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Sample Of Alternatives

Session 14: Hot and cool topics. Sample Of Alternatives. 11th National Transportation Planning Applications Conference May 6-10, 2007, Daytona Beach, Florida Ofir Cohen, PB, San-Francisco Christi Willison, PB, Albuquerque Andrew Stryker, PB, Portland. Agenda. Motivation – Why Sampling?

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Sample Of Alternatives

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  1. Session 14: Hot and cool topics Sample Of Alternatives 11th National Transportation Planning Applications Conference May 6-10, 2007, Daytona Beach, Florida Ofir Cohen, PB, San-Francisco Christi Willison, PB, Albuquerque Andrew Stryker, PB, Portland

  2. Agenda • Motivation – Why Sampling? • Sampling Algorithm • Random Sample • Smart sampling Concept- S.A.L.T • Correction Factor • Optimal sample size • Results – Disaggregate Commercial movement - Ohio Statewide model • Run Time improvement

  3. Motivation • Multinomial logit function can have a great number of alternatives – Destination Choice • Utilities can be cumbersome and include many parameters. • A Micro-Simulation model evaluates the utility of each alternative every time it applies the model. • This involves in a very intensive computing time.

  4. OHIO Statewide Disaggregate Commercial Model • Ohio State Wide model has 4248 Internal zones. • The model has 4.6M trips -> utility is evaluated ~20G times. • Java based software- EXP(), LOG() are rather “expensive functions” • Some parameter are calculated on the fly and therefore utilities can't be re-used • Run time is around 80 minutes. A faster yet unbiased approach is needed. Destination Choice Model

  5. Utility

  6. Simple concepts • Random selection • Apply model among selected alternatives only Zone 873 Y = X Y = X sample size=20 sample size=200 A better Algorithm is needed

  7. SALT – Sample of ALTernatives λ= 1/avg(dist) Define a simplified utility Uij = ln(Total_HH+Total_Jobs) +λ*dist(i, j) Pre-Calculated Compute a pre-defined static probability matrix (N^2). Draw a sample of alternatives (with replacement) based on the probability matrix Add Correction Factor Apply the full utility for each sampled alternative and draw the chosen alternative On the fly

  8. Correction Factor • P(alt)= P(In sample)*P(Full Utility| being sampled) • Fix the Monte-Carlo randomness error in the sample • Cf(ij)= -ln(freq. of j in sample set / (sample size * Pre Defined probability))

  9. Y = X Y = X Y = X Y = X

  10. Optimal Sample Size

  11. Destination Choice Distribution SALT NON SALT

  12. Destination Choice – Cleveland, OH SALT NON SALT

  13. SFCTA- Workplace Location using SALT • Simplified utility under-samples trips to Santa-Clara county (~25 miles) • U(j)=jobs + Exp(λ*Max(dist(j),20))

  14. SFCTA Workplace Location

  15. Conclusion • Simple – minor code modifications • Statistically unbiased • Reduce runtime drastically • Robust - various sampling method.

  16. Acknowledge • Peter Vovsha, PB, New-York • Greg Erhardt, PB, San-Francisco

  17. Questions?

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