workshop “modelling link flows and travel times for dynamic traffic assignment” queen’s...

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

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


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)


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


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


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


• 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


• 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


• 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


• 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


• 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


• 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


Our experiment

Platoon 1 Platoon 2

Extra - Urban Session 30B

UrbanSession 25B and 25C

Session 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 BiasExtra GPS Bias


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


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


The filtering procedure

spac

ing

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s12 with polar. error

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segnale non filtrato

segnale filtrato (V=0 + Butterw.)

segnale 'vero'

spee

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/s]

experimental data

filtered signal (low-paas ;MATLab)Kalman

Time [s]-5

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segnale 'vero'

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/s]

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Time [s]


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 1 Platoon 2

Extra - Urban Session 30B

Urban Session 25B and 25C Session 30C

Data availability 7 + 7 minutes 6 + 6 minutes


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:

xf(t+τn) = xL(t)-dn

• where xf and xL 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 dn

– which may vary from user to user


• Gipps:is a safety-based modelprovides 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 drivera(n) = maximum acceleration wanted by the follower,V*(n) = speed wanted by the follower,d(n) = maximum deceleration the follower wants to adoptd*(n)=follower’s estimate of maximum deceleration the leader intends to

adopt

nV

tnv

nV

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,025.0

,15.2,,

)1(*

),1(),(),()1(),1(2)()()(),(

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nd

tnvtnvtnxnstnxndndndtnvb



• 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

)()()()(

)()( ,, ttVtK

tX

tVta icf

nnnnn

nn

nniicfn

ii

i

i



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/sec2, 10 m/sec2) 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

Res

pons

e su

rfac

e (s

paci

ng)

NOTES about GM/Ahmed


• 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


Calibration/Validation procedure

36 ValidationsTrajectories of dataset

Calibration Session 25B Session 25 C Session 30B Session 30CSession 25B Drivers 1.1, 1.2, 1.3Session 25C Drivers 1.1, 1.2, 1.3Session 30B Driver 2.1, 2.2, 2.3Session 30C Driver 2.1, 2.2, 2.3


Calibration technique• Not sophisticated calibration

– observed vs. simulated measures (headways or speeds or spacing?)– minimising deviation (RMSE)

i

simi

obsi YY

NRMSe

21

;

i obsi

simi

obsi

Y

YY

NRMSPe

21

.

• 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


Newell

-0.5

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Systematic errors (Mean Error) Session 30C

Gipps

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Head Speed Spacing

Headway

Speed

Spacing

Head Speed Spacing

Headway

Speed

Spacing

GM/Ahmed

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Mea

n E

rro

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Head Speed Spacing

Headway

Speed

Spacing

In conclusionwe have minimised

simulated vs. observed spacing


Calibration results (RMSPE)

25B (urban)

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pair_1-2 pair_2-3 pair_3-4

RM

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25C (urban)

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• GM/Ahmed seems to behave respect to calibration– Simulated data better fit observations

• Newell seems to be the worst performer

30C (urban)

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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

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driver-1 driver-2 driver-3

GM/Ahmed

Gipps

Newell

Comparison on validation results 25CB

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GM/Ahmed

Gipps

Newell


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

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GM/Ahmed

Gipps

Newell

Comparison on validation results 30CB

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% v

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GM/Ahmed

Gipps

Newell


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?


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?


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


Other Conclusions

• Waiting for your contributions/opinions– …

– …

– …

workshop “modelling link flows and travel times for dynamic traffic assignment” queen’s...

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models problems of car

traffic context urban

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