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Network Equilibrium with Activity-Based Models: the New York Experience
Peter Vovsha, Robert Donnelly, Surabhi Gupta
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Session 8: How I Learned to Stop Worrying and Love the Activity Based Model
11th Planning Application Conference, May 6-10, 2007, Daytona Beach, FA 2
Network Equilibrium with AB Models
Essential for objective model outcomes Conventional 4-step models:
Established theory / proven existence and uniqueness
Effective algorithms and programming implementation
Based on continuous demand Still a challenge with AB models:
Analytical complexity with structural changes Discrete microsimulation and Monte-Carlo
variation
11th Planning Application Conference, May 6-10, 2007, Daytona Beach, FA 3
Specific Challenges of NY
Extreme example of highest congestion: Difficult to ensure assignment convergence Instable/fluctuating LOS skims
Huge dimensionality and long run times: 20,000,000 individuals 4,000×4,000 multi-class trip tables
Various possible responses contributing to instability/non-convergence: Switching mode Different destination Changing time of day
11th Planning Application Conference, May 6-10, 2007, Daytona Beach, FA 4
Averaging & Enforcement
Simple feeding back LOS variables does not ensure convergence
2 ways to ensure convergence by iterating: Averaging:
Continuous LOS variables: Highway skims for time and cost Transit skims generally cannot be averaged
Demand matrices: Microsimulation model is a generator of trip table Linkage to individual records is lost
Enforcement to ensure replication of discrete choices:
No theoretical foundation Arbitrary strategies
11th Planning Application Conference, May 6-10, 2007, Daytona Beach, FA 5
Enforcement Methods
Re-using same random numbers / seeds: Each household / person has a fixed seed Structural stability of decision chains by
reserving choice placeholders Gradual freezing:
Subsets of households Travel dimensions
Analytical discretizing of probability matrices
11th Planning Application Conference, May 6-10, 2007, Daytona Beach, FA 6
Monte-Carlo Effects
Characteristic Stable structure Variable structure
Choice dimensions Household car ownershipTour mode & destination
Tour formationStop location & trip mode
Impact on convergence
Theoretical convergence by iterating and averaging
Discontinuity and abrupt responses
Treatment Averaging Enforcement & averaging
11th Planning Application Conference, May 6-10, 2007, Daytona Beach, FA 7
Stable Structure
Same list of agents
Tour 1
Tour 2
Tour 3
Tour 4
Same random number
0.7543267
0.2635498
0.1135645
0.9797613
Same choices with convergent probabilities
Mode 1 Mode 2 Mode 3 Mode 4
0.5354
0.6623
0.2231
0.8988
0.5540
0.8632
0.5678
0.8989
0.7374
0.8944
0.6633
0.9800
1.0000
1.0000
1.0000
1.0000
With the same list of agents facing the same choices, using the same random numbers with convergent probabilities
will ensure convergence of the individual choices
11th Planning Application Conference, May 6-10, 2007, Daytona Beach, FA 8
Structural Variation – 1
Variable list of agents
Out stop 1
Out stop 2
Out stop 3
Inb stop 1
Same random number
0.7543267
0.2635498
0.1135645
0.9797613
Same choices with convergent probabilities
TAZ 1 TAZ 2 TAZ 3 TAZ 4
0.5354
0.6623
0.2231
0.8988
0.5540
0.8632
0.5678
0.8989
0.7374
0.8944
0.6633
0.9800
1.0000
1.0000
1.0000
1.0000
Inb stop 2
Inb stop 3
X
X
11th Planning Application Conference, May 6-10, 2007, Daytona Beach, FA 9
Structural Variation – 2
Variable list of agents
Out stop 1
Out stop 2
Out stop 3
Inb stop 1
Same random number
0.7543267
0.2635498
0.1135645
0.9797613
Same choices with convergent probabilities
TAZ 1 TAZ 2 TAZ 3 TAZ 4
0.5354
0.6623
0.0341
0.8988
0.5540
0.8632
0.3780
0.8989
0.7374
0.8944
0.6271
0.9800
1.0000
1.0000
1.0000
1.0000
With a variable list of agents facing the same choices, using the same sequence of random numbers
with convergent probabilities does not ensure convergence of the individual choices
Inb stop 2
Inb stop 3
X
X
11th Planning Application Conference, May 6-10, 2007, Daytona Beach, FA 10
Structural Variation – 3
Variable list of agents
Out stop 1
Out stop 2
Out stop 3
Inb stop 1
Same random number
0.7543267
0.2635498
0.0426459
0.9797613
Same choices with convergent probabilities
TAZ 1 TAZ 2 TAZ 3 TAZ 4
0.5354
0.6623
0.0341
0.8988
0.5540
0.8632
0.3780
0.8989
0.7374
0.8944
0.6271
0.9800
1.0000
1.0000
1.0000
1.0000
With a variable list of agents facing the same choices, using the same random numbers for each agent
with convergent probabilities will ensure convergence of the individual choices
Inb stop 2
Inb stop 3
X
X
0.1135645
0.5137942
11th Planning Application Conference, May 6-10, 2007, Daytona Beach, FA 11
Current Project Approach
No enforcement has been applied yet: Programming effort required Testing strategies required
Averaging strategies for skims (link volumes) and trip tables explored: Acceptable results for FTA New Starts:
Limited model sensitivity (mode choice) No individual record analysis (OD-pairs by
segments)
11th Planning Application Conference, May 6-10, 2007, Daytona Beach, FA 12
Averaging Methods
Direct feedback (full update) Factor=1
Link flow MSA Factor = 1/n Factor = 1/n (no advantage found)
Trip table MSA Factor = 1/n
11th Planning Application Conference, May 6-10, 2007, Daytona Beach, FA 13
Equilibrium Feedback Options
Microsimulation model
Conventional static assignment
Mode & TOD trip tables
Link volumes
Link times
OD skims
11th Planning Application Conference, May 6-10, 2007, Daytona Beach, FA 14
Naïve – Never Works
Microsimulation model
Conventional static assignment
Mode & TOD trip tables
Link volumes
Link times
OD skims
11th Planning Application Conference, May 6-10, 2007, Daytona Beach, FA 15
Intermediate Conclusion
With microsimulation, simple feeding back LOS skims
will never work
Enforcement on the microsimulation side and/or averaging of trip tables / skims should be applied
11th Planning Application Conference, May 6-10, 2007, Daytona Beach, FA 16
MSA Options
Microsimulation model
Conventional static assignment
Mode & TOD trip tables
Link volumes
Link times
OD skims
X
11th Planning Application Conference, May 6-10, 2007, Daytona Beach, FA 17
Most Effective
Microsimulation model
Conventional static assignment
Mode & TOD trip tables
Link volumes
Link times
OD skims
11th Planning Application Conference, May 6-10, 2007, Daytona Beach, FA 18
Adopted Strategy In many applications, microsimulation model
can be considered as trip table generator (FTA) Aggregate outcomes are important Tracing back individual record details is not
important Averaging strategy:
Averaging (stable) link volumes is more effective than travel times (exponential functions of volumes)
Convergence: Practically acceptable after 3-4 global iterations Maximum level after 9-10 iterations
11th Planning Application Conference, May 6-10, 2007, Daytona Beach, FA 19
RMSE: AM Highway Trip Table
0
500
1000
1500
2000
2500
3000
2 3 4 5 6 7 8 9
DirectMSARoot MSAMSA Trip
11th Planning Application Conference, May 6-10, 2007, Daytona Beach, FA 20
RMSE: MD Highway Trip Table
0
500
1000
1500
2000
2500
3000
3500
4000
2 3 4 5 6 7 8 9
DirectMSARoot MSAMSA Trip
11th Planning Application Conference, May 6-10, 2007, Daytona Beach, FA 21
RMSE: AM Transit Trip Table
0
500
1000
1500
2000
2500
3000
2 3 4 5 6 7 8 9
DirectMSARoot MSAMSA Trip
11th Planning Application Conference, May 6-10, 2007, Daytona Beach, FA 22
RMSE: MD Transit Trip Table
0
500
1000
1500
2000
2500
3000
2 3 4 5 6 7 8 9
DirectMSARoot MSAMSA Trip
11th Planning Application Conference, May 6-10, 2007, Daytona Beach, FA 23
RMSE: AM Link Flow
0
20
40
60
80
100
120
2 3 4 5 6 7 8 9
DirectMSARoot MSAMSA Trip
11th Planning Application Conference, May 6-10, 2007, Daytona Beach, FA 24
RMSE: MD Link Flow
0
20
40
60
80
100
120
140
160
180
2 3 4 5 6 7 8 9
DirectMSARoot MSAMSA Trip
11th Planning Application Conference, May 6-10, 2007, Daytona Beach, FA 25
%RMSE: AM Link Time
0%
1%
2%
3%
4%
5%
6%
7%
8%
2 3 4 5 6 7 8 9
DirectMSARoot MSAMSA Trip
11th Planning Application Conference, May 6-10, 2007, Daytona Beach, FA 26
%RMSE: MD Link Time
0%
1%
2%
3%
4%
5%
6%
7%
8%
2 3 4 5 6 7 8 9
DirectMSARoot MSAMSA Trip
11th Planning Application Conference, May 6-10, 2007, Daytona Beach, FA 27
Max AM Link Flow Difference
0
500
1,000
1,500
2,000
2,500
2 3 4 5 6 7 8 9
DirectMSARoot MSAMSA Trip
11th Planning Application Conference, May 6-10, 2007, Daytona Beach, FA 28
Max MD Link Flow Difference
0
1,000
2,000
3,000
4,000
5,000
6,000
7,000
8,000
2 3 4 5 6 7 8 9
DirectMSARoot MSAMSA Trip
11th Planning Application Conference, May 6-10, 2007, Daytona Beach, FA 29
Conclusions
NY region Highly congested – extreme example
Theoretically, convergence at large number of iterations (20-30): Reasonable convergence - trip tables
(4,000×4,000) Good level of convergence:
Network link volumes Aggregate county-to-county trip tables (29×29)
11th Planning Application Conference, May 6-10, 2007, Daytona Beach, FA 30
Conclusions
Effective Strategy: MSA of link volumes and MSA on trip tables
Number of global iterations: 8-9 practically enough Little improvement after 3-4 global iterations
Source of instability – stop-frequency, stop-location and TOD model
Tour mode and destination choice are more stable
11th Planning Application Conference, May 6-10, 2007, Daytona Beach, FA 31
Recommended Strategy “Cold” start:
9-10 iterations (1, ½, 1/3, ¼, …) Any reasonable starting skims (for year/level of
demand) Prior trip tables are not used in the process Run for each Base scenario / year Run only for exceptional Build scenarios with global
regional impacts (like Manhattan area pricing) “Warm” start:
3 iterations (1, ½, 1/3) Input skims for Base of final (last iteration) are used
as starting skims for Build transit and highway projects
Run for Build scenarios “Hot” start:
FTM New Start Methods 1 iteration only
11th Planning Application Conference, May 6-10, 2007, Daytona Beach, FA 32
Further Testing
Combination of averaging and enforcement to ensure consistence of microsimulation outcome and trip tables
Local / project-specific ways to speed up convergence