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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. Outline. Introduction
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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
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
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
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
Traffic Monitoring System (TSM) Data • 5,848 locations from 17,400 detector locations available • Three locations per classification selected
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
Processed Data Speed vs Density Speed by Time of Day Speed vs Flow
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
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
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.
Defining Interrupted Flow Rural Freeway example, with flow states identified
Percent with Interrupted Flow Interrupted Flow Histogram – Percent with Interrupted Flow vs. Flow Density
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)
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
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
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
Fitting Volume Delay Functions Urban Interstate
Fitting Volume Delay Functions Rural Interstate
Fitting Volume Delay Functions Urban Expressway
Fitting Volume Delay Functions Rural Principal Arterial
Fitting Volume Delay Functions Urban Other Principal Arterials
Fitting Volume Delay Functions Rural Minor Arterial
Fitting Volume Delay Functions Urban Minor Arterial
Fitting Volume Delay Functions Rural Collector
Fitting Volume Delay Functions Urban Collector
Fitting Volume Delay Functions Rural Local
Fitting Volume Delay Functions Summary of calibrated inputs to VDF fitting process
Fitting Volume Delay Functions Summarized results from VDF fitting process
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
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
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