1. Ofir Cohen | PB | 414-243-4645 | coheno@pbworld.com 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 Session 14: Hot and cool topics

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 A better Algorithm is needed sample size=20sample size=200 Y = X Zone 873

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

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)) Sample SizeFrequency of Chosen TAZ Pre-Calculated Probability Correction Factor 10110%0.00 10120%0.69 1013%-1.20

9. Y = X

10. Optimal Sample Size

11. Destination Choice Distribution SALTNON SALT

12. Destination Choice – Cleveland, OH SALT NON SALT

15. 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))

16. SFCTA Workplace Location

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

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

19. Questions?