For the travel pattern illustrated in Figure 12.20, develop the Fratar method of trip distribution for two iterations.
What will be an ideal response?
First Iteration
Next, use Equation 12.5 to solve the problem.
TAB = 300 × ((25 × 4) / [(25 × 4) + (50 × 2) + (25 × 1)])
TAB = 300 × (100 / 225)
TAB = 133.33
TAC = 300 × ((50 × 2) / [(25 × 4) + (50 × 2) + (25 × 1)])
TAC = 300 × (100 / 225)
TAC = 133.33
TAD = 300 × ((25 × 1) / [(25 × 4) + (50 × 2) + (25 × 1)])
TAD = 300 × (25 / 225)
TAD = 33.33
TBA = 1,000 × ((25 × 3) / [(25 × 3) + (150 × 2) + (75 × 1)])
TBA = 1,000 × (75 / 450)
TBA = 166.67
TBC = 1,000 × ((150 × 2) / [(25 × 3) + (150 × 2) + (75 × 1)])
TBC = 1,000 × (300 / 450)
TBC = 666.67
TBD = 1,000 × ((75 × 1) / [(25 × 3) + (150 × 2) + (75 × 1)])
TBD = 1,000 × (75 / 450)
TBD = 166.67
TCA = 800 × ((50 × 3) / [(50 × 3) + (150 × 4) + (200 × 1)])
TCA = 800 × (150 / 950)
TCA = 126.32
TCB = 800 × ((150 × 4) / [(50 × 3) + (150 × 4) + (200 × 1)])
TCB = 800 × (600 / 950)
TCB = 505.26
TCD = 800 × ((200 × 1) / [(50 × 3) + (150 × 4) + (200 × 1)])
TCD = 800 × (200 / 950)
TCD = 168.42
TDA = 300 × ((25 × 3) / [(25 × 3) + (75 × 4) + (200 × 2)])
TDA = 300 × (75 / 775)
TDA = 29.03
TDB = 300 × ((75 × 4) / [(25 × 3) + (75 × 4) + (200 × 2)])
TDB = 300 × (300 / 775)
TDB = 116.13
TDC = 300 × ((200 × 2) / [(25 × 3) + (75 × 4) + (200 × 2)])
TDC = 300 × (400 / 775)
TDC = 154.84
Next, calculate the movement between zones as well as the new growth factors.
A - B = (133.33 + 166.67) / 2 = 150
A - C = (133.33 + 126.32) / 2 = 129.83
A - D = (33.33 + 29.03) / 2 = 31.18
TOTAL = 311.01
New Growth factor for A = 300 / 311.01 = 0.965
B - A = (133.33 + 166.67) / 2 = 150
B - C = (666.67 + 505.26) / 2 = 585.97
B - D = (166.67 + 116.13) / 2 = 141.40
TOTAL = 877.37
New Growth factor for B = 1,000 / 877.37 = 1.140
C - A = (133.33 + 126.32) / 2 = 129.83
C - B = (666.67 + 505.26) / 2 = 585.97
C - D = (154.84 + 168.42) / 2 = 161.63
TOTAL = 877.43
New Growth factor for C = 800 / 877.43 = 0.912
D - A = (33.33 + 29.03) / 2 = 31.18
D - B = (166.67 + 116.13) / 2 = 141.40
D - C = (154.84 + 168.42) / 2 = 161.63
TOTAL = 334.21
New Growth factor for D = 300 / 334.21 = 0.898
Second Iteration
Next, use Equation 12.5 to solve the problem.
TAB = 300 × ((150 × 1.14) / [(150 × 1.1 4) + (129.83 × 0.912) + (31.18 ×
0.898)])
TAB = 300 × (171 / 317.40)
TAB = 161.63
TAC = 300 × ((129.83 × 0.912) / [(150 × 1.1 4) + (129.83 × 0.912) +
(31.18 × 0.898)])
TAC = 300 × (118.40 / 317.40)
TAC = 111.91
TAD = 300 × ((31.18 × 0.898) / [(150 × 1.1 4) + (129.83 × 0.912) + (31.18
× 0.898)])
TAD = 300 × (28 / 317.40)
TAD = 26.46
TBA = 1,000 × ((150 × 0.965) / [(150 × 0.965) + (585.97 × 0.912) + (141.4
× 0.898)])
TBA = 1,000 × (144.75 / 806.13)
TBA = 179.56
TBC = 1,000 × ((585.97 × 0.912) / [(150 × 0.965) + (585.97 × 0.912) +
(141.4 × 0.898)])
TBC = 1,000 × (534.40 / 806.13)
TBC = 662.92
TBD = 1,000 × ((141.40 × 0.898) / [(150 × 0.965) + (585.97 × 0.912) +
(141.4 × 0.898)])
TBD = 1,000 × (126.98 / 806.13)
TBD = 157.51
TCA = 800 × ((129.83 × 0.965) / [(129.83 × 0.965) + (585.97 × 1.14) +
(161.63 × 0.898)])
TCA = 800 × (125.29 / 938.44)
TCA = 106.80
TCB = 800 × ((585.97 × 1.14)/ [(129.83 × 0.965) + (585.97 × 1.14) +
(161.63 × 0.898)])
TCB = 800 × (668.01 / 938.44)
TCB = 569.46
TCD = 800 × ((161.63 × 0.898)/ [(129.83 × 0.965) + (585.97 × 1.14) +
(161.63 × 0.898)])
TCD = 800 × (145.14 / 938.44)
TCD = 123.73
TDA = 300 × ((31.18 × 0.965) / [(31.18 × 0.965) + (141.4 × 1.14) +
(161.63 × 0.912)])
TDA = 300 × (30.09 / 338.69)
TDA = 26.65
TDB = 300 × ((141.4 × 1.14) / [(31.18 × 0.965) + (141.4 × 1.14) + (161.63
× 0.912)])
TDB = 300 × (161.2 / 338.69)
TDB = 142.78
TDC = 300 × ((161.63 × 0.912) / [(31.18 × 0.965) + (141.4 × 1.14) +
(161.63 × 0.912)])
TDC = 300 × (147.41 / 338.69)
TDC = 130.57
Next, calculate the movement between zones.
A - B = (161.63 + 179.56) / 2 = 170.60
A - C = (111.91 + 106.80) / 2 = 109.36
A - D = (26.46 + 26.65) / 2 = 26.56
TOTAL = 306.52
B - A = (161.63 + 179.56) / 2 = 170.60
B - C = (662.92 + 569.46) / 2 = 616.19
B - D = (157.51 + 142.78) / 2 = 150.15
TOTAL = 936.94
C - A = (111.91 + 106.80) / 2 = 109.36
C - B = (662.92 + 569.46) / 2 = 616.19
C - D = (123.73 + 130.57) / 2 = 127.15
TOTAL = 852.70
D - A = (26.46 + 26.66) / 2 = 26.56
D - B = (157.51 + 142.78) / 2 = 150.15
D - C = (123.73 + 130.57) / 2 = 127.15
TOTAL = 303.86
These results could serve as the starting point for a third iteration.
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