TRB Planning Applications Conference - May 19, 2009

1. Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions for Travel Demand Models in Virginia TRB Planning Applications Conference - May 19, 2009 Presented by: Jaesup Lee, Virginia Department of Transportation Dean Munn, The Corradino Group

2. Outline • Introduction • Traffic Data used in basic analysis and model estimation • Data Development and Definition • Free Flow Speed • Traffic Flow (Uninterrupted vs. Interrupted) • Link Capacity • Various Curve Fittings by Functional Class • Findings and Further Research

3. Introduction • Project Goals • Use empirical data obtained from Virginia facilities to evaluate speed-flow relationships • Test various volume-delay functional forms for each facility type and determine which provides the best performance • Calibrate volume delay function parameters for each facility type • Outcome should be suitable for implementation in Virginia urban travel models

4. Introduction • Fundamental Elements of Volume-Delay Estimation • Converting spot speeds to space-mean speed • Characteristics of free-flow • Identifying boundary between uninterrupted and interrupted flow • Using knowledge of this boundary to estimate the maximum sustainable flow rate (Capacity) • Use empirical observations to fit VDF curve parameters

5. Traffic Monitoring System (TSM) Data • 5,848 locations from 17,400 detector locations available • Three locations per classification selected

6. Traffic Data • Data records are a summary of each 15 minute period • Speed bins are in 5 mph increments • Data records are organized by lane and vehicle class • CUBE/Voyager script simplifies data • Spot speeds are converted to Space Mean Speeds

7. Processed Data Speed vs Density Speed by Time of Day Speed vs Flow

8. Estimating Free Flow Speed • HCM recommends using mean value for low volume conditions • Standard practice also includes using 85th Percentile speed 73.7 mph 71.1 mph

9. Defining Interrupted Flow • Plots of flow vs density and speed vs density show two flow states • Others have defined the transition point as the maximum flow or the density at maximum speed, but this is not representative of typical conditions • Statistical techniques can define the transition between the two states Interrupted Flow Interrupted Flow Speed vs. Density Flow vs. Density

10. For our Rural Freeway example: The computed threshold is 62.58 MPH Defining Interrupted Flow • We define interrupted flow as: • Any speed below the threshold where there is 0.0001% probability that it is the same as freeflow.

11. Defining Interrupted Flow Rural Freeway example, with flow states identified

12. Percent with Interrupted Flow Interrupted Flow Histogram – Percent with Interrupted Flow vs. Flow Density

13. Estimating Capacity • Our data shows a classic logistic distribution • We estimated parameters (using density as the only variable) to create a probability function that best fits the data • Capacity corresponds to flow density with a 50% probability of being interrupted PI = 1/[1 + e(b1D+ b0)] , where D = Density (veh/mi)

14. Capacity Estimates 0.50% Probability of Interrupted Flow 50.0% Probability of Interrupted Flow 99.5% Probability of Interrupted Flow This example gives a 39.7 pc/mi Density Threshold or a 2384 pc/hr Max Flow Rate

15. BPR: R = R0[1 + a(V/C)^b] Conical: R=R0[2 + sqrt(a2(1-V/C) + b2) –a(1-V/C) – b] Akcelik: R=R0+D0+0.25T[(V/C-1)+sqrt{(V/C-1)2+(16J(V/C)L2)/T2}] Fitting Volume Delay Functions Volume-Delay Functions - Using the computed capacity, the following volume delay functions were estimated based on speeds during uninterrupted flow

16. Fitting Volume Delay Functions • Curve Fitting - non-linear regression • Goodness of Fit • R-squared • Root Mean Square Error • Non-Parametric tests e.g. Chi-Square • Other Criteria - suitability for model applications

17. Fitting Volume Delay Functions Urban Interstate

18. Fitting Volume Delay Functions Rural Interstate

19. Fitting Volume Delay Functions Urban Expressway

20. Fitting Volume Delay Functions Rural Principal Arterial

21. Fitting Volume Delay Functions Urban Other Principal Arterials

22. Fitting Volume Delay Functions Rural Minor Arterial

23. Fitting Volume Delay Functions Urban Minor Arterial

24. Fitting Volume Delay Functions Rural Collector

25. Fitting Volume Delay Functions Urban Collector

26. Fitting Volume Delay Functions Rural Local

27. Fitting Volume Delay Functions Summary of calibrated inputs to VDF fitting process

28. Fitting Volume Delay Functions Summarized results from VDF fitting process

29. Initial Findings • Standard VDF functions are all capable of performing adequately across road classes • For a given road class, VDF parameters fitted for one location, seem to be transferable to other locations • Goodness of fit measures do not strongly differentiate between functions • The Akcelik function, with its more rigorous theoretical underpinnings, seems to work very well

30. Next Steps • Additional facility types • Check model transferability to other facilities • Compare HCM capacity, planning capacity, and empirical capacity • Continue to automate analysis process • Test functions in urban models (assignment convergence, average travel speeds) • New VDF functional forms and calibrated parameters will become part VDOT modeling standards

31. Q & A • Thank you ! • Contact points • Jaesup Lee: jaesup.lee@VDOT.Virginia.gov • Dean Munn: dmunn@corradino.com • Jeremy Raw : jeremy.raw@VDOT.Virginia.gov