1. A. Khosravi

2. 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 Model aQUEUE - GIPS Optimal Velocity OV Cell Transition CT Cellular AutomatonCA Different Models Car-following: Pipes 1958

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

4. Formulation: 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: Relative spacing to two vehicle

5. 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 n the speed of the n th vehicle m,l are the constant must to be determined. The most vital part of the GHR model Experience

6. Optimal Velocity(OV) model 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:

7. So that:Model Driver Strategy OV to maintain a safe velocity according to relative position GHR Keeps a safe distance according to relative velocity

8. There are many specific forms of. A popular choice is: Traffic under congestion and vehicle should stop. The vehicle density is low and thus the vehicles could run at their maximum speed.

9. Fuzzy Logic Model Behavior of humanVehicle behavior A correct description of human A effective model Fuzzy model humanFuzzy controller InputsStatue message of the front car Output Decision made through a series of thinking

10. 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’= ‘not close’= ….

11. 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)

12. 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

13. 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 model If Distance Divergence is Too Far and relative speed is Closing then the driver’s response is No Action (keep current speed).

14. 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.

15. The LCO Model The 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

16. 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

17. Fuzzy Set Terms for the LCN Model Pressure from RearGap SatisfactionIntention 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.

18. 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.

19. Car-following Behavior Phase 1) Say f ollowing distance/relative speed using the verbal terms. Phase 2) T o follow a target vehicle at their ‘minimum safe distance’. Phase 3) To p erformed a number of acceleration/ braking Maneuvers. Phase 4) T o pass the target vehicle, find a slower vehicle and approach from over 100m until his desired headway was reached. Phase 5) I n ‘free mode’, the driver was again questioned regarding closing speed.

20. 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..

21. The recorded subjective verbal assessments from subjects Data recorded simultaneously by the instrumented vehicles Fuzzy Data Base

22. 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

23. The Fuzzy Rule Base for the Car-Following Model (in Matrix Structure)

24. Validation Test: Comparison of Accelerations (Subject 1)

25. Validation Test: Comparison of Speeds (Subject 1)

26. Validation Test: Comparison of Relative Speeds (Subject 1)

27. Comparison of SE on Acceleration Rates for Different Car-following Models (Subject 1) Comparison with other models

28. Comparison of SE on Speeds for Different Car-following Models (Subject 1)

29. Comparison of SE on Relative Speeds for Different Car-following Models (Subject 1)

30. Lane-Changing Model Validation Lane-changing Rates Comparison between Data from Survey and Simulation

31. Lane Occupancy Comparison for Lane 1

32. Lane Occupancy Comparison for Lane 2

33. Lane Occupancy Comparison for Lane 3

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

35. Any question?