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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 Volume Delay Functions for Travel Demand Models

  • 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 Volume Delay Functions for Travel Demand Models

  • 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 Volume Delay Functions for Travel Demand Models

  • 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 Volume Delay Functions for Travel Demand Models

  • 5,848 locations from 17,400 detector locations available

  • Three locations per classification selected


Traffic Data Volume Delay Functions for Travel Demand Models

  • 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 Volume Delay Functions for Travel Demand Models

Speed vs Density

Speed by Time of Day

Speed vs Flow


Estimating Free Flow Speed Volume Delay Functions for Travel Demand Models

  • 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 Volume Delay Functions for Travel Demand Models

  • 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: Volume Delay Functions for Travel Demand Models

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 Volume Delay Functions for Travel Demand Models

Rural Freeway example, with flow states identified


Percent with Interrupted Flow Volume Delay Functions for Travel Demand Models

Interrupted Flow

Histogram – Percent with Interrupted Flow vs. Flow Density


Estimating Capacity Volume Delay Functions for Travel Demand Models

  • 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 Volume Delay Functions for Travel Demand Models

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 Volume Delay Functions for Travel Demand Models : 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 Volume Delay Functions for Travel Demand Models

  • 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 Volume Delay Functions for Travel Demand Models

Urban Interstate


Fitting Volume Delay Functions Volume Delay Functions for Travel Demand Models

Rural Interstate


Fitting Volume Delay Functions Volume Delay Functions for Travel Demand Models

Urban Expressway


Fitting Volume Delay Functions Volume Delay Functions for Travel Demand Models

Rural Principal Arterial


Fitting Volume Delay Functions Volume Delay Functions for Travel Demand Models

Urban Other Principal Arterials


Fitting Volume Delay Functions Volume Delay Functions for Travel Demand Models

Rural Minor Arterial


Fitting Volume Delay Functions Volume Delay Functions for Travel Demand Models

Urban Minor Arterial


Fitting Volume Delay Functions Volume Delay Functions for Travel Demand Models

Rural Collector


Fitting Volume Delay Functions Volume Delay Functions for Travel Demand Models

Urban Collector


Fitting Volume Delay Functions Volume Delay Functions for Travel Demand Models

Rural Local


Fitting Volume Delay Functions Volume Delay Functions for Travel Demand Models

Summary of calibrated inputs to VDF fitting process


Fitting Volume Delay Functions Volume Delay Functions for Travel Demand Models

Summarized results from VDF fitting process


Initial Findings Volume Delay Functions for Travel Demand Models

  • 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 Volume Delay Functions for Travel Demand Models

  • 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 Volume Delay Functions for Travel Demand Models


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