Analysis of Carfollowing Models Using Real Traffic Microscopic Data

1
Analysis of Car-following Models Using Real
Traffic Microscopic Data
Università degli Studi di Napoli Federico
IIFacoltà di Ingegneria D.I.T. Dipartimento di
Ingegneria dei Trasporti
2
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
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
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
Calibration of car-following models

• 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

6
Car-following parameters calibration

• 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

7
Calibrating for different contexts

• 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

8
Calibration of dispersion among drivers

• 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

9
Calibration of car following parameters

• 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)

10
Our experiment

• 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

11
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

12
Our experiment

• 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
Obtaining data from experiments Post-processing

• Experts/perpetrators of the post-processing
  V.Punzo and D.Formisano (not me, neither Fulvio)
  ?
• Apply Differential-GPS postprocessing in order to
  increase positioning accuracy
• 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
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-Torr
  ieri, 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
The filtering procedure
16
CALIBRATION AIMS

• We cant 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 GIPPS5
  NEWELL2)

17
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 followers behaviour
  is
• xf(ttn) 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

18
CALIBRATED/TESTED MODELS

• 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)followers estimate of maximum
  deceleration the leader intends to adopt

19
CALIBRATED/TESTED MODELS

• 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

20
NOTES about GM/Ahmed

• 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/decelerat
  ion (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

Response surface (spacing)
?acc
?dec
21
Calibration/Validation procedure

• 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

22
Calibration/Validation procedure

• 36 Validations

23
Calibration technique

• Not sophisticated calibration
• observed vs. simulated measures (headways or
  speeds or spacing?)
• minimising deviation (RMSE)

• LINDOs 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
Systematic errors (Mean Error) Session 30C
Newell
3.5
GM/Ahmed
3
2.5
3.5
2
3
1.5
2.5
1
2
Mean Error
0.5
1.5
0
1
-0.5
0.5
0
-0.5
Gipps
3.5
3
In conclusionwe have minimisedsimulated vs.
observed spacing
2.5
2
1.5
1
0.5
0
-0.5
25
Calibration results (RMSPE)

• GM/Ahmed seems to behave respect to calibration
• Simulated data better fit observations
• Newell seems to be the worst performer

26
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

27
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

28
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
• Newells 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
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
The real truth about our experiment

• May be real behaviours have been influenced
• Surely, less influenced than how generally
  happens in test-track experiments

31
Other Conclusions

• Waiting for your contributions/opinions