trb planning applications conference - may 19, 2009
DESCRIPTION
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 - PowerPoint PPT PresentationTRANSCRIPT
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 TransportationDean Munn, The Corradino Group
Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions
for Travel Demand Models in Virginiafor Travel Demand Models in Virginia TRB Planning Applications Conference, May 19, 2009TRB Planning Applications Conference, May 19, 2009
• 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
Outline
Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions
for Travel Demand Models in Virginiafor Travel Demand Models in Virginia TRB Planning Applications Conference, May 19, 2009TRB Planning Applications Conference, May 19, 2009
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
Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions
for Travel Demand Models in Virginiafor Travel Demand Models in Virginia TRB Planning Applications Conference, May 19, 2009TRB Planning Applications Conference, May 19, 2009
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
Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions
for Travel Demand Models in Virginiafor Travel Demand Models in Virginia TRB Planning Applications Conference, May 19, 2009TRB Planning Applications Conference, May 19, 2009
Traffic Monitoring System (TSM) Data
• 5,848 locations from 17,400 detector locations available• Three locations per classification selected
Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions
for Travel Demand Models in Virginiafor Travel Demand Models in Virginia TRB Planning Applications Conference, May 19, 2009TRB Planning Applications Conference, May 19, 2009
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
LINKID COUNTERNUMLANE STARTDATEVEHICLEB_1 VEHICLEB_2 VEHICLEB_3 INTERVAL SPEEDBINLABIN01 BIN02 BIN03 BIN04 BIN05 BIN06 BIN07 BIN08 BIN09 BIN10 BIN11 BIN12 BIN13 BIN14 BIN15 BIN16 BIN17 BIN18 BIN19 BIN20 BIN21 SPEEDQUALI010148 1 1 9/1/2007 6 1 1 15 65 0 0 0 0 0 0 1 0 1 3 3 7 4 1 0 0 0 0 0 0 0 5010148 1 1 9/1/2007 6 1 2 15 65 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 5010148 1 1 9/1/2007 6 1 3 15 65 0 0 0 0 0 0 2 2 2 0 0 1 3 0 0 0 0 0 0 0 0 5010148 1 2 9/1/2007 6 1 1 15 65 0 0 0 0 0 0 0 0 0 3 3 1 3 2 1 0 0 0 0 0 0 5010148 1 2 9/1/2007 6 1 2 15 65 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5010148 1 2 9/1/2007 6 1 3 15 65 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5010148 1 1 9/1/2007 6 1 1 15 65 0 0 0 0 0 0 0 1 0 1 6 4 5 6 2 0 0 0 0 0 0 5010148 1 1 9/1/2007 6 1 2 15 65 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5010148 1 1 9/1/2007 6 1 3 15 65 0 0 0 0 0 0 1 1 5 3 3 3 0 0 0 0 0 0 0 0 0 5010148 1 2 9/1/2007 6 1 1 15 65 0 0 0 0 0 0 0 0 0 0 2 6 1 5 1 0 0 0 0 0 0 5010148 1 2 9/1/2007 6 1 2 15 65 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5
• CUBE/Voyager script simplifies data• Spot speeds are converted to Space Mean Speeds
Filed Description TIME_PER Time Period TOT_AUTOS Total number of Autos TOT_TRUCK Total number of Trucks TOT_VEH Total Vehicles LANES Maximum number of lanes FRATE Flow rate BLANK1 Separator column AUTO1 Harmonic Space mean speed for autos TRUCK1 Harmonic Space mean speed for trucks BOTH1 Harmonic Space mean speed for all vehicles FDEN1 Flow Density for all vehicles with harmonic space mean speed BLANK2 Separator column AUTO2 Space mean speed for autos ( as per the formula from paper) TRUCK2 Space mean speed for trucks ( as per the formula from paper) BOTH2 Space mean speed for all vehicles ( as per the formula from paper) FDEN2 Flow Density for all vehicles for paper space mean speed
Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions
for Travel Demand Models in Virginiafor Travel Demand Models in Virginia TRB Planning Applications Conference, May 19, 2009TRB Planning Applications Conference, May 19, 2009
Processed Data
0.0
10.0
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40.0
50.0
60.0
70.0
80.0
0.00 20.00 40.00 60.00 80.00 100.00 120.00
Density (Veh/ Mi/ Ln)
Speed vs Density
0 5 10 15 20 250
100
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600
0 5 10 15 20 2510
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80
0 5 10 15 20 250
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0 5 10 15 20 250.1
0.2
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0.6
Time of Day
Lane1
Lane2
Lane3
Lane1
Lane2
Lane3
Lane1
Lane2
Lane3
Lane1
Lane2
Lane3
0.0
10.0
20.0
30.0
40.0
50.0
60.0
70.0
80.0
0 200 400 600 800 1000 1200 1400 1600 1800 2000
Flow (Veh/ Hr/ Ln)
Speed vs Flow
Speed by Time of Day
Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions
for Travel Demand Models in Virginiafor Travel Demand Models in Virginia TRB Planning Applications Conference, May 19, 2009TRB Planning Applications Conference, May 19, 2009
Estimating Free Flow Speed
0.0
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50.0
60.0
70.0
80.0
0.00 20.00 40.00 60.00 80.00 100.00 120.00
Density (Veh/ Mi/ Ln)
1. HCM recommends using mean value for low volume conditions2. Standard practice also includes using 85th Percentile speed
0.0
10.0
20.0
30.0
40.0
50.0
60.0
70.0
80.0
0.00 20.00 40.00 60.00 80.00 100.00 120.00
71.1 mph
73.7 mph
Min Max Min Max
55.5 75.2 71.1 1.8 73.0 5.3 76.0 71.1 6.5 73.7
Alternative MethodAll Flow Conditions
Observed Speed Range
Mean85th
PercentileStandard Deviation
Low Volume ConditionsHCM Method
Observed Speed Range
Mean85th
PercentileStandard Deviation
Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions
for Travel Demand Models in Virginiafor Travel Demand Models in Virginia TRB Planning Applications Conference, May 19, 2009TRB Planning Applications Conference, May 19, 2009
0
500
1000
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3000
0.00 20.00 40.00 60.00 80.00 100.00 120.00
Density (Veh/Mi/Ln)
Flo
w (
Veh
/Hr/
Ln
)
Defining Interrupted Flow
1. Plots of flow vs density and speed vs density show two flow states
2. Others have defined the transition point as the maximum flow or the density at maximum speed, but this is not representative of typical conditions
3. Statistical techniques can define the transition between the two states
0.0
10.0
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50.0
60.0
70.0
80.0
0.00 20.00 40.00 60.00 80.00 100.00 120.00
Density (Veh/ Mi/ Ln)
Flow vs. Density
Speed vs. Density
Interrupted Flow Interrupted Flow
Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions
for Travel Demand Models in Virginiafor Travel Demand Models in Virginia TRB Planning Applications Conference, May 19, 2009TRB Planning Applications Conference, May 19, 2009
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.
Speed Distribution
0
500
1000
1500
2000
2500
3000
3500
4000
50 55 60 65 70 75 80
Observed Speed
Fre
qu
ency
Observed
Freeflow Normal Distribution
For our Rural Freeway example:The computed threshold is 62.58 MPH
Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions
for Travel Demand Models in Virginiafor Travel Demand Models in Virginia TRB Planning Applications Conference, May 19, 2009TRB Planning Applications Conference, May 19, 2009
0.0
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80.0
0.00 20.00 40.00 60.00 80.00 100.00 120.00
Density
Sp
eed Uninterrupted
Interrupted
Defining Interrupted Flow
Rural Freeway example, with flow states identified
Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions
for Travel Demand Models in Virginiafor Travel Demand Models in Virginia TRB Planning Applications Conference, May 19, 2009TRB Planning Applications Conference, May 19, 2009
Interrupted Flow
Histogram – Percent with Interrupted Flow vs. Flow Density
0.00%
10.00%
20.00%
30.00%
40.00%
50.00%
60.00%
70.00%
80.00%
90.00%
100.00%
2.50
7.50
12.5
017
.50
22.5
027
.50
32.5
037
.50
42.5
047
.50
52.5
057
.50
62.5
067
.50
72.5
077
.50
82.5
087
.50
92.5
097
.50
102.
50
Flow Density
Pro
bab
ility
of
Inte
rru
pte
d F
low
Per
cen
t w
ith
Inte
rru
pte
d F
low
Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions
for Travel Demand Models in Virginiafor Travel Demand Models in Virginia TRB Planning Applications Conference, May 19, 2009TRB Planning Applications Conference, May 19, 2009
Estimating Capacity1. Our data shows a classic logistic distribution2. We estimated parameters (using density as the only variable) to
create a probability function that best fits the data
3. Capacity corresponds to flow density with a 50% probability of
being interrupted
PI = 1/[1 + e(1D+
0)] , where D = Density (veh/mi)
Probability Function
0.00%
20.00%
40.00%
60.00%
80.00%
100.00%
120.00%
2.50
7.50
12.50
17.50
22.50
27.50
32.50
37.50
42.50
47.50
52.50
57.50
62.50
67.50
72.50
77.50
82.50
87.50
92.50
97.50
102.5
0
Flow Density
Pro
bab
ilit
y
0.00%
20.00%
40.00%
60.00%
80.00%
100.00%
120.00%
Fre
qen
cy
Observed Frequency
Predicted byProbability Function
Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions
for Travel Demand Models in Virginiafor Travel Demand Models in Virginia TRB Planning Applications Conference, May 19, 2009TRB Planning Applications Conference, May 19, 2009
0
500
1000
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3000
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
Flow Density
Mea
n F
low
(O
bse
rved
)
99.5% Probability of Interrupted Flow
0.50% Probability of Interrupted Flow
50.0% Probability of Interrupted Flow
Capacity Estimates
This example gives a 39.7 pc/mi Density Threshold or a 2384 pc/hr Max Flow Rate
Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions
for Travel Demand Models in Virginiafor Travel Demand Models in Virginia TRB Planning Applications Conference, May 19, 2009TRB Planning Applications Conference, May 19, 2009
Fitting Volume Delay Functions
Volume-Delay Functions - Using the computed capacity, the following volume delay functions were estimated based on speeds during uninterrupted flow
BPR: R = R0[1 + (V/C)^]
Akcelik: R=R0+D0+0.25T[(V/C-1)+sqrt{(V/C-1)2+(16J(V/C)L2)/T2}]
Conical: R=R0[2 + sqrt(2(1-V/C) + 2) –(1-V/C) – ]
Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions
for Travel Demand Models in Virginiafor Travel Demand Models in Virginia TRB Planning Applications Conference, May 19, 2009TRB Planning Applications Conference, May 19, 2009
• 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
Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions
for Travel Demand Models in Virginiafor Travel Demand Models in Virginia TRB Planning Applications Conference, May 19, 2009TRB Planning Applications Conference, May 19, 2009
Fitting Volume Delay Functions
Urban Interstate
0.0
10.0
20.0
30.0
40.0
50.0
60.0
70.0
80.0
0.00 0.50 1.00 1.50 2.00 2.50
Density Ratio
Sp
eed
Observed Traffic
BPR Function
Conical Function
Akcelik Function
Alpha Beta R-squared RMSEBPR 0.24 3.82 0.947 6.017%Conical 34.5 1.0 0.954 9.489%Akcelik 1.11E-04 1.0 0.957 8.787%
J T
Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions
for Travel Demand Models in Virginiafor Travel Demand Models in Virginia TRB Planning Applications Conference, May 19, 2009TRB Planning Applications Conference, May 19, 2009
Fitting Volume Delay Functions
Rural Interstate
0.0
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30.0
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70.0
80.0
0.00 0.50 1.00 1.50 2.00 2.50
Density Ratio
Sp
eed
Observed Traffic
BPR Function
Conical Function
Akcelik Function
Alpha Beta R-squared RMSEBPR 0.15 4.18 0.790 4.491%Conical 78.9 1.0 0.790 8.381%Akcelik 4.89E-05 1.0 0.812 7.376%
J T
Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions
for Travel Demand Models in Virginiafor Travel Demand Models in Virginia TRB Planning Applications Conference, May 19, 2009TRB Planning Applications Conference, May 19, 2009
Fitting Volume Delay Functions
Urban Expressway
0.0
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20.0
30.0
40.0
50.0
60.0
70.0
80.0
0.00 0.50 1.00 1.50 2.00 2.50
Density Ratio
Sp
eed
Observed Traffic
BPR Function
Conical Function
Akcelik Function
Alpha Beta R-squared RMSEBPR 0.18 4.63 0.666 4.162%Conical 49.1 1.0 0.625 6.430%Akcelik 8.41E-05 1.0 0.646 5.770%
J T
Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions
for Travel Demand Models in Virginiafor Travel Demand Models in Virginia TRB Planning Applications Conference, May 19, 2009TRB Planning Applications Conference, May 19, 2009
Fitting Volume Delay Functions
Rural Principal Arterial
0.0
10.0
20.0
30.0
40.0
50.0
60.0
0.00 0.50 1.00 1.50 2.00 2.50
Density Ratio
Sp
eed
Observed Traffic
BPR Function
Conical Function
Akcelik Function
Alpha Beta R-squared RMSEBPR 0.69 1.68 0.880 5.674%Conical 3.1 1.2 0.862 6.442%Akcelik 1.63E-03 1.0 0.780 10.362%
J T
Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions
for Travel Demand Models in Virginiafor Travel Demand Models in Virginia TRB Planning Applications Conference, May 19, 2009TRB Planning Applications Conference, May 19, 2009
Fitting Volume Delay Functions
Urban Other Principal Arterials
0.0
10.0
20.0
30.0
40.0
50.0
60.0
0.00 0.50 1.00 1.50 2.00 2.50
Density Ratio
Sp
eed
Observed Traffic
BPR Function
Conical Function
Akcelik Function
Alpha Beta R-squared RMSEBPR 0.24 2.86 0.874 4.602%Conical 19.0 1.0 0.770 14.797%Akcelik 2.42E-04 1.0 0.784 13.860%
J T
Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions
for Travel Demand Models in Virginiafor Travel Demand Models in Virginia TRB Planning Applications Conference, May 19, 2009TRB Planning Applications Conference, May 19, 2009
Fitting Volume Delay Functions
Rural Minor Arterial
0.0
10.0
20.0
30.0
40.0
50.0
60.0
70.0
0.00 0.50 1.00 1.50 2.00 2.50
Density Ratio
Sp
eed
Observed Traffic
BPR Function
Conical Function
Akcelik Function
Alpha Beta R-squared RMSEBPR 0.14 1.51 0.248 4.752%Conical 19.2 1.0 0.243 5.348%Akcelik 2.30E-04 1.0 0.245 5.282%
J T
Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions
for Travel Demand Models in Virginiafor Travel Demand Models in Virginia TRB Planning Applications Conference, May 19, 2009TRB Planning Applications Conference, May 19, 2009
Fitting Volume Delay Functions
Urban Minor Arterial
0.0
10.0
20.0
30.0
40.0
50.0
60.0
0.00 0.50 1.00 1.50 2.00 2.50
Density Ratio
Sp
eed
Observed Traffic
BPR Function
Conical Function
Akcelik Function
Alpha Beta R-squared RMSEBPR 0.16 4.53 0.475 4.270%Conical 57.7 1.0 0.521 8.560%Akcelik 1.00E-04 1.0 0.545 6.880%
J T
Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions
for Travel Demand Models in Virginiafor Travel Demand Models in Virginia TRB Planning Applications Conference, May 19, 2009TRB Planning Applications Conference, May 19, 2009
Fitting Volume Delay Functions
Rural Collector
0.0
10.0
20.0
30.0
40.0
50.0
60.0
0.00 0.50 1.00 1.50 2.00 2.50
Density Ratio
Sp
eed
Observed Traffic
BPR Function
Conical Function
Akcelik Function
Alpha Beta R-squared RMSEBPR 0.35 1.94 0.172 9.346%Conical 7.0 1.1 0.200 9.186%Akcelik 8.28E-04 1.0 0.203 9.196%
J T
Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions
for Travel Demand Models in Virginiafor Travel Demand Models in Virginia TRB Planning Applications Conference, May 19, 2009TRB Planning Applications Conference, May 19, 2009
Fitting Volume Delay Functions
Urban Collector
Alpha Beta R-squared RMSEBPR 0.21 3.06 0.566 5.345%Conical 28.1 1.0 0.549 8.234%Akcelik 1.79E-04 1.0 0.569 7.419%
J T
0.0
10.0
20.0
30.0
40.0
50.0
60.0
70.0
0.00 0.50 1.00 1.50 2.00 2.50
Density Ratio
Sp
eed
Observed Traffic
BPR Function
Conical Function
Akcelik Function
Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions
for Travel Demand Models in Virginiafor Travel Demand Models in Virginia TRB Planning Applications Conference, May 19, 2009TRB Planning Applications Conference, May 19, 2009
Fitting Volume Delay Functions
Rural Local
0.0
10.0
20.0
30.0
40.0
50.0
60.0
70.0
80.0
0.00 0.50 1.00 1.50 2.00 2.50
Density Ratio
Sp
eed
Observed Traffic
BPR Function
Conical Function
Akcelik Function
Alpha Beta R-squared RMSEBPR 0.26 1.00 0.050 10.611%Conical 5.3 1.1 0.074 11.155%Akcelik 1.15E-03 1.0 0.077 11.316%
J T
Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions
for Travel Demand Models in Virginiafor Travel Demand Models in Virginia TRB Planning Applications Conference, May 19, 2009TRB Planning Applications Conference, May 19, 2009
Fitting Volume Delay Functions
Summary of calibrated inputs to VDF fitting process
Low High Low High Low High
Rural Interstate 70.3 73.7 1747 2384 28.3 39.9Rural Other Principal Arterial 49.0 51.5 980 1130 23.2 41.3Rural Minor Arterial 41.6 57.8 922 1188 19.1 35.9Rural Major Collector 34.1 47.8 450 589 17.0 25.5Rural Local 28.4 45.7 368 377 11.9 19.3Urban Interstate 63.6 66.0 1442 1710 29.5 32.7Urban Freeways and Expressways 46.7 65.4 810 1981 14.2 36.6Urban Other Principal Arterials 45.2 52.9 888 1291 25.1 29.7Urban Minor Arterial 39.6 51.9 752 1181 18.9 28.4Urban Collector 40.6 51.2 669 853 17.4 28.0
Miles per Hour Hourly PCE/Lane Hourly PCE/Mile
CapacityFlow Rate Flow DensityFreeflow Speed
Functional Classification
VDF Inputs
Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions
for Travel Demand Models in Virginiafor Travel Demand Models in Virginia TRB Planning Applications Conference, May 19, 2009TRB Planning Applications Conference, May 19, 2009
Fitting Volume Delay Functions
Summarized results from VDF fitting process
Low High Low High Low High Low High
Rural Interstate 0.15 0.15 4.2 5.0 78.9 178.9 2.5E-05 4.9E-05Rural Other Principal Arterial 0.25 0.69 1.7 3.2 3.1 29.4 1.8E-04 1.6E-03Rural Minor Arterial 0.11 0.14 1.5 1.9 19.2 23.9 2.3E-04 2.7E-04Rural Major Collector 0.35 0.37 1.4 1.9 5.3 7.0 8.3E-04 1.4E-03Rural Local 0.26 0.41 1.0 1.9 5.3 6.0 1.2E-03 1.4E-03Urban Interstate 0.16 0.24 3.3 3.8 29.2 57.6 7.5E-05 1.4E-04Urban Freeways and Expressways 0.10 0.42 1.9 8.7 6.6 89.0 5.2E-05 7.1E-04Urban Other Principal Arterials 0.24 0.28 1.9 2.9 14.8 19.0 2.4E-04 3.6E-04Urban Minor Arterial 0.16 0.29 2.0 4.5 15.6 57.7 1.0E-04 4.0E-04Urban Collector 0.08 0.35 0.4 3.5 12.7 28.1 1.8E-04 5.2E-04
BPRAlpha JAlpha Beta
Functional Classification
ConicalVolume Delay Functions
Akcelik
Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions
for Travel Demand Models in Virginiafor Travel Demand Models in Virginia TRB Planning Applications Conference, May 19, 2009TRB Planning Applications Conference, May 19, 2009
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
Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions
for Travel Demand Models in Virginiafor Travel Demand Models in Virginia TRB Planning Applications Conference, May 19, 2009TRB Planning Applications Conference, May 19, 2009
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
Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions
for Travel Demand Models in Virginiafor Travel Demand Models in Virginia TRB Planning Applications Conference, May 19, 2009TRB Planning Applications Conference, May 19, 2009
Q & A
Thank you !
Contact points
Jaesup Lee: [email protected]
Dean Munn: [email protected]
Jeremy Raw : [email protected]