1. Source: NHI course on Travel Demand Forecasting, Ch. 6 (152054A) Trip Distribution

2. Objectives Describe inputs and outputs to gravity model Explain concept of friction factors Explain how friction factors are obtained Apply gravity model to sample data set

3. Terminology Friction factor Gravity model K-factors Trip Distribution

4. Key concepts Trip distribution is a method to determine where trips are going from and to Trip interchange, or OD “match up” the productions and attractions Calibrate to reflect current travel patterns Apply (aka evaluate) to forecast future travel patterns

5. Calculating TAZ “Attractiveness”

6. Gravity Model

8. K-Factors K-factors account for socioeconomic linkages not accounted for by the gravity model Common application is for blue-collar workers living near white collar jobs (can you think of another way to do it?) K-factors are i-j TAZ specific (but could use a lookup table – how?) If i-j pair has too many trips, use K-factor less than 1.0 (& visa-versa) Once calibrated, keep constant? for forecast (any problems here???) Use dumb K-factors sparingly Can you design a “smart” k factor? (TTYP)

9. Example Problem

10. Input data How do models compute this? See next pages… Does this table need to be symmetrical? Is it usually?

11. Convert Travel Times into Friction Factors Yes, but how did we get these?

12. 1234 5678 9 101112 14151613 6 3 1 2 3 2 3 3 4 4 4 4 1 3 21 1 3 21 2 4 21 Find the shortest path from node to all other nodes (from Garber and Hoel) 1 Yellow numbers represent link travel times in minutes 3 Here’s how …

13. 1234 5678 9 101112 14151613 6 3 1 2 3 2 3 3 4 4 4 4 1 3 21 1 3 21 2 4 21 STEP 1 1 2

14. 1234 5678 9 101112 14151613 6 3 1 2 3 2 3 3 4 4 4 4 1 3 21 1 3 21 2 4 21 STEP 2 1 2 4 5

15. 1234 5678 9 101112 14151613 6 3 1 2 3 2 3 3 4 4 4 4 1 3 21 1 3 21 2 4 21 STEP 3 1 2 4 5 4 4

16. 1234 5678 9 101112 14151613 6 3 1 2 3 2 3 3 4 4 4 4 1 3 21 1 3 21 2 4 21 STEP 4 1 2 4 4 Eliminate 5 >= 4 4 5

17. 1234 5678 9 101112 14151613 6 3 1 2 3 2 3 3 4 4 4 4 1 3 21 1 3 21 2 4 21 STEP 5 1 2 4 4 4 10 6

18. 1234 5678 9 1112 14151613 6 3 1 2 3 2 3 3 4 4 4 4 1 3 21 1 3 21 2 4 21 STEP 6 1 2 4 4 4 10 6 7 Eliminate 7 >= 6 7

19. 6 1234 5678 9 101112 14151613 6 3 1 2 3 2 3 3 4 4 4 4 1 3 21 1 3 21 2 4 21 STEP 7 1 2 4 4 4 10 6 Eliminate 8 >= 7 8 7

20. 7 8 6 1234 5678 9 101112 14151613 6 3 1 2 3 2 3 3 4 4 4 4 1 3 21 1 3 21 2 4 21 STEP 8 1 2 4 4 4 10 7 6

21. 7 8 6 1234 5678 9 1112 14151613 6 3 1 2 3 2 3 3 4 4 4 4 1 3 21 1 3 21 2 4 21 STEP 9 1 2 4 4 4 10 7 6

22. 7 8 6 1234 5678 9 1112 14151613 6 3 1 2 3 2 3 3 4 4 4 4 1 3 21 1 3 21 2 4 21 STEP 10 1 2 4 4 4 10 7 6 Eliminate 10 >= 7 10 Eliminate 10 >= 10

23. 7 8 6 1234 5678 9 101112 14151613 6 3 1 2 3 2 3 3 4 4 4 4 1 3 21 1 3 21 2 4 21 STEP 11 1 2 4 4 4 10 7 6 8

24. 7 8 6 1234 5678 9 1112 14151613 6 3 1 2 3 2 3 3 4 4 4 4 1 3 21 1 3 21 2 4 21 STEP 12 1 2 4 4 4 10 7 6 8 9 9 Eliminate 10 > 9 Eliminate 10 >= 9

25. 7 8 6 1234 5678 9 101112 14151613 6 3 1 2 3 2 3 3 4 4 4 4 1 3 21 1 3 21 2 4 21 STEP 13 1 2 4 4 4 7 6 10 8 9 9 12 Eliminate 12 >= 10

26. 7 8 6 1234 5678 9 101112 14151613 6 3 1 2 3 2 3 3 4 4 4 4 1 3 21 1 3 21 2 4 21 STEP 14 1 2 4 4 4 7 6 10 8 9 9 1210 Eliminate 12 >= 10

27. 7 8 6 1234 5678 9 101112 14151613 FINAL 1 2 4 4 4 7 6 10 8 9 9

28. Calculate the Attractiveness of Each Zone

29. Calculate the Relative Attractiveness of Each Zone Make sense?

30. Distribute Productions to TAZs

31. First Iteration Distribution

32. Comparing and Adjusting Zonal Attractions Balanced attractions from trip generation = 76 The gravity model estimated more attractions to TAZ 3 than estimated by the trip generation model. What can we do? (see homework)

33. Forecasting for Future Year Assignments After successful base year calibration and validation (review … how?) Use forecast land use, socioeconomic data, system changes Forecasted production and attractions, and future year travel time skims Apply gravity model to forecast year Friction factors remain constant over time (what to you think?) In-class exercise