1. Freeway Segment Traffic State Estimation
Heterogeneous Data Sources and Uncertainty Quantification:
A Stochastic Three-Detector Approach
Wen Deng
Xuesong Zhou
University of Utah
Prepared for INFORMS 2011

2. Needs for Traffic State Estimation
Sensor Data
Traffic State Estimation
Traffic Flow/Control Optimization

3. Motivating Questions
How to estimate freeway segment traffic states from heterogeneous measurements?
Point mean speed
Bluetooth travel time records
Semi-continuous GPS data
Semi-continuous
path trajectory
Continuous
path trajectory
Point
Point-to-point
Loop Detector
Automatic Vehicle Identification
Automatic Vehicle Location
Video Image Processing

4. Motivating Questions How much information is sufficient?
How to locate point sensors on a traffic segment?
How to locate Bluetooth reader locations?
How much AVI/GPS market penetration rate is sufficient?

5. Existing Method 1: Kalman Filtering
Eulerian sensing framework
Muñoz et al., 2003; Sun et al., 2003; Sumalee et al., 2011
Linear measurement equations to incorporate flow and speed data from point detectors
Extended Kalman filter framework
second-order traffic flow model
Wang and Papageorgiou (2005)

6. Existing Method 2: Cell Transmission Model
Cell inflow inequality
qi,j(t) = Min { vfree  ki,j(t) , qmax i,j(t) , w  (kjam - ki,j(t))  Δ x }
Switching-mode model (SMM)
set of piecewise linear equations
qi,j(t) =  [vfree  ki,j(t) ] +  [vfree  ki,j(t) ]

7. Existing Method 3: Lagrangian sensing
Nanthawichit et al., 2003; Work et al., 2010; Herrera and Bayen, 2010
Establish linear measurement equations
Utilize semi-continuous samples from moving observers or probes

8. Existing Method 4: Interpolation method
Treiber and Helbing, 2002
“kernel function” that builds the state equation for forward and backward waves
Linear state equation through a speed measurement-based weighting scheme
Figure Source: Treiber and Helbing, 2002

9. Challenge No.1 1. Unified measurement equations to incorporate
Point, point-to-point and semi-continuous data

10. Our New Perspective
Dr. Newell’s three-detector model provides a unified framework
N(t,x)=Min {Nupstream(t-BWTT)+Kjam*distance, Ndownstream(t-FFTT)}

11. 1: From Point Sensor Data to Boundary N-curves
Cell density and flow are all functions of cumulative flow counts

12. 2: From Bluetooth Travel Time to Boundary N-curves
Downstream and upstream N-Curves between two time stamps are connected

13. 3: From to GPS Trajectory Data to Boundary N-curves
Under FIFO conditions, GPS probe vehicle keeps the same N-Curve number (say m) m m m m m

14. 4: From Boundary N-curves to Everything inside

15. Challenge No. 2 All sensors have errors error propagation
Surveillance Type
Data Quality
Point Detectors
High accuracy and relatively low reliability
Automatic
Vehicle Identification
Accuracy depends on market penetration level of tagged vehicles
Mobile GPS location sensors
Accuracy depends on market penetration level of probe vehicles
Trajectory data from video image processing
Accuracy depends on machine vision algorithms

16. The Question We have to Answer
Under error-free conditions, Newell’s model provides a good traffic state description tool
N(t,x) =Min {Nupstream(*), Ndownstream(*)}
With measurement errors
What are the mean and variance of
Min {Nupstream(*)+eu, Ndownstream(*) +ed}

17. Quick Review: Probit Model and Clark’s Approximation
Probit model (discrete choice model for min of two alternatives’ random utilities )
U = min (U1+e1, U2+e2)
Route choice application
Clark’s approximation
minimization of two random variables can be approximated by a third random variables

18. Proposed Stochastic 3-Detector Model

19. Discussion 1: Consistency Checking
When Uncertainties of boundary values are 0, the stochastic 3-detector model reduces to deterministic 3-detertor model

20. Discussion 2: Weights under Different Traffic Conditions

21. Discussion 3: Quantify Uncertainty of Inside-Traffic-State Estimates
Variance or trace of estimates determine the value of information

23. Numerical Example

24. Input: Queue Spillback

25. Ground truth Arrive-departure Curves

26. Estimated Density Profile

27. Estimated Uncertainty profile
Before
After

28. Impact of Additional Sensors

29. Possible (Un-captured) Modeling Errors
Stochastic free-flow speed,
Stochastic backward wave speed;
Heterogeneous driving behavior
Upper plot: original NGSIM vehicle trajectory data
Lower plot: reconstructed vehicle trajectory based on flow count measurements

30. Conclusions Proposed stochastic 3-detertor Model
Estimate freeway segment traffic states from heterogeneous measurements
Quantify the degree of estimation uncertainty and value of information, under different sensor deployment plans