1. Cooperative lane changing and forced merging model Moshe Ben-Akiva, Charisma Choudhury, Tomer Toledo, Gunwoo Lee, Anita Rao ITS Program January 21, 2007

2. 2 Outline Introduction Lane changing –Model structure –Estimation results –Validation results Acceleration research plan

3. 3 Introduction

4. 4 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

5. 5 Merging Behavior Vehicle merging –Lane changing through gap acceptance –Models fail in dense traffic Additional merging mechanisms –Lag vehicle may provide courtesy –Vehicle may force a lane change Merging mechanism affects –Gap acceptance –Acceleration decisions

6. 6 Lane Changing

7. 7 Combined Lane Changing Model

8. 8 Combined Lane Changing Model: Detailed Structure

9. 9 Available Gap Adjacent gap changes if either lead or lag vehicle changes

10. 10 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 –Anticipated gap acceptable Courtesy merging Driver initiates lane change

11. 11 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

12. 12 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

13. 13 NGSIM I-80 Study Area

14. 14 Estimation Data Set 45 minute data 540 merging vehicles X and Y coordinates every 1/10 th sec Estimation based on 17352 observations Summary statistics –Average speed of merging vehicles 15.1 km/hr –Average speed in Lane 6 16.5 km/hr –Average d/s density in Lane 6 68.4 veh/km

15. 15 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

16. 16 Estimation Results Median critical lag gap variation with relative lag speed - Effect of type of merge Median critical lag gap (m)

17. 17 Estimation Results (2) Median critical lag gap variation with remaining distance - Effect of driver heterogeneity

18. 18 Model Comparison Tested against a single level gap acceptance model –No explicit courtesy or forced merge component ModelLikelihoodParameters Normal only-1639.6917 Full model-1609.6542 Reject normal only model at 95% confidence

19. 19 Estimation, Calibration and Validation Framework

20. 20 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 ‘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

21. 21 Validation Results Previous Model Combined Model Percent Improvement RMSE (vehicles/5 mins)20.9113.2258.18% RMSPE10.81%7.52%43.83% Comparison of Lane-Specific Counts Comparison of Lane-Specific Speeds Previous Model Combined Model Percent Improvement RMSE (mph)12.818.8245.17% RMSPE29.73%22.26%33.58%

22. 22 Validation Results (2) Comparison of Location of Merges

23. 23 Acceleration Research Plan

24. 24 Motivation Drivers unable to merge immediately –Target gaps –Accelerate/decelerate to facilitate merging

25. 25 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

26. 26 Extended Model Framework

27. 27 Target Gap Selection Conditional on the decision of not initiating a courtesy/forced merge Utility of gap j for individual n at time t

28. 28 Target Gap Selection (2) Candidate explanatory variables –Size of gap –Trend of gap –Distance traversed to be adjacent to the gap

29. 29 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

30. 30 Proposed Acceleration Model The driver responds to different stimuli depending on merging mechanism and target gap choice Current leader may constrain desired acceleration

31. 31 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

32. 32 Car-following acceleration or deceleration based on relative speed of leader in target lane 1. Lane Changing Acceleration

33. 33 1. Lane-changing Acceleration (2) Variables affecting acceleration/deceleration functions –speed of subject vehicle –spacing with lead vehicle

34. 34 2. Target Gap Acceleration Models General Structure a. Constrained regime b. Unconstrained regimes - based on time headway

35. 35 2a. Constrained Regime Car-following acceleration or deceleration based on relative speed of current front vehicle Variables –speed of subject vehicle, spacing with front vehicle, roadway conditions (e.g. density) etc. Same functional form for forward, backward and adjacent gaps

36. 36 2b. Unconstrained Regime a.Forward gap acceleration - function of desired and current positions, relative speed with leader etc. b.Backward gap acceleration - function of desired and current positions, subject speed etc.

37. 37 2b. Unconstrained Regime (2) c. Adjacent gap acceleration - function of desired and current positions, relative speed of lag etc.

38. 38 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.

39. 39 Maximum likelihood technique –Joint estimation of all model parameters Data –NGSIM I-80 trajectory data –May be enriched by US 101 trajectory data Estimation

40. 40 Implemented in MITSIMLab –Compared against default MITSIMLab models Data –US 101 ‘synthetic’ sensor flows and speeds Calibration/Validation

41. 41 Alternative Structure 1

42. 42 Alternative Structure 2