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Workshop “Modelling link flows and travel times for dynamic traffic assignment” Queen’s University of Belfast ----- Wed-Thurs 15-16 Analysis of Car-following.

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Presentation on theme: "Workshop “Modelling link flows and travel times for dynamic traffic assignment” Queen’s University of Belfast ----- Wed-Thurs 15-16 Analysis of Car-following."— Presentation transcript:

1 Workshop “Modelling link flows and travel times for dynamic traffic assignment” Queen’s University of Belfast Wed-Thurs Analysis of Car-following Models Using Real Traffic Microscopic Data Università degli Studi di Napoli “Federico II” Facoltà di Ingegneria D.I.T. Dipartimento di Ingegneria dei Trasporti

2 Workshop “Modelling link flows and travel times for dynamic traffic assignment” Queen’s University of Belfast Wed-Thurs Context and definitions (here and now) Demand models (e.g. route choice model) –Aggregate (users/class of users – collective memory/choices can be taken into account) –Disaggregate (microscopic?) Individual history (actual previous choices) can be taken into account Supply models –Congestion model –Actual/Istantaneous path cost model –Flow propagation model Macroscopic (flow modelling) Microscopic (vehicle modelling) –Longitudinal models (e.g.: car-following) –Lateral models (e.g.: lane-changing)

3 Workshop “Modelling link flows and travel times for dynamic traffic assignment” Queen’s University of Belfast Wed-Thurs Why micro? (provided that we are not micro-supporters) Because sometimes details are relevant In perspective (where micro-models will be really consolidated): –Because they could be (potentially) more “behavioural” than other approaches Analytical, LWR, Cell transmission, … are (in part) inherently descriptive –“Capacity”, critical density, flow-density/speed curves, … should be calibrated (at least in principle) for each link (for each class of link) of each network (of each modelling context) Micro-simulation is potentially behavioural –Car following (+ others) model parameters depends on driver behaviours –In principle driver behaviours are stable for extended geographic areas »Given traffic context (urban, extra-urban) and not traffic conditions (traffic conditions are outputs of micro-simulation models) –Calibrate drivers’ parameters and use them for all links of all network

4 Workshop “Modelling link flows and travel times for dynamic traffic assignment” Queen’s University of Belfast Wed-Thurs Calibration of car-following models Problems of car-following models in reproducing real traffic also depend on complexity of calibration. A plenty of microscopic laws and models attempting to capture longitudinal interactions among vehicles have been proposed. Not very much studies have been carried out for calibrating and validating these models Most probably because of difficulties in gathering accurate field data Models have been generally validated by comparing outputs aggregated at a macroscopic level

5 Workshop “Modelling link flows and travel times for dynamic traffic assignment” Queen’s University of Belfast Wed-Thurs Recent technology developments could help calibration of car-following models against disaggregate data? Brakstone and Mac Donalds (2003) – Validation of a fuzzy-logic based model –One test vehicles, with ground speed measurement system and front microwave radar unit –10 Hz time series databases on distance keeping behaviour between the test vehicle and a preceding vehicle –Data gathered along UK motorway Brockfeld et alii (2004) and Ranjitkar et alii (2004) – testing of several car- following models –time series data of nine vehicles forming a single platoon –equipped with GPS + post-processing allowing for an accuracy of about 1 cm –Data gathered on a test-track in Japan Calibration of car-following models

6 Workshop “Modelling link flows and travel times for dynamic traffic assignment” Queen’s University of Belfast Wed-Thurs Given a car-following model  A set of parameters needs to be calibrated Car-following parameters are expected to be: –Different in different contexts (because of different driving behaviours) Extra urban (controlled accesses, ramps, few disturbance from turn- movements, …) “Urban” (intersections, …  major non-freeway roads) –Distributed among drivers Given a context –Ability to reproduce traffic conditions should be in the model it- self, not in parameters –Parameters should be calibrated over a wide variety of traffic conditions (more or less heavy congestion, different average speeds, … )  over a wide variety of leader trajectories Car-following parameters calibration

7 Workshop “Modelling link flows and travel times for dynamic traffic assignment” Queen’s University of Belfast Wed-Thurs Fix the driver –For each given context Let the leader behave in a wide variety of ways Observe the driver (as a follower) over time Capture reactions to leader trajectory over time  calibrate parameters –If you have a platoon, you can simultaneously gather data for more than one follower Assuming all drivers are similar (each driver is the leader for the following one) –calibrate (average) parameter values for the given context by using more data from a single experiment Calibrating for different contexts

8 Workshop “Modelling link flows and travel times for dynamic traffic assignment” Queen’s University of Belfast Wed-Thurs Like in the previous case, but… Fix the context –Observe several drivers (as followers) and their reaction to leaders’ trajectories (the most various is possible) By using long platoons And/or by repeating several time the experiment in the same context with a different driver (as follower) –Calibrate not only average drivers’ behaviours but also dispersion of parameters distribution Calibration of dispersion among drivers

9 Workshop “Modelling link flows and travel times for dynamic traffic assignment” Queen’s University of Belfast Wed-Thurs Calibration for different contexts (one driver or “similar” driver) require less data (is less expensive) than calibration of parameters dispersion Also, is less useful in microscopic models practical implementations (almost all of them assume different drivers groups) Calibration of car following parameters

10 Workshop “Modelling link flows and travel times for dynamic traffic assignment” Queen’s University of Belfast Wed-Thurs Experiment on-field (real context) 5 professional GPS devices (rent of 35K€ for 10 months – not specifically available for car-following experiments) –1 device as ground-control (in order to apply differential post- processing techniques) –1 device to observe the trajectory of the leader of the platoon –3 device to gather data for the platoon of the 3 followers Platoons of max 3 followers Our experiment

11 Workshop “Modelling link flows and travel times for dynamic traffic assignment” Queen’s University of Belfast Wed-Thurs GPS devices shared with others (for different purposes) –Available drivers 2 Leaders (Vincenzo Punzo & Fulvio Simonelli) 6 Followers (Students: Andrea, Davide, Domenico, Carlo, Carmine, Emilio) –2 Platoons (platoon 1 and platoon 2) Experiments in “live-traffic” from October 2003 to July 2004 –The experiments have been carefully controlled on-field in order to identify and eliminate from the calibration database unwanted situations like the intrusion of a foreign vehicle into the platoon Up to now –Four experimental sessions completely processed in order to gather data for car-following calibration Our experiment

12 Workshop “Modelling link flows and travel times for dynamic traffic assignment” Queen’s University of Belfast Wed-Thurs Our experiment Platoon 1Platoon 2 Extra - UrbanSession 30B UrbanSession 25B and 25CSession 30C Data gathered with GPS have been post-processed –Expected positioning accuracy: 8 mm –Trajectories verified to be biased Electromagnetic interference due to several physical obstacles Naples is the NATO Navy Headquarter for Mediterranean –September 11 + Afghanistan + Iraq + …. + “Triple B disaster” (Bush + Blair + Berlusconi) After post-processing (filtering) –Sessions 25B and 25C: 7 min of uninterrupted trajectories –Sessions 30B and 30C: 6 min of uninterrupted trajectories Standard GPS Bias Extra GPS Bias

13 Workshop “Modelling link flows and travel times for dynamic traffic assignment” Queen’s University of Belfast Wed-Thurs Obtaining data from experiments: Post-processing Experts/perpetrators of the post-processing: V.Punzo and D.Formisano (not me, neither Fulvio) 1.Apply Differential-GPS postprocessing in order to increase positioning accuracy 2.Apply filter in order to: Obtain a further increase of accuracy; Have “smooth trajectories” (smoothing speed profiles) Smoothing the randomness of the signal Eliminating unrealistic (incorrect) values of speed and/or acceleration Fill (small) gaps in data

14 Workshop “Modelling link flows and travel times for dynamic traffic assignment” Queen’s University of Belfast Wed-Thurs The filtering procedure (for details remember to ask to Punzo or Formisano) Filtering has been applied simultaneously to all vehicles of the platoon By taking into account both speed and spacing This avoids some common systematic errors that can arise also from slightly noisy raw data –Even slight (repeated) errors in speed profile, could determine negative spacing in case of a vehicle stop –Even more evident for experiments in live traffic A Kalman filter was designed (Punzo-Formisano-Torrieri, 2004) –allows to simultaneously estimate trajectories of vehicles of a platoon from DGPS data in a joined and consistent approach –It cannot be generally used with GPS measurements in case of only one vehicle –has been here fruitfully used by including also inter-spacing (in addition to speed) as an additional measurement

15 Workshop “Modelling link flows and travel times for dynamic traffic assignment” Queen’s University of Belfast Wed-Thurs The filtering procedure

16 Workshop “Modelling link flows and travel times for dynamic traffic assignment” Queen’s University of Belfast Wed-Thurs CALIBRATION AIMS We can’t calibrate parameter dispersion among drivers We can: –Calibrate parameters (for given drivers) in different contexts –Calibrate for different microscopic simulation models Try to argue on robustness of models to parameter calibration Considered models have been: –Newell –Gipps –GM/Ahmed They are different: –In the modelling approach –In the complexity –In the number of parameters (GM =11 ; GIPPS=5 ; NEWELL=2) Platoon 1Platoon 2 Extra - UrbanSession 30B UrbanSession 25B and 25CSession 30C Data availability7 + 7 minutes6 + 6 minutes

17 Workshop “Modelling link flows and travel times for dynamic traffic assignment” Queen’s University of Belfast Wed-Thurs CALIBRATED/TESTED MODELS Newell (Trans. Res. B, 2002): –A simplified car-following theory: a lower-order model –Very simple (simplistic?) –minimum number of parameters –The equation regulating the follower’s behaviour is: x f (t+τ n ) = x L (t)-d n where x f and x L represent the positions of the follower and of the leader –The trajectory of the follower is basically the same of the leader Except for a translation in time and space regulated by parameters  n and d n –which may vary from user to user

18 Workshop “Modelling link flows and travel times for dynamic traffic assignment” Queen’s University of Belfast Wed-Thurs Gipps: is a safety-based model provides two different functional approaches according to the two different driving regimes (free or conditioned flow) Parameters adopted in the model are therefore:  = reaction time of the driver a(n) = maximum acceleration wanted by the follower, V*(n) = speed wanted by the follower, d(n) = maximum deceleration the follower wants to adopt d*(n)=follower’s estimate of maximum deceleration the leader intends to adopt CALIBRATED/TESTED MODELS

19 Workshop “Modelling link flows and travel times for dynamic traffic assignment” Queen’s University of Belfast Wed-Thurs GM/Ahmed (as implemented in MITSIMLab – M.I.T.): represents a development of the GM model classic model of the kind Response =Sensitivity x Stimulus Moreover: –If not in car-following regime, two heuristic approaches are adopted for the free-flow regime and the emergency-regime (to avoid vehicles collision) –the term taking into account density of the segment in which the vehicle is moving has been neglected density measurements were missing in the tests performed (and because of its controversial consistency within a microscopic approach) Random term has been not explicitly considered CALIBRATED/TESTED MODELS

20 Workshop “Modelling link flows and travel times for dynamic traffic assignment” Queen’s University of Belfast Wed-Thurs IS NOT SMOOTH !!! Response in the car-following regime may lead to improbable acceleration- deceleration values for some values of the parameters this tend to make the model unstable. Limits to maximum values of acceleration/deceleration (5 m/sec 2, 10 m/sec 2 ) are normally introduced, but these limits inevitably cause that the spacing- function is non-smooth These considerations are none relevant for the Gipps and Newell models  acc  dec Response surface (spacing) NOTES about GM/Ahmed

21 Workshop “Modelling link flows and travel times for dynamic traffic assignment” Queen’s University of Belfast Wed-Thurs Calibration + Validation (calibrate on a set of measures + validate against a different, comparable set of measure) 36 calibrations –Driver 1.1 (platoon 1), Session 25B and 25C (2 sessions), 3 set of parameters (Newell, Gipps, MITSIM) = 6 calibrations –Driver 1.2, as driver 1.1 = 6 calibrations –Driver 1.3, as driver 1.1 = 6 calibrations –Driver 2.1 (platoon 2), Session 30B and 30C (2 sessions), 3 set of parameters (Newell, Gipps, MITSIM) = 6 calibrations –Driver 2.2, as driver 2.1 = 6 calibrations –Driver 2.3, as driver 2.1 = 6 calibrations Calibration/Validation procedure

22 Workshop “Modelling link flows and travel times for dynamic traffic assignment” Queen’s University of Belfast Wed-Thurs Calibration/Validation procedure 36 Validations Trajectories of dataset CalibrationSession 25BSession 25 CSession 30BSession 30C Session 25BDrivers 1.1, 1.2, 1.3 Session 25CDrivers 1.1, 1.2, 1.3 Session 30BDriver 2.1, 2.2, 2.3 Session 30CDriver 2.1, 2.2, 2.3

23 Workshop “Modelling link flows and travel times for dynamic traffic assignment” Queen’s University of Belfast Wed-Thurs Calibration technique Not sophisticated calibration –observed vs. simulated measures (headways or speeds or spacing?) –minimising deviation (RMSE) ;. LINDO’s API have been used for solving the minimization problem above. Multi-point non linear optimisation algorithm: Search for minimum starting from different points (to circumvent local minima) Which measure has to be chosen for calibration? Headway? Speed? Spacing? All models reproduce speeds better than spacing or headway, but… Calibrating on speeds implies not negligible errors on headway and spacing

24 Workshop “Modelling link flows and travel times for dynamic traffic assignment” Queen’s University of Belfast Wed-Thurs Newell Systematic errors (Mean Error) Session 30C Gipps HeadSpeedSpacing Headway Speed Spacing HeadSpeedSpacing Headway Speed Spacing GM/Ahmed Mean Error HeadSpeedSpacing Headway Speed Spacing In conclusion we have minimised simulated vs. observed spacing

25 Workshop “Modelling link flows and travel times for dynamic traffic assignment” Queen’s University of Belfast Wed-Thurs Calibration results (RMSPE) 25B (urban) pair_1-2pair_2-3pair_3-4 RMSPe [% values] 25C (urban) pair_1-2pair_2-3pair_3-4 RMSPe [% values] GM/Ahmed Gipps Newell 30B (extra-urban) pair_1-2pair_2-3pair_3-4 RMSPe [% values] GM/Ahmed seems to behave respect to calibration –Simulated data better fit observations Newell seems to be the worst performer 30C (urban) pair_1-2pair_2-3pair_3-4 RMSPe [% values]

26 Workshop “Modelling link flows and travel times for dynamic traffic assignment” Queen’s University of Belfast Wed-Thurs Validation results “Error surplus” (should be null for perfectly successful validation) GM/Ahmed seems to be the worst performer Newell performs quite good Gipps is controversial Comparison on validation results 25BC driver-1driver-2driver-3 GM/Ahmed Gipps Newell Comparison on validation results 25CB driver-1driver-2driver-3 RMSPe [% values] GM/Ahmed Gipps Newell

27 Workshop “Modelling link flows and travel times for dynamic traffic assignment” Queen’s University of Belfast Wed-Thurs Validation results “Error surplus” (should be null for perfectly successful validation) GM/Ahmed seems to be the worst performer Newell performs quite good Gipps is controversial Comparison on validation results 30BC driver-1driver-2driver-3 RMSPe [% values] GM/Ahmed Gipps Newell Comparison on validation results 30CB driver-1driver-2driver-3 RMSPe [% values] GM/Ahmed Gipps Newell

28 Workshop “Modelling link flows and travel times for dynamic traffic assignment” Queen’s University of Belfast Wed-Thurs Preliminary Conclusions The RMSPEs are surprisingly in agreement with the values by Brockfeld et al (2004) Worst values in validation are achieved in the urban/extra-urban cross-validation –This could confirms the behavioural difference of these different contexts GM/Ahmed (11 parameters to be calibrated) tends to overfit observed data? Gipps and Newell models show a more robust behaviour Newell’s model performances are really surprising: despite of its simplicity it outperforms other models in the validation process –Let say: “It is wrong, but never drastically wrong” –Does drivers’ behaviour tends to be as “simple” as in the Newell model?

29 Workshop “Modelling link flows and travel times for dynamic traffic assignment” Queen’s University of Belfast Wed-Thurs General Conclusions Validation is problematic –Something is missed in all investigated specifications –They do not show a behavioural robustness –Our feeling is that the missing phenomenon is “looking ahead” We should continue with all session of experiments –Testing/developing also other model specifications Use of different techniques for gathering trajectories should be investigated –Could be aerial-recording (and recognising) a more effective technique?

30 Workshop “Modelling link flows and travel times for dynamic traffic assignment” Queen’s University of Belfast Wed-Thurs The real truth about our experiment Aware of the experiment aims: “Please, drive avoiding platoon dispersion (slow, but not too much)” Unaware of the experiment aims, but… “Please, don’t change lane! Follows the leader” May be real behaviours have been influenced –Surely, less influenced than how generally happens in test-track experiments

31 Workshop “Modelling link flows and travel times for dynamic traffic assignment” Queen’s University of Belfast Wed-Thurs Other Conclusions Waiting for your contributions/opinions –…


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