1 / 25

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

vedgar
Download Presentation

DaySim Activity-Based Model

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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)

More Related