1. Jorge A. Laval Workshop: Mathematical Foundations of Traffic IPAM, September 2015 1

2. 2 Multilane instabilities – FD scatter

3. 3 3 Introduction: NGSIM US-101

4. 4 Measurement method

5. 5

6. 6 Timid and aggressive behaviors Laval and Leclercq, Phil. Trans. Royal Society A, 2010.

7. 7 Today’s hypothesis the random error in drivers acceleration processes may be responsible for most traffic instabilities: –Formation and propagation of oscillations –Oscillations growth –Hysteresis Laval, Toth, and Zhou (2015), A parsimonious model for the formation of oscillations in car-following models. Transportation Research Part B 70, 228- 238.

8. 8 Outline stochastic desired acceleration model –for a single unconstrained vehicle plugin to Newell’s car-following model –upgrade simulation experiment –car-following experiment

9. 9 Scope Car-following only, no lane changes Single lane Homogeneous drivers, no trucks

10. 10 Stochastic desired accelerations Data collected with android app Platoon leader accelerating at traffic lights; i.e., an unconstrained vehicle

11. 11 Stochastic desired accelerations desired acceleration  vehicle downstream does not constrain the motion

12. 12 The SODE

13. 13 Solution of the SODE Speed and position are Normally distributed:

14. 14 Dimensionless formulation

15. 15 An example acceleration process datamodel

16. 16 Coefficient of Variation /  2 Parameter-free most variability at the beginning and for low speeds

17. 17 Outline stochastic desired acceleration model –for a single unconstrained vehicle plugin to Newell’s car-following model –upgrade simulation experiment –car-following experiment

18. 18 Plugin to Newell’s car-following model

19. 19 The upgrade simulation experiment Single lane, 100m-100G% upgrade

20. 20

21. 21 Model captures oscillation growth

22. 22 Model captures hysteresis Trajectory Explorer (trafficlab.ce.gatech.edu)

23. 23 Model captures “concavity” Tian et al, Trans. Res. B (2015) Jian et al, PloS one (2014)

24. 24 The upgrade simulation experiment cont’d: analysis of oscillations

25. 25 Fourier spectrum analysis period = 3.3 min amplitude = 21.5 km/hr

26. 26 Oscillations period and amplitude Large variance PDF not symmetric

27. 27 Average speed at the botlleneck

28. 28 Oscillations period and amplitude

29. 29 Outline stochastic desired acceleration model –for a single unconstrained vehicle plugin to Newell’s car-following model –upgrade simulation experiment –car-following experiment

30. 30 Car-following experiment 6-vehicle platoon, unobstructed leader 5Hz GPS devices and Android app in each vehicle two-lane urban streets around Georgia Tech campus Objective: –compare 6 th trajectory with model prediction –given: leader trajectory and grade G=G( x )

31. 31 Car-following experiment

32. 32 Example data

33. 33 Trailing vehicle speed peak

34. 34 Trailing vehicle speed peak: oblique trajectories

35. 35 Trailing vehicle speed peak: oblique trajectories

36. 36 Car-following experiment #1

37. 37 Car-following experiment #2

38. 38 Car-following exp. #2–Social force model

39. 39 Car-following experiment #3

40. 40 Car-following experiment

41. 41 Q & A 41 THANK YOU !

42. 42 90%-probability interval

43. 43 Car-following experiment

44. 44 Trajectory Explorer www.trafficlab.ce.gatech.edu

45. 45 Source: NGSIM (2006) Models that predict Oscillations Unstable car-following models 2 nd -order models Delayed ODE type: oscillation period predicted ~ a few seconds (Kometani and Sasaki, 1958, Newell, 1961) ODE type, a few minutes (Wilson, 2008) Fully Stochastic Models Random perturbations not connected with driver behavior (NaSch, 1992, Barlovic et al., 1998, 2002, Del Castillo, 2001 and Kim and Zhang, 2008) Behavioral models Human error (Yeo and Skabardonis, 2009) Heterogeneous behavior in congestion (Laval and Leclercq, 2010, Chen et al, 2012a,b)

46. 46 Parameter-free representation

47. 47