1. Travel Demand Forecasting: Trip Distribution CE331 Transportation Engineering

2. Land Use and Socio- economic Projections Trip Generation Trip Distribution Modal Split Traffic Assignment Transportation System Specifications Direct User Impacts Overall Procedure

3. Trip Distribution Where to go? Choice may vary with trip purpose Input Trips generated from and attracted to each zone (step 1 output) Interzonal transportation cost (travel time, distance, out-of-pocket cost, …) Output – trip interchange between zones Presented as Origin-Destination (OD) matrix

4. Process Allocate trips originating from each zone to all possible destination zones Assume destination zones are competing with each other in attracting trips produced by zone i

5. Types of Models Gravity Model Trips are attracted to a zone as gravity “attracts” objects Utility Maximization Assumes that a traveler makes the decision that maximizes his/her utility

6. Calculating TAZ “Attractiveness”

7. Gravity Model

9. 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)

10. Gravity Model Example Problem

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

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

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 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 …

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 1 1 2

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 2 1 2 4 5

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 3 1 2 4 5 4 4

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 4 1 2 4 4 Eliminate 5 >= 4 4 5

18. 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

19. 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

20. 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

21. 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

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 9 1 2 4 4 4 10 7 6

23. 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

24. 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

25. 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

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 13 1 2 4 4 4 7 6 10 8 9 9 12 Eliminate 12 >= 10

27. 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

28. 7 8 6 1234 5678 9 101112 14151613 FINAL 1 2 4 4 4 7 6 10 8 9 9

29. Calculate the Attractiveness of Each Zone

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

31. Distribute Productions to TAZs

32. First Iteration Distribution Advanced Concepts – not required for CE331

33. 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) Advanced Concepts – not required for CE331

34. 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 Advanced Concepts – not required for CE331

35. A Simple Gravity Model t ij = P i T j /(d ij n A j ) Where P i – trips generated from zone i; d ij – distance or time; T j – trips attracted to zone j; A j – balancing factor; A j =Σ (P i /d ij n ) n – parameter.

36. Example – 1 A new theater is expected to attract 700 trips from 2 zones with daily trip productions of 1500 and 3000. The distances to the new theater are 2 and 3 miles, respectively. The factor n is approximately 2. How many trips from each zone will be attracted to the theatre?

37. Example (cont’d) A 1 = Σ (P i /d ij n ) = (1500/2 2 )+ (3000/3 2 )= 708.3 t 11 =P 1 T 1 /(d 11 2 A 1 )=1500(700)/[2 2 (708.3)]= 370.6 t 21 =P 2 T 1 /(d 21 2 A 1 )=3000(700)/[3 2 (708.3)]=32 9.4

38. Utility Maximization Consider travelers’ choice in trip- making decision Use utility function (U) to reflect the attractiveness of an alternative (in this case, destination) U = b 0 + b 1 *z 1 + b 2 *z 2 + … + b n *z n b0, b1, …: parameters z1, z2, …: attributes of the alternative

39. Utility Maximization: Logit Model Pr(i): probability of choosing alternative i over all other alternatives; U i : utility value of alternative (destination) i.