to be determined.
The most vital part of the GHR model
m  [0,2]
Experience
l [1,2]
Optimal Velocity(OV) model
an (t )  c[V
desired
n
(t )  vn (t )]
The desired velocity of the n th vehicle at time t.
In GHR model:
desired
n
V
(t )  vn1 (t )
In the OV model, the desired velocity is considered to be relevant to the
relative spacing:
desired
n
V
(t )  V
opt
(xn (t ))
So that:
an (t )  c[V opt (xx (t ))  vn (t )]
Model
OV
GHR
Driver Strategy
to maintain a safe
velocity according
to relative position
Keeps a safe
distance according
to relative velocity
There are many specific forms of
V (xn (t ))
opt
. A popular choice is:
Traffic under congestion and vehicle should stop.
0 x  x A


opt
V (x)   f (x) x A  x  xB

vmax xB  x

The vehicle density is low and thus the vehicles
could run at their maximum speed.
Fuzzy Logic Model
Behavior of human
Vehicle behavior
A correct description of human
A effective model
Fuzzy model
human
Fuzzy controller
Inputs
Statue message of the front car
Output
Decision made through a series of
thinking
Example:
The vehicle should be decelerated when relative distance is too close.
‘too close’ is a fuzzy value and the response of ‘decelerate’ is a
fuzzy decision-making.
At first tried to Fuzzify the GHR Model [10].
x | x  0.5
‘not close’= x | x  2
‘too close’=
….
FUZZY SETS AND SYSTEMS FOR A MOTORWAY MICROSCOPIC
SIMULATION MODEL
The two basic models describing driver behavior:
-Car-following (the speed-distance relationship)
- Lane-changing (the interaction between adjacent lanes)
FUZZY SETS AND SYSTEMS FOR A
CAR-FOLLOWING MODEL
Car-following model has two principal premise variables:
• Relative speed (DV)
• Distance divergence, DSSD (the ratio of vehicle separation,
DS, to the driver’s desired following distance)
Fuzzy Sets: Triangular Membership
function
Fuzzy Set Terms Used in the Car-following Model
Relative Speed
(DV)
Distance
Divergence
(DSSD)
Driver Response
(Acceleration Rate)
Opening Fast (V1)
Much Too Far (S1)
Strong Acceleration
Opening (V2)
Too Far (S2)
Light Acceleration
About Zero (V3)
Satisfied (S3)
No Action
Closing (V4)
Too Close (S4)
Light Deceleration
Closing Fast (V5)
Much Too Close
(S5)
Strong Deceleration
A fuzzy rule for car-following model
If Distance Divergence is Too Far and relative speed is Closing
then the driver’s response is No Action (keep current speed).
FUZZY SETS AND SYSTEMS FOR A
LANE-CHANGING MODEL
Two different models:
1. Lane Change to Offside(LCO):
A driver’s motivation to move to the offside lane is to get
some form
of speed benefit.
2. Lane Change to Nearside(LCN)
The motivation to move to the nearside lane is to reduce
impedance
to fast moving vehicles approaching from behind.
The LCO Model
The LCO model
variables:
has
two
principal
premise
• Overtaking benefit (speed gain)
• Opportunity (Safety
change)
and Comfort of the lane
Fuzzy Sets: Triangular Membership
function
Fuzzy Set Terms Used in the Car-following Model
Overtaking
Opportunity
Intention of LCO
Benefit
High (OB1)
Good (OP1)
High
Medium (OB2)
Moderate (OP2)
Medium
Low (OB3)
Bad (OP3)
Low
The LCN Model
The LCN model has two premise variables:
• Pressure from rear is measured as the time
headway of the following vehicle.
• Gap satisfaction is measured by the period
of time for which it would be possible for the
vehicle to stay in the gap in the nearside
lane, without reducing speed.
Fuzzy Sets: Triangular Membership
function
Fuzzy Set Terms for the LCN Model
Pressure from Rear
Gap Satisfaction
Intention of LCN
High (PR1)
High (GS1)
High
Medium (PR2)
Medium (GS2)
Medium
Low (PR3)
Low (GS3)
Low
A fuzzy rule for an LCO model
If Overtaking Benefit is High and Opportunity is Good then
Intention of LCO is High.
Data Collection
Two types of data are required:
1- The membership functions
2- Obtain dynamic car-following and lane-changing data
in a range of circumstances, against which the model
can be calibrated.
Car-following Behavior
Phase 1) Say following distance/relative speed using the
verbal terms .
Phase 2) To follow a target vehicle at their ‘minimum safe
distance’.
Phase 3) To performed a number of acceleration/ braking
Maneuvers.
Phase 4) To pass the target vehicle, find a slower vehicle and
approach from over 100m until his desired headway was
reached.
Phase 5) In ‘free mode’, the driver was again questioned
regarding closing speed.
Lane-changing Behavior
Phase1) About every half minute, the observer asked the
subject whether he had the intention to make a lane change to
the nearside/offside lane.
Phase 2) With each successful lane change, the subject gave a
description about the intention level and the reasons, such as
‘overtaking benefit was high’ and the ‘opportunity was good’
etc..
The recorded subjective
verbal assessments from
subjects
Data recorded
simultaneously by the
instrumented vehicles
Fuzzy Data Base
FUZZY SETS AND SYSTEMS CALIBRATION
The fuzzy set calibration, assigns the detailed numerical
values collected in the survey to each verbalized fuzzy set.
A Sample Survey
Result
The Membership Function for the Fuzzy Set ‘about zero’ of Premise Variable,
The Fuzzy Rule Base for the Car-Following Model (in Matrix
Structure)
Validation Test: Comparison of Accelerations (Subject 1)
Validation Test: Comparison of Speeds (Subject 1)
Validation Test: Comparison of Relative Speeds (Subject 1)
Comparison with other models
Comparison of SE on Acceleration Rates for
Different
Car-following Models (Subject 1)
Comparison of SE on Speeds for Different Car-following Models (Subject 1)
Comparison of SE on Relative Speeds for Different
Car-following Models (Subject 1)
Lane-Changing Model Validation
Lane-changing Rates Comparison between Data from Survey and Simulation
Lane Occupancy Comparison for Lane 1
Lane Occupancy Comparison for Lane 2
Lane Occupancy Comparison for Lane 3
Conclusion
Fuzzy Logic is the best approach for carfollowing & Lane-changing modeling.
Any question?
Thanks