1. A demonstration of distribution-based calibration Ioulia MARKOU, Vasileia PAPATHANASOPOULOU, Constantinos ANTONIOU National Technical University of Athens, Greece MT-ITS 20153-5. June 2015, Budapest

2. Outline Motivation Overview Methodology Experimental set-up Application and results Conclusion and future research prospects MT-ITS 2015 3-5. JUNE 2015, BUDAPEST 2

3. Capturing heterogeneity MT-ITS 2015 3-5. JUNE 2015, BUDAPEST 3  Calibration essential for traffic simulation models  Heterogeneity in driving behavior => lots of useful information  Point/aggregate measures miss a lot of information  Not a single distribution, but distributions of subgroups

4. Overview MT-ITS 2015 3-5. JUNE 2015, BUDAPEST 4  Capture the behavior of drivers in relation with the preceding vehicle in the same lane  Multi-agent models with differential equations, each of which captures a different state Car – Following Models

5. Overview MT-ITS 2015 3-5. JUNE 2015, BUDAPEST 5  A comprehensive methodology that will allow quick and efficient calibration of models parameters is important  The Simultaneous Perturbation Stochastic Approximation (SPSA) could be a fairly promising algorithm Optimization approach

6. Overview MT-ITS 2015 3-5. JUNE 2015, BUDAPEST 6 SPSA Algorithm

7. Overview MT-ITS 2015 3-5. JUNE 2015, BUDAPEST 7 Calibration using Distributions Most of the proposed calibration approaches choose to calibrate a few selected parameters for simplicity In emergency situations, it is important to depart from point values and restrict the necessary assumptions by dealing with distributions The proposed approach assumes as input a set of measured distributions The data need to be appropriately preprocessed Distributions have been used in some off-line calibration studies

8. Methodology MT-ITS 2015 3-5. JUNE 2015, BUDAPEST 8 Calibration using Distributions  Point values of surveillance data have been used in this research  A distribution of values for each parameter has been defined.  SPSA identifies the optimal combination of parameters for each observation

9. Methodology MT-ITS 2015 3-5. JUNE 2015, BUDAPEST 6 Determination of calibration parameters Collection of historical measurements Selection of calibration algorithm Choice of Loss Function Start of Calibration

10. Experimental set-up MT-ITS 2015 3-5. JUNE 2015, BUDAPEST 10 Car-following model of TransModeler Traffic Simulation Software

11. Experimental set-up MT-ITS 2015 3-5. JUNE 2015, BUDAPEST 11

12. Experimental set-up MT-ITS 2015 3-5. JUNE 2015, BUDAPEST 12 City of Naples, Italy October 2002 (Punzo et al., 2005, Papathanasopoulou and Antoniou, 2012)

13. Application MT-ITS 2015 3-5. JUNE 2015, BUDAPEST 13

14. Results MT-ITS 2015 3-5. JUNE 2015, BUDAPEST 14 No. of necessary iteration sets for SPSA termination No. of iteration sets No. of records

15. Results MT-ITS 2015 3-5. JUNE 2015, BUDAPEST 15

16. Results MT-ITS 2015 3-5. JUNE 2015, BUDAPEST 16 Acceleration Deceleration

17. Results MT-ITS 2015 3-5. JUNE 2015, BUDAPEST 17 Acceleration Deceleration

18. Results MT-ITS 2015 3-5. JUNE 2015, BUDAPEST 18 Driver 1 Driver 2 Driver 3

19. Results MT-ITS 2015 3-5. JUNE 2015, BUDAPEST 19 Driver 2 mean = -1,16 Driver 3 mean = -1,48 Driver 1 mean = -1,51

20. Conclusion MT-ITS 2015 3-5. JUNE 2015, BUDAPEST 20  Developed distributions of car-following model parameters  Captured heterogeneous driver behavior  Utilized state-of-the-art efficient optimization algorithms (SPSA)

21. Future research prospects MT-ITS 2015 3-5. JUNE 2015, BUDAPEST 21 Application of the methodology in more complex situations Incorporation of the distribution of model parameter values into a simulation model The phenomena observed in the present application should be explained through further extensive experiments Vehicle dynamics and the correlation between different parameter values should also be taken into account

22. A demonstration of distribution-based calibration Ioulia MARKOU ioulia@central.ntua.gr National Technical University of Athens, Greece MT-ITS 20153-5. June 2015, Budapest Vasileia PAPATHANASOPOULOU vpapath@central.ntua.gr Constantinos Antoniou antoniou@central.ntua. gr