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# Trip Distribution

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

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## Trip Distribution

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

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

7. 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)

8. Example Problem

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

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

11. Find the shortest path from node to all other nodes (from Garber and Hoel) 1 3 6 1 Here’s how … 1 2 3 4 4 2 2 1 3 2 2 5 6 7 8 3 1 2 1 3 3 4 9 10 11 12 3 1 2 1 4 4 4 13 14 15 16 Yellow numbers represent link travel times in minutes 3

12. STEP 1 1 3 6 1 1 2 3 4 4 2 2 1 2 3 2 2 5 6 7 8 3 1 2 1 3 3 4 9 10 11 12 3 1 2 1 4 4 4 13 14 15 16

13. STEP 2 1 4 3 6 1 1 2 3 4 4 2 2 1 2 5 3 2 2 5 6 7 8 3 1 2 1 3 3 4 9 10 11 12 3 1 2 1 4 4 4 13 14 15 16

14. STEP 3 1 4 3 6 1 1 2 3 4 4 2 2 1 2 5 3 2 2 5 6 7 8 4 3 1 2 1 4 3 3 4 9 10 11 12 3 1 2 1 4 4 4 13 14 15 16

15. STEP 4 1 4 3 6 1 1 2 3 4 Eliminate 4 2 2 1 5 >= 4 2 5 3 2 2 5 6 7 8 4 3 1 2 1 4 3 3 4 9 10 11 12 3 1 2 1 4 4 4 13 14 15 16

16. STEP 5 1 4 10 3 6 1 1 2 3 4 4 2 2 1 2 6 3 2 2 5 6 7 8 4 3 1 2 1 4 3 3 4 9 10 11 12 3 1 2 1 4 4 4 13 14 15 16

17. STEP 6 1 4 10 3 6 1 1 2 3 4 4 2 2 1 2 6 3 2 2 5 6 7 8 4 7 Eliminate 7 >= 6 3 1 2 1 4 7 3 3 4 9 10 11 12 3 1 2 1 4 4 4 13 14 15 16

18. STEP 7 1 4 10 3 6 1 1 2 3 4 4 2 2 1 2 6 3 2 2 5 6 7 8 4 3 1 2 1 4 7 3 3 4 9 10 11 12 8 Eliminate 8 >= 7 3 1 2 1 6 4 4 4 13 14 15 16

19. STEP 8 1 4 10 3 6 1 1 2 3 4 4 2 2 1 2 6 8 3 2 2 5 6 7 8 4 3 1 2 1 4 7 7 3 3 4 9 10 11 12 3 1 2 1 6 4 4 4 13 14 15 16

20. STEP 9 1 4 10 3 6 1 1 2 3 4 4 2 2 1 2 6 8 3 2 2 5 6 7 8 4 3 1 2 1 4 7 7 3 3 4 9 10 11 12 3 1 2 1 10 6 4 4 4 13 14 15 16

21. STEP 10 1 4 10 3 6 1 1 2 3 4 4 2 2 1 2 6 8 3 2 2 5 6 7 8 4 3 1 2 1 4 7 7 3 3 4 9 10 11 12 10 Eliminate 10 >= 7 Eliminate 3 1 2 1 10 6 4 4 4 13 14 15 16 10 10 >= 10

22. STEP 11 1 4 10 3 6 1 1 2 3 4 4 2 2 1 2 6 8 3 2 2 5 6 7 8 4 3 1 2 1 4 10 7 7 3 3 4 9 10 11 12 3 1 2 1 8 6 4 4 4 13 14 15 16 10

23. 10 > 9 Eliminate STEP 12 1 4 10 3 6 1 1 2 3 4 9 4 2 2 1 2 6 8 3 2 2 5 6 7 8 4 3 1 2 1 10 >= 9 9 4 10 7 7 3 3 4 9 10 11 12 Eliminate 3 1 2 1 8 6 4 4 4 13 14 15 16 10

24. STEP 13 1 4 3 6 1 1 2 3 4 9 4 2 2 1 2 6 8 3 2 2 5 6 7 8 4 3 1 2 1 9 4 7 7 3 3 4 9 10 11 12 3 1 2 1 12 >= 10 12 8 12 6 4 4 4 13 14 15 16 10 Eliminate

25. STEP 14 1 4 3 6 1 1 2 3 4 9 4 2 2 1 2 6 8 3 2 2 5 6 7 8 4 3 1 2 1 9 4 7 7 3 3 4 9 10 11 12 3 1 2 1 12 >= 10 8 12 10 6 4 4 4 13 14 15 16 10 Eliminate

26. FINAL 1 4 1 2 3 4 9 2 6 8 5 6 7 8 4 9 4 7 7 9 10 11 12 8 10 6 13 14 15 16 10

27. Calculate the Attractiveness of Each Zone

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

29. Distribute Productions to TAZs

30. First Iteration Distribution

31. 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)

32. 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

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