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DaySim Activity-Based Model

Convergence of an Activity-Based Travel Model System to Equilibrium Experimental Designs and Findings John Gibb, DKS Associates in collaboration with John Bowman and Mark Bradley. DaySim Activity-Based Model. Replaces Trip Generation, Distribution, Mode Choice, Time-of-Day Choice

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DaySim Activity-Based Model

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  1. Convergence of an Activity-Based Travel Model System to EquilibriumExperimental Designs and FindingsJohn Gibb, DKS Associatesin collaboration withJohn Bowman and Mark Bradley

  2. DaySim Activity-Based Model • Replaces Trip Generation, Distribution, Mode Choice, Time-of-Day Choice • Inputs: population, parcel, employment data, and travel cost “skim” matrices • Output: Simulated activity & trip diary of each person for one day • Monte-Carlo microsimulation, single outcomes

  3. Application Flow Travel Cost Skim Matrices Network DaySim Model Auxiliary Models Equilibration (“Feedback”) Assignment

  4. Equilibrium Problem • Direct feedback – inefficient, unreliable • Method of Successive Averages “MSA” well established Xi = (1-λi)Xi-1 + λiYi i = current iteration number Yi = demand model results (trips, volumes) Xi = MSA demand λi = step size parameter (0 to 1)

  5. Choice of Step Size • No objective function for optimal step size • Proven predetermined step sizes: • 1/i – customary, reliable, can be slow • Constant, e.g. 0.5 – can converge quicker, unless overestimated

  6. Noise Problem • Each trip is a nearly independent event with a very low probability • Standard deviation of an aggregation of D trips is approximately sqrt(D) • Disturbs equilibrium convergence?

  7. Run Times • Very long... • DaySim governed by number of households simulated rather than number of zones or iterations • DaySim can run a selected sample of households

  8. Application with Sampling • Scale results up to the population • Increased noise: Standard deviation of trips factors up by approximately • Early iterations with high “convergence noise” tolerate more “sampling noise”

  9. Coordinate Step Sizes and Sampling • Random noise minimized with step size • Preserves relative weight of each household’s simulation, from any iteration • Sample without replacement, until population exhausted

  10. Example 1 • Declining step size=1/i • Constant sample rates

  11. Example 2 • Constant step size = 1/2 • Sample doubles with each iteration

  12. Demonstration Case #1 • Early declining-step-size models needed lots of iterations to converge well. • Improvement: Staged declining-step-size • A few warm-up iterations before full schedule

  13. Demonstration Case #1

  14. Demonstration Case #2 • Fixed step size of one-half • Sample size starts small, but doubles with each iteration • 8 iterations, plus final full pass

  15. Demonstration Case #2

  16. Convergence Progress...

  17. MSA-Preload Equilibrium Assignment • In typical fixed-demand equilibrium assignment programs: • Preload volume = (1-λ)Vi-1 • Assign λ•[iteration demand trips] (This λ is the predetermined system-equilibrium step size, not of the internal iterations of assignment) Example in Voyager code: V=@lambda@*(V1+V2)+(1-@lambda@)*lw.prevvol

  18. MSA-Preload Performance • Achieves a gap-based closure criterion in fewer iterations • Smaller step size→fewer iterations • Volumes are close (but not exact) to conventional assignments • Gap criterion important for system equilibrium

  19. Conclusions • Small number of household simulations bring model system near equilibrium • Travel times steady even with demand “noise” • Constant step size effective & efficient • Declining step size good for fallback or later iterations • Demonstrated an efficient assignment strategy

  20. Further Directions • Stopping criteria • Travel time • Link volumes • Trips • Optimizations • Origin-based assignment (Bar-Gera)

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