Peter Vovsha, Robert Donnelly, Surabhi Gupta pb Session 8: How I Learned to Stop Worrying and Love the Activity Based Model Network Equilibrium with Activity-Based Models: the New York Experience Peter Vovsha, Robert Donnelly, Surabhi Gupta pb

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

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

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

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

Monte-Carlo Effects Characteristic Stable structure Variable structure Choice dimensions Household car ownership Tour mode & destination Tour formation Stop 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

Stable Structure Same list of agents Same random number Same choices with convergent probabilities Mode 1 Mode 2 Mode 3 Mode 4 Tour 1 0.7543267 0.5354 0.5540 0.7374 1.0000 Tour 2 0.2635498 0.6623 0.8632 0.8944 1.0000 Tour 3 0.1135645 0.2231 0.5678 0.6633 1.0000 Tour 4 0.9797613 0.8988 0.8989 0.9800 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

Structural Variation – 1 Variable list of agents Same random number Same choices with convergent probabilities TAZ 1 TAZ 2 TAZ 3 TAZ 4 Out stop 1 0.7543267 0.5354 0.5540 0.7374 1.0000 Out stop 2 0.2635498 0.6623 0.8632 0.8944 1.0000 Out stop 3 0.1135645 0.2231 0.5678 0.6633 1.0000 Inb stop 1 0.9797613 0.8988 0.8989 0.9800 1.0000 Inb stop 2 X Inb stop 3 X 11th Planning Application Conference, May 6-10, 2007, Daytona Beach, FA

Structural Variation – 2 Variable list of agents Same random number Same choices with convergent probabilities TAZ 1 TAZ 2 TAZ 3 TAZ 4 Out stop 1 0.7543267 0.5354 0.5540 0.7374 1.0000 Out stop 2 0.2635498 0.6623 0.8632 0.8944 1.0000 Out stop 3 X Inb stop 1 0.1135645 0.8988 0.8989 0.9800 1.0000 Inb stop 2 0.9797613 0.0341 0.3780 0.6271 1.0000 Inb stop 3 X 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 11th Planning Application Conference, May 6-10, 2007, Daytona Beach, FA

Structural Variation – 3 Variable list of agents Same random number Same choices with convergent probabilities TAZ 1 TAZ 2 TAZ 3 TAZ 4 Out stop 1 0.7543267 0.5354 0.5540 0.7374 1.0000 Out stop 2 0.2635498 0.6623 0.8632 0.8944 1.0000 Out stop 3 X 0.1135645 Inb stop 1 0.9797613 0.8988 0.8989 0.9800 1.0000 Inb stop 2 0.0426459 0.0341 0.3780 0.6271 1.0000 Inb stop 3 X 0.5137942 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 11th Planning Application Conference, May 6-10, 2007, Daytona Beach, FA

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

Averaging Methods Direct feedback (full update) Link flow MSA Factor=1 Link flow MSA Factor = 1/n Factor = 1/n (no advantage found) Trip table MSA 11th Planning Application Conference, May 6-10, 2007, Daytona Beach, FA

Equilibrium Feedback Options Microsimulation model Mode & TOD trip tables Conventional static assignment Link volumes Link times OD skims 11th Planning Application Conference, May 6-10, 2007, Daytona Beach, FA

Microsimulation model Conventional static assignment Naïve – Never Works Microsimulation model Mode & TOD trip tables Conventional static assignment Link volumes Link times OD skims 11th Planning Application Conference, May 6-10, 2007, Daytona Beach, FA

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

Microsimulation model Conventional static assignment MSA Options Microsimulation model X Mode & TOD trip tables Conventional static assignment Link volumes Link times OD skims 11th Planning Application Conference, May 6-10, 2007, Daytona Beach, FA

Microsimulation model Conventional static assignment Most Effective Microsimulation model Mode & TOD trip tables Conventional static assignment Link volumes Link times OD skims 11th Planning Application Conference, May 6-10, 2007, Daytona Beach, FA

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

RMSE: AM Highway Trip Table 11th Planning Application Conference, May 6-10, 2007, Daytona Beach, FA

RMSE: MD Highway Trip Table 11th Planning Application Conference, May 6-10, 2007, Daytona Beach, FA

RMSE: AM Transit Trip Table 11th Planning Application Conference, May 6-10, 2007, Daytona Beach, FA

RMSE: MD Transit Trip Table 11th Planning Application Conference, May 6-10, 2007, Daytona Beach, FA

RMSE: AM Link Flow 11th Planning Application Conference, May 6-10, 2007, Daytona Beach, FA

RMSE: MD Link Flow 11th Planning Application Conference, May 6-10, 2007, Daytona Beach, FA

%RMSE: AM Link Time 11th Planning Application Conference, May 6-10, 2007, Daytona Beach, FA

%RMSE: MD Link Time 11th Planning Application Conference, May 6-10, 2007, Daytona Beach, FA

Max AM Link Flow Difference 11th Planning Application Conference, May 6-10, 2007, Daytona Beach, FA

Max MD Link Flow Difference 11th Planning Application Conference, May 6-10, 2007, Daytona Beach, FA

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

Conclusions Effective Strategy: Number of global iterations: 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

Recommended Strategy “Cold” start: “Warm” start: “Hot” 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

Further Testing Combination of averaging and enforcement to ensure consistence of microsimulation outcome and trip tables Local / project-specific ways to speed up convergence 11th Planning Application Conference, May 6-10, 2007, Daytona Beach, FA