Integration of Dynamic Traffic Assignment in a Four-Step Model Framework –
A Deployment Case Study in PSRC Model
13TH TRB National Transportation Planning Applications Conference
By:
Robert Tung, PhD
With:
Yi-Chang Chiu, PhD (U of Arizona)
Sarah Sun (FHWA)
WSDOT
PSRC
Motives
• Static trip based macro model is limited in solving modern transportation issues.
• Activity Based Model (ABM) is promising by may be costly to implement.
• DTA tools are increasingly sophisticate and efficient in handling large multimodal network.
• Combination of 4-Step model and DTA is potentially a Low-Hanging Fruit & cost-effective approach to add temporal dynamics to static trip based models.
Tung & Chiu : Integration of DTA in a 4-Step Model Framework 2
Objectives
• Implement a full DTA feedback mechanism in a static 4-step trip based model framework (PSRC)
• Document the findings and issues learned from the process.
• Focus on network development, calibration and validation, scenario analysis, and computing resources.
• Deriving insights from comparing the proposed DTA-embedded approach with the existing method.
• Understand the cost and benefit of integrating DTA in the 4-step process.
3Tung & Chiu : Integration of DTA in a 4-Step Model Framework
Multi-Resolution Modeling (MRM)
Tung & Chiu : Integration of DTA in a 4-Step Model Framework 4
MACRO MICRO
MESO•Static/Instantaneous Paths•Region Wide•Zonal Trips•Analytical Equilibrium•Demand Driven•Planning/Forecasting
•Static Paths•Corridor/Intersection•Individual Vehicles•Simulation One-Shot•Supply Driven•Operational
•Dynamic/Time Varying Paths•Subarea / Corridor•Vehicle Platoons
•Simulation Equilibrium•Supply Driven•Planning/Operational
O/D
DTA
MRM Issues
Tung & Chiu : Integration of DTA in a 4-Step Model Framework 5
Macro-Micro Approach:Pros:
• Widely used in practice. Many tools are available.Cons:
• Macro demand are not consistent with micro network.• No temporal dynamics on demand slices.• No feedback.
Macro-Meso-Micro Approach:Pros:
• Meso demand are more consistent with micro network.• Demand reflect temporal dynamics.
Cons:• Learning curve for planners.• Require more computing resource.• Mostly auto only.• No feedback.
DTA Primer
Tung & Chiu : Integration of DTA in a 4-Step Model Framework 6
STA DTA MICRO
Loading Analytical Meso Sim Micro Sim
Shortest Path Instantaneous Time Dependent Instantaneous
Route Choice FW/OBA/TAPAS GFV Logit/MSA
Connectivity Link Link/Lane Lane/Turn
Resolution Hour Minute Second
Solution UE DUE Non-UE
Convergence Unique Non-Unique Non-Unique
Speed Static Average Time Varying Time Varying
Flow Model VDF Speed-Density Car Following
Arrival Time Profile No Yes Yes
DTA Integration in PSRC
7Tung & Chiu : Integration of DTA in a 4-Step Model Framework
Land Use
Trip Generation
Trip Distribution
Modal Choice
Time of Day
Trip AssignmentDTA Auto
Skims
DTA Integration Concept
8Tung & Chiu : Integration of DTA in a 4-Step Model Framework
Land Use
Generation
Distribution
Modal Choice
Assignment
Land Use
Generation
Distribution
Modal Choice
DTA
Task Outline
• Network Conversion & Enhancement• Intersection Controls• Time-of-Day Model and 24-Hour Demand• Interface between DTA and TDM• 24-Hour Continuous DTA Simulation &
Assignment• Calibration and Validation• Scenario Analysis (HOT, Tolling, Work Zone)
9Tung & Chiu : Integration of DTA in a 4-Step Model Framework
Network Conversion
Tung & Chiu : Integration of DTA in a 4-Step Model Framework 10
Centroids:• From single point to multi-point loading• Use arterial links as trip generation and apply
loading weights• Use standard nodes as trip destination
Links/Nodes:• Maintain realistic connectivity and GIS shape• Nodal orientation is important
Controls:• Use actuated signals as default if real data are not
available• Use reasonable max and min green times
Demand Conversion
Tung & Chiu : Integration of DTA in a 4-Step Model Framework 11
Period SOV HOV Truck Total
AM 983,292 176,292 104,580 1,264,164
Mid-day 1,721,472 536,416 201,042 2,458,930
PM 1,124,537 382,502 116,784 1,623,823
Evening 888,251 410,576 57,164 1,355,991
Night 490,499 105,715 44,203 640,417
Daily 5,208,051 1,611,501 523,773 7,343,325
0:001:30
3:004:30
6:007:30
9:0010:30
12:0013:30
15:0016:30
18:0019:30
21:0022:30
0.0000
0.0100
0.0200
0.0300
0.0400
0.0500
0.0600
SOVHOV
• Use temporal (departure) profile derived from survey or TDM with directionality and peaking characteristics retained
• Assemble 24-hour demand from time varying period O-D tables
• Use smaller time interval as possible (15-minute)• Separate demand by mode and purpose
PSRC 2006 Diurnal Profile
PSRC 2006 Auto Demand by Period
DynusT
Tung & Chiu : Integration of DTA in a 4-Step Model Framework 12
• Simple , lean and easy to integrate with macro and micro models
• Developed since 2002, tested (in test) for 20 regions since 2005
• Used in several national projects• Memory efficient
• Capable of large-Scale multimodal 24-hr simulation assignment
• Fast simulation/computation• Multi-threaded
• Realistic microlike mesoscopic traffic simulation• Anisotropic Mesoscopic Simulation (AMS)
• Managed Open Source in 2010/2011
DynusT Algorithmic Structure
Tung & Chiu : Integration of DTA in a 4-Step Model Framework 13
Method of Isochronal Vehicle Assignment
Epoch k Traffic Assignment
Time-Dependent Shortest-Path Algorithm
Gap Function Vehicle Based TrafficAssignment Algorithm
k = k + 1
Stop
All Epochs Assigned?No
Assignment Converged? No
Iteration n Traffic Simulation
Generated Vehicles with AssignedAttributes
Anisotropic Mesoscopic Simulation (AMS)
Information Strategy Initial Path
Time-dependent OD, networkInitial/Intermediate Vehicle Paths
Model MoEsEvacuation Time, Exposure Level, Casualty, etc.
n = n + 1
Yes
TD O-D
TD Network
AMS Simulation
TD SP
Assignment
Convergence
Anisotropic Mesoscopic Simulation (AMS)
Tung & Chiu : Integration of DTA in a 4-Step Model Framework 14
• Stimulus-response model
• Net influence for speed adjustment primarily comes from traffic in the front (SIR)
• Can define different “average traffic conditions” to model uninterrupted and interrupted flow conditions
Uninterrupted Flow
Interrupted Flow
right lane
Vehicle i
Speed Influencing Region SIRi
l
left lane
right lane
Vehicle i
Speed Influencing Region SIRi
l
AMS q-k-v Curves
Tung & Chiu : Integration of DTA in a 4-Step Model Framework 15
1 20 40 60 80100
120140
160180
200220
240260
010203040506070
Speed Density Curve
Density (k)
Spee
d (v
)
1 20 40 60 80100
120140
160180
200220
240260
0
500
1000
1500
2000
2500
Flow Density Curve
Density (k)
Flow
(q)
0 500 1000 1500 2000 25000
10203040506070
Speed-Flow Curve
Flow (q)
Spee
d(v)
• Modified Greenshield’s model:
AMS Examples
Tung & Chiu : Integration of DTA in a 4-Step Model Framework 16
α=3.35 Jam Density = 200 Density Breakpoint = 25Free Flow Speed = 60 Minimum Speed = 6 Speed Intercept=92
1 13 25 37 49 61 73 85 97 1091211331451571691811930
10203040506070
AMS Speed Density Curves
Freeway
Density (k)
Spee
d (v
)
1 13 25 37 49 61 73 85 97 109 121 133 145 157 169 181 1930
400
800
1200
1600
2000
AMS Flow Density Curves
Freeway
Density (k)
Flow
(q)
AMS Examples continued…
Tung & Chiu : Integration of DTA in a 4-Step Model Framework 17
Jam Density = 200 Density Breakpoint = 25Free Flow Speed = 60 Minimum Speed = 6
1 5 9 13 17 21 25 29 33 37 410
10
20
30
40
50
60
70
AMS Speed Density Curves
α=3.75α=3.35
Density (k)
Spee
d (v
)
1 6 11 16 21 26 31 36 410
500
1000
1500
2000
2500
AMS Flow Density Curves
α=3.75α=3.35
Density (k)
Flow
(q)
0 50 100 150 200 2500.0
0.5
1.0
1.5
2.0
2.5
BPR Flow-Density Curve
Density
V/C
Ratio
0.0 0.5 1.0 1.5 2.0 2.50.01.02.03.04.05.06.07.08.0
BPR Volume-Delay Curvet = t0[1+0.15(v/c)4]
V/C Ratio
Trav
el T
ime
Fact
or
0.0 0.5 1.0 1.5 2.0 2.50
10
20
30
40
50
60
70
BPR Speed-Flow Curve
V/C Ratio
Spee
d
Compare BPR to AMS
Tung & Chiu : Integration of DTA in a 4-Step Model Framework 18
0 50 100 150 200 2500
10
20
30
40
50
60
70
BPR Speed-Density Curve
Density
Spee
d
BPR Examples
Tung & Chiu : Integration of DTA in a 4-Step Model Framework 19
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.00
10
20
30
40
50
60
70
BPR Speed Curves
α=0.15 β=4.0α=0.72 β=7.2α=0.60 β=5.8
V/C Ratio
Spee
d
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.00.0
5.0
10.0
15.0
20.0
25.0
BPR Travel Time Curve
α=0.15 β=4.0α=0.72 β=7.2α=0.60 β=5.8
V/C Ratio
Trav
el T
ime
Fact
or
STA vs. DTA ComparisonSimple Network Example
Tung & Chiu : Integration of DTA in a 4-Step Model Framework 20
BPR: α=0.6 β=5.8 AMS: α=3.35
STA vs. DTA ComparisonSimple Network Example
Tung & Chiu : Integration of DTA in a 4-Step Model Framework 21
Demand STA DTA
250x3 2.8 2.2
350x3 3.1 2.4
450x3 4.6 6.6
550x3 8.7 14.0
650x3 18.5 21.7
750x3 38.9 29.1
1,000x3 194.7 47.8
1,500x3 2,017.7 85.0
Average Trip Time by Demand Level
250 350 450 550 650 750 1,000 1,5000.0
20.0
40.0
60.0
80.0
100.0
120.0
140.0
160.0
180.0
200.0
STADTA
Demand
Avg
Trip
Tim
e
Time Dependent Shortest Path
Tung & Chiu : Integration of DTA in a 4-Step Model Framework 22
• The key feature in DTA
• Able to produce Experienced travel time and route that is far more realistic than Instantaneous travel time and route produced in STA.
• Experienced travel time is affected by vehicles departing earlier and later
• Experienced travel time can only be realized after the trip is completed (Arrival Time Profile)
PSRC Time of Day Model
Tung & Chiu : Integration of DTA in a 4-Step Model Framework 23
Discrete Logit Choice Model by 30-Minute IntervalAggregated to five periods: AM, MD, PM, EV & NI
Uijkpm = ak + c1kDijk + c2kDijkSE + c3kDijkSE2 + c4kDijkSL + c5kDijkSL2 + v + d
Where: i = Production zone j = Attraction zonek = Time interval p = Purpose (HBW, HBO, HBShop)m= Mode (SOV, HOV) D = Delays SE = Shift early factor SL = Shift late factorV = Socio-demographic variablesd = Dummy variables
0:001:00
2:003:00
4:005:00
6:007:00
8:009:00
10:0011:00
12:0013:00
14:0015:00
16:0017:00
18:0019:00
20:0021:00
22:0023:00
-0.0500
0.0000
0.0500
0.1000
0.1500
0.2000
0.2500
0.3000
A-PP-A
PSRC Time of Day Model
Tung & Chiu : Integration of DTA in a 4-Step Model Framework 24
Time of Day Choice ModelPros & Cons
Tung & Chiu : Integration of DTA in a 4-Step Model Framework 25
Variations of TOD Profiles by Period
AM MD PM EV NI
• Comparing to static TOD model, choice model adds temporal dynamics that enables peak spreading
• The Shift variables can reasonably spread peak trips over shoulder periods
• The model is sensitive to changes in delays or generalized costs that is crucial for congestion relief studies
• Because TOD was calibrated based on base year HH survey and skims data, the model coefficients become questionable for future years of much higher demand and congestion, and resulting TOD profiles are often unrealistic.
DTA Based TOD Model
Tung & Chiu : Integration of DTA in a 4-Step Model Framework 26
Time of Day Model
24-Hour Temporal
24-Hour DTA
Time Varying Skims
Baseline Year Model Development: Start from initial departure time profile Delay calculated by DynusT can be fed back by
30 min increment to the TOD model TOD model will adjust the departure time
profile Iterative process until convergence Consistency between TOD and DTA is
establishedFuture Year Development Considerations:
Departure or arrival time profiles based on trip purposes
Minimizing total schedule delay + travel time based on trip purposes
Decisions applied to future years
DTA Based TOD Model
Tung & Chiu : Integration of DTA in a 4-Step Model Framework 27
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 970.00
20.00
40.00
60.00
80.00
100.00
120.00
140.00
Average Trip Time by Departure Time
SOV_06TRK_06HOV_06SOV_30TRK_30HOV_30
15-Minute Interval
Trip
Tim
e
1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 970.00000.00200.00400.00600.00800.01000.01200.01400.01600.01800.0200
Departure & Arrival Time Profiles
Departure_06Arrival_06Departure_30Arrival_30
15-Minute Interval
TOD
Shar
es
Next…
Tung & Chiu : Integration of DTA in a 4-Step Model Framework 28
• On-going research project funded by FHWA to investigate the costs and benefits of integrating DTA in a 4-step framework. Results are pending in 2012.
• Findings of this project will be shared with modeling community.
• Contact Robert Tung [email protected] for more information.
Thank you !