friction factors and trip lengths; bpr curves and speeds · friction factors and trip lengths; bpr...
TRANSCRIPT
Friction Factors and Trip Lengths;
BPR Curves and Speeds
presented by
Michelle Arnold, AICP, EI
Transportation Planner
AECOM
September 3, 2015
Parts and Format
• Part A: Friction Factors and Trip Lengths
• Part B: BPR Curves and Speeds
• Format
– What are they?
– How are they generated?
– Where are they used in the model?
2
What are Friction Factors
• Friction factors are parameters used in the
gravity model to account for travel time
separation between zones.
• An impedance factor.
• The gravity model distributes trips to the traffic
analysis zones based on impedance between the
traffic analysis zones and their attractions.
3
Gravity Equation
� = �����
��
�= the force between masses
�= gravitation constant
��= the first mass
��= the second mass
�= the distance between the centers of the masses
m1m2
r
4
Gravity Model Equation
��� = ��
�� ���� ��
∑ �� ���� ��"�#�
���= Trips from zone i to zone j
��= Total trips sent from zone i
��= Total trips received by zone j
����= Travel time factor for time between zone i and zone j ((((friction factorfriction factorfriction factorfriction factor))))
��= Socioeconomic adjustment factor for interchanges
.= Number of analysis zones5
Gravity Model
Zone 3
602 Work Trip
Productions
76 Work Trip
Attractions
Zone 4
47 Work Trip
Attractions
Zone 5
82 Work Trip
Attractions
Zone 2
531 Work Trip
Attractions
Zone 1
1080 Work
Trip
Attractions
10
min
ute
s
20 minutes
6
Why are Friction Factors Used
• Obtaining calibrated friction factors is the
principal operation of gravity model calibration.
• The product of the attractions and the friction
factor represents each zone’s relative
attractiveness and accessibility.
• Used to replicate observed trip length frequency
distributions.
7
How Are Friction Factors Generated
Friction factors are created for each trip purpose.
• Household travel surveys; OD surveys.
• Borrowed from another study area or model.
• Census Journey-to-Work for work-based trips.
• Roadside surveys for internal-external trips.
• Formulas.
8
Friction Factors Formulas
• Power function: ��� = 01
where a common value of the exponent a is 2
• Exponential function: ��� = 234�
where m represents the mean travel time
• Gamma function: ��� = a0526�
where t is travel impedance (time in minutes)
a, b, and c are model parameters9
Gamma Function
• Lookup tables are widely used in FSUTMS, although more recently some models use a gamma function.
• Whichever model’s parameters are chosen, they should be checked against observed trip length frequencies for each trip purpose.
• The parameters should be adjusted as needed to obtain the most reasonable model for the region.
10
Friction Factor Quiz
Friction factors attempt to show the effect of
travel time or impedance on trip making.
True or False. A way to estimate the initial
friction factors is to use the factors from a
previous study in a similar area. True
11
Initial Friction Factors Development
• To create initial friction factors, the productions and attractions trip table and a network skims matrix are needed.
• The survey data from an OD matrix provide the trip lengths.
• The trip length frequencies from the initial friction factors are compared to observed trip frequencies from the survey for reasonability.
12
Friction Factors in Calibration
Calibrating a gravity model involves adjusting the
friction factors until the model adequately
reproduces the productions and attractions trip
table and matches the observed average trip
length and frequencies from the survey.
13
Calibration Process
Initial Friction Factors, Travel Time Tables and
Trip Tables
Apply Gravity Model and Distribute Trips
Compare Attractions
Compare Trip Time Distribution and
Average Trip Time
Calibrated Friction Factors
Adjust
Friction
Factors
Adjust
Attraction
Factors
Not Balanced
Balanced?
Not Good
Good Comparison?
14
Calibrated Friction Factors
• Calibrated friction factors
for home-based work.
• Friction factors are
inversely proportional to
the travel time.
• Friction factors have no
units.
15
Friction Factors in the Model
Gravity model done manually.
Gravity model as a function.
16
Trip Distribution Trip Length Frequency
Florida Statewide Model—TLF Distance
17
Trip Distribution Trip Length Frequency
Florida Statewide Model-TLF Minute
18
Trip Distribution Chart
FLSWM Trip Distribution Trip Length Frequency
0
1,000,000
2,000,000
3,000,000
4,000,000
5,000,000
6,000,000
7,000,000
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75
Pe
rso
n T
rip
s
Distance (Miles)
HBW HBSH HBSR HBO NHB
19
Trip Distribution Chart
FLSWM Trip Distribution Trip Length Frequency
0
500,000
1,000,000
1,500,000
2,000,000
2,500,000
3,000,000
3,500,000
4,000,000
4,500,000
5,000,000
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125
Pe
rso
n T
rip
s
Distance (Minutes)
HBW HBSH HBSR HBO NHB
20
Calibration and Validation Standards
21
Calibration and Validation Standards
Model HBW HBSH HBSR HBO NHB
Statistic
(minutes)
12-35 9-19 11-19 8-20 6-19
FLSWM 19 17 16 17 14
FSUTMS-Cube Framework Phase II: Model Validation and Calibration Standards
October 2, 2008
Average Trip Length and Frequencies by Purpose
22
Friction Factor Quiz
• The output of the gravity model calibration is a
set of calibrated friction factors.
• If the output attractions do not balance with
the input attractions, the attractions are
adjusted and the model is rerun.
• True or False. If the trip time frequency
distribution and average trip time inputs and
outputs do compare satisfactorily, the friction
factors need to be changed. False.23
Calibration with Friction Factors
Matching average observed trip lengths or even
complete trip length frequency distributions is
not sufficient to say that trip distribution model
is validated. The orientation of trips must be
geographically correct or reasonable.
24
What are BPR Curves
• Bureau of Public Roads (BPR) curves are a type
of volume-delay functions used to describe the
speed-flow relationships in a travel demand
model network based on the available link
capacity.
25
BPR Formula
0� = 00� 1 + :;�
<�
=
0�= Congestion flow travel time on link i;
00�= Free-flow travel time on link i;
;�= Volume of traffic on link i per unit of time (flow
attempting to use link i);
<�= Capacity of link i per unit of time;
:= Alpha coefficient, which was assigned a value of 0.15 in
the original BPR curve; and
K= Beta coefficient, the exponent of the power function,
which was assigned a value of 4 in the original BPR curve
26
BPR Formula Meaning
• The formula basically shows that as volume
increases or flow increases relative to capacity,
the speed decreases and travel time increases.
• In the original BPR function, the capacity, ci, used
LOS C, but common practice now is to use LOS E
from the Highway Capacity Manual.
27
Why are BPR Curves Used
• FSUTMS uses equilibrium highway assignment
which means that no trip can be made by an
alternate path without increasing the total
travel time in the network.
• Equilibrium accounts for congestion in traffic
assignment. The process is iterative and
requires adjustments.
28
Why are BPR Curves Used
• BPR curves are used in a capacity restraint assignment to introduce congested time/speed in the route choice.
• For example, if Road X is within your shortest route and it is at free-flow speed, and everyone will take it; but Road X reaches capacity or overcapacity. The BPR curve increases the time for travelers on that road (congested time) so that in the next assignment iteration, Traveler Z remains on Road X and you use Road Y.
29
BPR Curve Criticisms
• Some modelers feel that the standard
BPR curve overestimates speeds for
volume-to-capacity (v/c) ratios
greater than or equal to 1.0 and
underestimates speeds for v/c ratios
less than 1.0.
• In the real world, v/c greater than 1.0
does not exist. There are queues and
stop-and-go traffic flows.
30
Updated BPR Parameters
31
BPR In the Model
32
Standard BPR Curve Example 1
0.000
0.200
0.400
0.600
0.800
1.000
1.200
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00
Co
ng
est
ed
/Un
con
ge
ste
d S
pe
ed
Ra
tio
Volume-Delay
BPRorg
Interstate
Div Arterial
Undiv Art.
Collector
Centroid
Toll
33
Standard BPR Curve Example 2
0.000
0.200
0.400
0.600
0.800
1.000
1.200
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00
Co
ng
est
ed
/Un
con
ge
ste
d S
pe
ed
Ra
tio
Volume-Delay
BPRorg
FT10
FT20
FT30
FT40
FT50
FT60
FT65
FT70
FT80
FT90
34
Other Volume Delay Functions
• BPR Curve (Modified, Fitted, Updated, etc.)
• Davidson and Modified Davidson Function
• Akçelik Function
• Conical Delay (Spiess) Function
• Linear
• Logarithmic
• Exponential
• Power
35
Comparison of VDF Curves
36
Calibration and Validation Standards
• Adjustments to BPR factors should be based on
more sophisticated calculations of capacity-
related attributes and not arbitrarily modified
solely to improve model validity for selected
facility types.
• One should not manipulate speeds and/or
capacities to fit validation statistics.
37
FSUTMS Recommended VFACTORS
38
FSUTMS Recommended VFACTORS
39
Speeds in FSUTMS Models
• Use a lookup table of area types, facility types, and lanes that assign speeds and capacities.
• Use posted speeds instead a lookup table for speed values. Posted speeds are readily available from FDOT’s Roadway Characteristics Inventory (RCI).
• The speeds in the FSUTMS lookup tables are based on very limited data.
40
Updating SPDCAP and VDFs
• Development of Speed Models for Improving Travel Forecasting and Highway Performance Evaluation (December 2013)
• It recommended traffic assignment improvement through changes in speed values and volume-delay function factors.
• The research noted that different volume-delay functions corresponded well to certain facility types.
41
SPDCAP File
42
FSUTMS Default Model Parameters
43
Speed Data
• Volume-delay functions require free flow
speeds.
• Speed data collection may not be feasible due to
time or budget constraints.
• FDOT has HERE and INRIX data.
44
HERE Data
• 30 million IDs available in Florida.
• Each ID corresponds to a NAVTEQ network
segment.
• Each record has a timestamp with a 5-minute
interval for a total of 288 intervals per day.
• Uses the Traffic Message Channel (TMC) system.
• Updated monthly.
• Speed must be computed.
45
HERE Data Example
46
HERE Data User Limits
• HERE data is only available for license to
DOTs, MPOs, FHWA and its federal partners.
• Selected government users may allow access
to their contractors to support their work
only.
• Unless you have an agreement with a
designated user, you must purchase the data.
47
INRIX Data
• Over 711 million records in Florida from July 1, 2010 to June 30, 2011.
• Average speeds in 5-minute intervals for 24 hours per day.
• Average speed computed by INRIX.
• Uses the Traffic Message Channel (TMC) system.
• FDOT purchased the data to support speed research. No new data has been purchased.
• Restricted to FDOT and MPO for their projects only.
48
HERE and INRIX Data
• Mainly gauge congestion.
• Used for other purposes, e.g., volume-delay functions.
• The quality of data varies depending on the facility type.
• User limited to FDOT, MPOs and other government agencies.
• Model Task Force May 2015 contain a presentation that compared HERE, Bluetooth, and INRIX speed data.
49
References
• Development of Speed Models for Improving Travel Forecasting and
Highway Performance Evaluation (Moses, Ren et al, 2013).
• Greater Treasure Coast Regional Planning Model Version 3.3
(GTCRPM3.3) Model Enhancements and Application Draft Report
(Corradino Group, 2010).
• An Introduction to Urban Travel Demand Forecasting—A Self
Instructional Text (FHWA, 1977).
• NCHRP Report 716: Travel Demand Forecasting: Parameters and
Techniques (TRB, 2012).
• FSUTMS-Cube Framework Phase I: Default Model Parameters (FDOT
Systems Planning, 2007)
• FSUTMS-Cube Framework Phase II: Model Calibration and Validation
Standards (FDOT Systems Planning, 2008)
50
Questions
51
Contact Information
Michelle Arnold, AICP, EI
Transportation Planner
AECOM
(850) 402-6329
52