1. Transportation Planning Asian Institute of Technology
Trip Distribution 1
Transportation Planning
Asian Institute of Technology

2. Contents Input and Output for Trip Distribution Model
Types of Trip Distribution Model
Uniform Growth Factor Model
Average Factor Model
Detroit Growth Model
Fratar Growth Model

3. Input and Output for Trip Distribution Model
Production, Pi
Attraction, Aj
Trip Costs (Out-of-pocket, distance, convenience)
Output
Trip Matrix

4. Types of Trip Distribution Model
Growth Factor Method
Uniform Growth
Average Factor
Detroit Model
Fratar Model
Single Constrain
Double Constrain
Theory Based Method
Gravity Model
Intervening Opportunity Model
Wilson’s Entropy

5. Uniform Growth Factor Model
Trip growth factor equals to the ratio of the total projected trips to the total existing trips.
Trip between any given O-D in the study area uses the same growth factor.
Disadvantages
Land use in each subarea does not change at the average rate.
The actual growth is not constant, but changes with time.

6. Uniform Growth Factor Model
Example 1 1 2 4 3 1 2 3 4
SPi 12 10 18 40 14 6 32 38
SAj
148
SSTij
280

7. Uniform Growth Factor Model1 2 3 4
SPi 23 19 34 76 26 11 60 72
SAj
280 1 2 3 4
SPi 12 10 18 40 14 6 32 38
SAj
148

8. Average Factor Model
Trip growth factor equals to the ratio of the total projected trips to the total existing trips.
Trips between O-D in the study area use average growth factor between production and attraction.
kth iteration
Disadvantages
Factors do not indicate actual growth.
Calculation may need a large number of iterations

9. Average Factor Model Example 2 1 2 3 4 SPi 12 10 18 40 14 6 32 38 SAj12 10 18 40 14 6 32 38
SAj
148
SPi 80 48
114 38
280
SAj 80 48
114 38
280

10. Average Factor Model Iteration 1 1 2 3 4 SPi 12 10 18 40 14 6 32 3812 10 18 40 14 6 32 38
SAj
148
SPi* 80 48
114 38
280 Fi 2
1.5 3 1
SAj* 80 48
114 38
280 Fj 2
1.5 3 1

11. Average Factor Model Iteration 2 1 2 3 4 SPi 21 25 27 73 31.5 7.5 6021 25 27 73
31.5
7.5 60 28
84.5
62.5
SAj
280
SPi* 80 48
114 38
280 Fi
1.096
0.800
1.349
0.608
SAj* 80 48
114 38
280 Fj
1.096
0.800
1.349
0.608

12. Average Factor Model Iteration 3 1 2 3 4 SPi 19.91 30.56 23.00 73.47
19.91
30.56
23.00
73.47
33.85
5.28
59.04
27.40
91.81
55.68
SAj
280
SPi* 80 48
114 38
280 Fi
1.089
0.813
1.242
0.682
SAj* 80 48
114 38
280 Fj
1.089
0.813
1.242
0.682

13. Average Factor Model Iteration 25 1 2 3 4 SPi 12 56 80 34 48 24 114 3812 56 80 34 48 24
114 38
SAj
280
SPi* 80 48
114 38
280
SAj* 80 48
114 38
280

14. Detroit Growth Model Ensuing development from average growth model
Considers both subarea growth and total growth.
kth iteration

15. Detroit Growth Model Example 3 1 2 3 4 SPi 12 10 18 40 14 6 32 38 SAj12 10 18 40 14 6 32 38
SAj
148
SPi* 80 48
114 38
280
SAj* 80 48
114 38
280

16. Detroit Growth Model Iteration 1 1 2 3 4 SPi 12 10 18 40 14 6 32 3812 10 18 40 14 6 32 38
SAj
148
SPi* 80 48
114 38
280 Fi 2
1.5 3 1
SAj* 80 48
114 38
280
F = 1.892 Fj 2
1.5 3 1

17. Detroit Growth Model Iteration 2 1 2 3 4 SPi 19.03 31.71 69.77 33.30
19.03
31.71
69.77
33.30
4.76
57.09
22.20
87.21
45.99
SAj
260.06
SPi* 80 48
114 38
280 Fi
1.147
0.841
1.307
0.826
SAj* 80 48
114 38
280
F = 1.077 Fj
1.147
0.841
1.307
0.826

18. Detroit Growth Model Iteration 3 1 2 3 4 SPi 19.91 30.56 23.00 77.93
19.91
30.56
23.00
77.93
33.85
5.28
54.10
27.40
100.41
42.09
SAj
274.53
SPi* 80 48
114 38
280 Fi
1.027
0.887
1.135
0.903
SAj* 80 48
114 38
280
F = 1.020 Fj
1.027
0.887
1.135
0.903

19. Detroit Growth Model Iteration 11 1 2 3 4 SPi 12 56 80 34 48 24 114 3812 56 80 34 48 24
114 38
SAj
280
SPi* 80 48
114 38
280
SAj* 80 48
114 38
280

20. Fratar Growth Model Trips from i to j vary with Trips from i to j
Productioin from zone i (Pi)
Growth factor of TAZ (F)
Location Factor (L)
Trips from i to j
where
Disadvantages
Complex calculation
Does not tak into account accessibility

21. Fratar Growth Model Example 4 Find Fi and Fj 1 2 4 3 1 2 3 4 SPi 12 1012 10 18 40 14 6 32 38
SAj
148
SPi* 80 48
114 38
280 Fi 2
1.5 3 1
SAj* 80 48
114 38
280 Fj 2
1.5 3 1

22. Fratar Growth Model Iteration 1: Find Li (i = j; Li = Lj) Li/Lj 1 2 34 -
0.6061/0.4444
0.6061/0.6909
0.6061/0.4368
0.4444/0.6061
0.4444/0.6909
0.4444/0.4368
0.6909/0.6061
0.6909/0.4444
0.6909/0.4368
0.4368/0.6061
0.4368/0.4444
0.4368/0.6909

23. Fratar Growth Model 1 2 3 4 SPi 0.00 18.91 38.91 18.77 76.59 35.76
3.97
58.64
23.68
98.35
46.42
SAj
280
SPi* 80 48
114 38
280 Fi
1.0445
0.8186
1.1591
SAj* 80 48
114 38
280 Fj
1.0445
0.8186
1.1591

24. Fratar Growth Model Iteration 9 1 2 3 4 SPi 12 56 80 34 48 24 114 3812 56 80 34 48 24
114 38
SAj
280
SPi* 80 48
114 38
280
SAj* 80 48
114 38
280

25. Assignment #5
District A is divided into 4 TAZs. It is expected that there will be different economic growth by area in the next ten years after a new town plan. This results in production and attraction as shown in the following table:
Determine future OD trip matrix using Uniform Growth Factor, Average Growth Factor and Fratar Models. 1 2 3 4
SPi
SPi, 2023 20 44 16 80 90 36 14 70
110
100
140 50 60
SAj
300
SAj , 2023
130
120
400

26. Gravity Model Derived from Newton’s gravity model
Trips between i and j
Tij = trips from i to j
Pi = Production from i
Aj = Attraction by j
f(cij) = “generalized cost function” or “deterrence function”
cij = trip costs (usually in form of distance)

27. Travel Cost Function Exponential function Power function
Combined function

28. Model Calibration Non-constrained Method Production-constrained Method
Attraction-constrained Method
Double-constrained Method

29. Non-constrained Model
When total trips are not constrained
Tij = trips from i to j

30. Non-constrained Model
Example 5: Observed trips between zones are as follows:
and distances bewteen zones are
Zone 1 2 3
SPi
150 60
210
130
120
250 70
190
SAi
200
270
180
650
Zone 1 2 3 7 5

31. Non-constrained Model
Average travel distance
Distance, ci km.
Frequency, fi
fici 3
280
840 5
240
1200 7
130
910
Total
650
2950