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
Workshop “Modelling link flows and travel times for dynamic traffic assignment”
Queen’s University of Belfast ----- Wed-Thurs 15-16
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)
Workshop “Modelling link flows and travel times for dynamic traffic assignment”
Queen’s University of Belfast ----- Wed-Thurs 15-16
Why micro? (provided that we are not micro-supporters)
• Because sometimes details are relevant
• In perspective (where micro-models
consolidated):
will
be
really
– 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
Workshop “Modelling link flows and travel times for dynamic traffic assignment”
Queen’s University of Belfast ----- Wed-Thurs 15-16
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
Workshop “Modelling link flows and travel times for dynamic traffic assignment”
Queen’s University of Belfast ----- Wed-Thurs 15-16
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 carfollowing 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
Workshop “Modelling link flows and travel times for dynamic traffic assignment”
Queen’s University of Belfast ----- Wed-Thurs 15-16
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 turnmovements, …)
• “Urban” (intersections, …  major non-freeway roads)
– Distributed among drivers
• Given a context
– Ability to reproduce traffic conditions should be in the model itself, 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
Workshop “Modelling link flows and travel times for dynamic traffic assignment”
Queen’s University of Belfast ----- Wed-Thurs 15-16
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
 calibrate parameters
over
time
– 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
Workshop “Modelling link flows and travel times for dynamic traffic assignment”
Queen’s University of Belfast ----- Wed-Thurs 15-16
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
Workshop “Modelling link flows and travel times for dynamic traffic assignment”
Queen’s University of Belfast ----- Wed-Thurs 15-16
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)
Workshop “Modelling link flows and travel times for dynamic traffic assignment”
Queen’s University of Belfast ----- Wed-Thurs 15-16
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 postprocessing 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
Workshop “Modelling link flows and travel times for dynamic traffic assignment”
Queen’s University of Belfast ----- Wed-Thurs 15-16
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
Workshop “Modelling link flows and travel times for dynamic traffic assignment”
Queen’s University of Belfast ----- Wed-Thurs 15-16
Our experiment
Platoon 1
Extra - Urban
Urban
Platoon 2
Session 30B
Session 25B and 25C Session 30C
• Data gathered with GPS have been post-processed
– Expected positioning accuracy: 8 mm
– Trajectories verified to be biased
Standard
GPS Bias
Extra GPS
Bias
• 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
Workshop “Modelling link flows and travel times for dynamic traffic assignment”
Queen’s University of Belfast ----- Wed-Thurs 15-16
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
Workshop “Modelling link flows and travel times for dynamic traffic assignment”
Queen’s University of Belfast ----- Wed-Thurs 15-16
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
Workshop “Modelling link flows and travel times for dynamic traffic assignment”
Queen’s University of Belfast ----- Wed-Thurs 15-16
The filtering procedure
15
experimental
data
segnale non filtrato
segnalesignal
filtrato(low-paas
(V=0 + Butterw.)
filtered
;MATLab)
Kalman
segnale 'vero'
10
velocità [m/s]
speed [m/s]
5
0
120
140
160
-5
Time
tempo [s][s]
speed [m/s]
spacing [m]
v1
v2
s12
s12 with polar. error
time [s]
Workshop “Modelling link flows and travel times for dynamic traffic assignment”
Queen’s University of Belfast ----- Wed-Thurs 15-16
CALIBRATION AIMS
Platoon 1
Extra - Urban
•
•
•
•
Platoon 2
Session 30B
Urban
Session 25B and 25C
Session 30C
Data availability
7 + 7 minutes
6 + 6 minutes
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)
Workshop “Modelling link flows and travel times for dynamic traffic assignment”
Queen’s University of Belfast ----- Wed-Thurs 15-16
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
Workshop “Modelling link flows and travel times for dynamic traffic assignment”
Queen’s University of Belfast ----- Wed-Thurs 15-16
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)=follower’s estimate of maximum deceleration the leader intends to adopt

vn, t  
va n, t     vn, t   2.5 a n   1  *

 V n  
0.025 
vn, t 
V * n 

v(n  1, t ) 2 
vb (n, t   )  d (n)  d (n)   d (n) 2x(n  1, t )  s(n  1)  x(n, t )  v(n, t ) 

d * (n  1) 

2
2
Workshop “Modelling link flows and travel times for dynamic traffic assignment”
Queen’s University of Belfast ----- Wed-Thurs 15-16
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:
an
cf ,i
(t )  
i
Vn (t   n ) 
i
X n (t   n )
K n (t   n )  Vn (t   n )
i
i
i
  ncf ,i (t )
– 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
Workshop “Modelling link flows and travel times for dynamic traffic assignment”
Queen’s University of Belfast ----- Wed-Thurs 15-16
NOTES about GM/Ahmed
Response surface (spacing)
IS NOT SMOOTH !!!
Response in the car-following regime may lead to improbable accelerationdeceleration 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 spacingfunction is non-smooth
These considerations are none relevant for the Gipps and Newell models
acc
dec
Workshop “Modelling link flows and travel times for dynamic traffic assignment”
Queen’s University of Belfast ----- Wed-Thurs 15-16
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
Workshop “Modelling link flows and travel times for dynamic traffic assignment”
Queen’s University of Belfast ----- Wed-Thurs 15-16
Calibration/Validation procedure
36 Validations
Calibration Session 25B
Session 25B
Session 25C Drivers 1.1, 1.2, 1.3
Session 30B
Session 30C
Trajectories of dataset
Session 25 C
Session 30B
Drivers 1.1, 1.2, 1.3
Session 30C
Driver 2.1, 2.2, 2.3
Driver 2.1, 2.2, 2.3
Workshop “Modelling link flows and travel times for dynamic traffic assignment”
Queen’s University of Belfast ----- Wed-Thurs 15-16
Calibration technique
• Not sophisticated calibration
– observed vs. simulated measures (headways or speeds or spacing?)
– minimising deviation (RMSE)
RMSe 
1
N
i Yi
obs
 Yi

sim 2
RMSPe 
 Yi obs  Yi sim 
1


N i  Yi obs 
2
• 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
Workshop “Modelling link flows and travel times for dynamic traffic assignment”
Queen’s University of Belfast ----- Wed-Thurs 15-16
Systematic errors (Mean Error)
Session 30C
Newell
3.5
GM/Ahmed
3
Headway
Speed
2
1.5
Spacing
1
0.5
0
-0.5
Head Speed Spacing
3.5
3
Mean Error
2.5
2.5
Headway
Speed
2
1.5
Spacing
1
0.5
0
-0.5
Gipps
Head Speed Spacing
3.5
3
Headway
Speed
2.5
2
1.5
Spacing
1
0.5
0
-0.5
Head Speed Spacing
In conclusion
we have minimised
simulated vs. observed
spacing
Workshop “Modelling link flows and travel times for dynamic traffic assignment”
Queen’s University of Belfast ----- Wed-Thurs 15-16
Calibration results (RMSPE)
25C (urban)
50
50
45
45
40
40
35
35
RMSPe [% values]
RMSPe [% values]
25B (urban)
30
25
20
15
30
25
20
15
10
10
5
5
0
0
pair_1-2
pair_2-3
pair_1-2
pair_3-4
30B (extra-urban)
pair_3-4
30C (urban)
50
45
45
40
40
RMSPe [% values]
50
35
RMSPe [% values]
pair_2-3
30
25
20
15
35
30
25
20
15
10
10
5
5
0
0
pair_1-2
pair_2-3
pair_3-4
pair_1-2
pair_2-3
pair_3-4
• GM/Ahmed seems to behave respect to calibration
– Simulated data better fit observations
• Newell seems to be the worst performer
GM/Ahmed
Gipps
Newell
Workshop “Modelling link flows and travel times for dynamic traffic assignment”
Queen’s University of Belfast ----- Wed-Thurs 15-16
Validation results
“Error surplus” (should be null for perfectly successful validation)
Comparison on validation results 25BC
30
25
20
GM/Ahmed
15
Gipps
10
Newell
• GM/Ahmed
seems to be the
worst performer
5
0
driver-1
driver-2
• Newell performs
quite good
driver-3
Comparison on validation results 25CB
RMSPe [% values]
30
25
20
GM/Ahmed
15
Gipps
10
Newell
5
0
driver-1
driver-2
driver-3
• Gipps is
controversial
Workshop “Modelling link flows and travel times for dynamic traffic assignment”
Queen’s University of Belfast ----- Wed-Thurs 15-16
Validation results
“Error surplus” (should be null for perfectly successful validation)
Comparison on validation results 30BC
RMSPe [% values]
30
25
20
GM/Ahmed
15
Gipps
10
Newell
• GM/Ahmed
seems to be the
worst performer
5
• Newell performs
quite good
0
driver-1
driver-2
driver-3
Comparison on validation results 30CB
RMSPe [% values]
30
25
20
GM/Ahmed
15
Gipps
10
Newell
5
0
driver-1
driver-2
driver-3
• Gipps is
controversial
Workshop “Modelling link flows and travel times for dynamic traffic assignment”
Queen’s University of Belfast ----- Wed-Thurs 15-16
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?
Workshop “Modelling link flows and travel times for dynamic traffic assignment”
Queen’s University of Belfast ----- Wed-Thurs 15-16
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?
Workshop “Modelling link flows and travel times for dynamic traffic assignment”
Queen’s University of Belfast ----- Wed-Thurs 15-16
The real truth about our experiment
Unaware of the experiment aims, but…
“Please, don’t change lane! Follows the leader”
Aware of the experiment aims: “Please, drive avoiding
platoon dispersion (slow, but not too much)”
•
May be real behaviours have been influenced
– Surely, less influenced than how generally happens in test-track experiments
Workshop “Modelling link flows and travel times for dynamic traffic assignment”
Queen’s University of Belfast ----- Wed-Thurs 15-16
Other Conclusions
• Waiting for your contributions/opinions
– …
– …
– …