Car-following Model of Vehicle Car-following Model of Vehicle TrafficTraffic

Car-following Model of Vehicle Car-following Model of Vehicle TrafficTraffic

In the name of GodIn the name of God

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.

……

-GHR

-Fuzzy

MITSim-ModelMITSIM

a Queuing ModelaQUEUE

--GIPS

Optimal Velocity OV

Cell TransitionCT

Cellular AutomatonCA

Different Models

Car-following: Pipes 1958

Gazis-Herman-Rothery(GHR) model (1958)

][][Re Stimulussponse n

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:

)()( Ttvctan

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 timec: sensitivity coefficient

Above equation is very different from real situation. In order to make the model more realistic:

)(

)()(

Ttx

Ttvctan

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:

)(

)()(

Ttx

Ttvcvta

lmnn

Vn the speed of the n th vehiclem,l are the constant must to be determined.

The most vital part of the GHR model

Experience

]2,0[m

]2,1[l

Optimal Velocity(OV) model

)]()([)( tvtVcta ndesirednn

The desired velocity of the n th vehicle at time t.

In GHR model:

In the OV model, the desired velocity is considered to be relevant to the relative spacing:

))(()( txVtV noptdesired

n

)()( 1 tvtV ndesiredn

So that:

)]())(([)( tvtxVcta nxopt

n

ModelModel Driver StrategyDriver Strategy

OVOVto maintain a safe velocity according to relative position

GHRGHRKeeps a safe

distance according to relative velocity

There are many specific forms of ))(( txV nopt . A popular choice is:

xxv

xxxxf

xx

xV

B

BA

Aopt

max

)(

0

)(

Traffic under congestion and vehicle should stop.

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 modelFuzzy model

humanhuman Fuzzy controller

Inputs Inputs Statue message of the front car

OutputOutputDecision 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].

‘too close’= 5.0| xx‘not close’= 2| xx

….

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

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

Fuzzy Set Terms Used in the Car-following Model

A fuzzy rule for car-following modelIf 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 ModelThe LCO model has two principal premise

variables:

• Overtaking benefit (speed gain)

• Opportunity (Safety and Comfort of the lane change)

Fuzzy Sets: Triangular Membership function

Low

Medium

High

Intention of LCO

Bad (OP3)

Moderate (OP2)

Good (OP1)

Opportunity

High (OB1)

Low (OB3)

Medium (OB2)

Overtaking Benefit

Fuzzy Set Terms Used in the Car-following Model

The LCN ModelThe 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 modelIf 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.

The Membership Function for the Fuzzy Set ‘about zero’ of Premise Variable, DV

A Sample Survey Result

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 of SE on Acceleration Rates for Different

Car-following Models (Subject 1)

Comparison with other models

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

ConclusionConclusion

Fuzzy Logic is the best approach for car-following & Lane-changing modeling.

Any question?Any question?

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