1. Arterial Lane Selection Model Moshe Ben-Akiva, Charisma Choudhury, Varun Ramanujam, Tomer Toledo ITS Program January 21, 2007

2. 2 Outline 1. Introduction and dataset 2. Estimation 2.1 Lane choice at intersection 2.2 Lane changing within section 3. Validation 3.1 Methodology 3.2 Data 3.2 Results

3. 3 1. Introduction and dataset

4. 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. 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. 6 Dataset (cont.) 1 2 3 4

7. 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. 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. 9 2.1 Lane choice at intersection

10. 10 Lane choice at intersection

11. 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 Turning Directions of Vehicles in Lankershim, CA 1 2 3 Section traversed

12. 12 2.1.2 Model structure

13. 13 Probability of driver n selecting lane l as target lane 2.1.2 Model structure (cont.)

14. 14 Driver classes Myopic driver (considers immediate section only) Driver who plans-ahead (considers more than one section ahead)

15. 15 Probability of driver n selecting lane i as immediate lane given that the target lane is l 2.1.2 Model structure (cont.)

16. 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

17. 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. 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. 19 2.1.4 Estimation results

20. 20 2.1.4 Estimation results (cont.)

21. 21 2.1.4 Estimation results (cont.) Utility associated with target lane l for vehicle n

22. 22 2.1.4 Estimation results (cont.) Utility associated with immediate lane i for vehicle n given his target lane is l

23. 23 Anticipated Delay Delay associated with lane l for driver class k: 2.1.5 Interpretation of results

24. 24 2.1.5 Interpretation of results (cont.) Next section - Lane 4 does not continue 12341234 Effect of path-plan in target lane choice

25. 25 2.1.5 Interpretation of results (cont.) Aggressive Driver -Lower inertia to stay in current lane

26. 26 2.1.6 Model selection StatisticBase Model New Model Log likelihood value-2120.4-2115.8 Number of parameters (K)1920 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. 27 2.2 Lane-changing within section

28. 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. 29 2.2.2 Model structure

30. 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

31. 31 2.2.2 Model structure: Gap acceptance Evaluate adjacent lead and lag gaps Accept gap if Available gap >= Critical gap

32. 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:

33. 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

34. 34 2.2.2 Model structure (cont.) Probability of driver n executing lane action l Modeling unobserved aggressiveness Aggressiveness –Individual specific random term

35. 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. 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. 37 2.2.3 Variables: Execution of lane change May depend on –Speed of the subject vehicle –Remaining distance to the turn –Density

38. 38 2.2.4 Estimation results: Target lane

39. 39 2.2.4 Estimation results: Gap acceptance

40. 40 2.2.4 Estimation results: Execution of lane change

41. 41 Utility associated with lane i for vehicle n at time t : 2.2.4 Estimation results Target lane choice

42. 42 2.2.4 Estimation results Gap acceptance Critical Lead Gap Critical Lag Gap

43. 43 2.2.5 Interpretation of results Inertia and path plan effect Trade-off between current lane inertia and path plan effect Distance to exit = 410 m ( 2 sections), Turning/exit lane = Lane 4 * *Lane 4 is the rightmost lane, Lane 1 is the leftmost lane

44. 44 Trade-off between current lane inertia and path plan effect Distance to exit = 150 m (1 section), Turning/exit lane = Lane 4* 2.2.5 Interpretation of results Inertia and path plan effect (cont.)

45. 45 2.2.5 Interpretation of results Inertia and path plan effect (cont.) Trade-off between current lane inertia and path plan effect Distance to exit = 75 m, Turning/exit lane = Lane 4*

46. 46 2.2.5 Interpretation of results Heterogeneity in critical gap

47. 47 2.2.6 Model selection StatisticBase Model New Model Log likelihood value-1186.9-1004.1 Number of parameters (K)1722 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

48. 48 3. Validation

49. 49 Overall Model Development Process

50. 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

51. 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

52. 52 3.2 Model comparison (cont.) Comparison of lane specific speeds

53. 53 3.2 Model comparison (cont.) Comparison of lane distributions

54. 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