Network Equilibrium with Activity-Based Models: the New York Experience

Network Equilibrium with Activity-Based Models: the New York Experience

Peter Vovsha, Robert Donnelly, Surabhi Gupta

pb

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


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


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


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


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


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


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


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




Out stop 1

Out stop 2

Out stop 3

Inb stop 1

Same random number

0.7543267

0.2635498

0.1135645

0.9797613



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




Out stop 1

Out stop 2

Out stop 3

Inb stop 1

Same random number

0.7543267

0.2635498

0.0426459

0.9797613



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


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)


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


Equilibrium Feedback Options

Microsimulation model

Conventional static assignment

Mode & TOD trip tables

Link volumes

Link times

OD skims


Naïve – Never Works




Link volumes

Link times

OD skims


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


MSA Options




Link volumes

Link times

OD skims

X


Most Effective




Link volumes

Link times

OD skims


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


RMSE: AM Highway Trip Table

0

500

1000

1500

2000

2500

3000

2 3 4 5 6 7 8 9

DirectMSARoot MSAMSA Trip


RMSE: MD Highway Trip Table

0

500

1000

1500

2000

2500

3000

3500

4000

2 3 4 5 6 7 8 9



RMSE: AM Transit Trip Table

0

500

1000

1500

2000

2500

3000

2 3 4 5 6 7 8 9



RMSE: MD Transit Trip Table

0

500

1000

1500

2000

2500

3000

2 3 4 5 6 7 8 9



RMSE: AM Link Flow

0

20

40

60

80

100

120

2 3 4 5 6 7 8 9



RMSE: MD Link Flow

0

20

40

60

80

100

120

140

160

180

2 3 4 5 6 7 8 9



%RMSE: AM Link Time

0%

1%

2%

3%

4%

5%

6%

7%

8%

2 3 4 5 6 7 8 9



%RMSE: MD Link Time

0%

1%

2%

3%

4%

5%

6%

7%

8%

2 3 4 5 6 7 8 9



Max AM Link Flow Difference

0

500

1,000

1,500

2,000

2,500

2 3 4 5 6 7 8 9



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



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)


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


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


Further Testing

Combination of averaging and enforcement to ensure consistence of microsimulation outcome and trip tables

Local / project-specific ways to speed up convergence

Network Equilibrium with Activity-Based Models: the New York Experience

Documents

Transcript of Network Equilibrium with Activity-Based Models: the New York Experience