The Jeffersonville Transportation Study area has been divided into four traffic zones. The following data have been compiled. Complete the second iteration.
What will be an ideal response?
Calculate the adjusted attraction factors using Equation 12.4.
Zone 1
Ajk = (1,000 / 869) × 1,000
Ajk = 1,151
Zone 2
Ajk = (700 / 707) × 700
Ajk = 693
Zone 3
Ajk = (6,000 / 6,110) × 6,000
Ajk = 5,892
Zone 4
Ajk = (500 / 514) × 500
Ajk = 486
Now apply the gravity model formula for Iteration 2 using the above adjusted
attraction factors.
Iteration 2
T11 = 1,000 × ((1,151 × 1.3) /
((1,151 × 1.3) + (693 × 0.95) + (5,892 × 0.8) + (486 × 0.65)))
T11 = 1,000 × (1,496 / 7,184)
T11 = 208
T12 = 1,000 × ((693 × 0.95) /
((1,151 × 1.3) + (693 × 0.95) + (5,892 × 0.8) + (486 × 0.65)))
T12 = 1,000 × (658 / 7,184)
T12 = 92
T13 = 1,000 × ((5,892 × 0.8) /
((1,151 × 1.3) + (693 × 0.95) + (5,892 × 0.8) + (486 × 0.65)))
T13 = 1,000 × (4,714 / 7,184)
T13 = 656
T14 = 1,000 × ((486 × 0.65) /
((1,151 × 1.3) + (693 × 0.95) + (5,892 × 0.8) + (486 × 0.65)))
T14 = 1,000 × (316 / 7,184)
T14 = 44
T21 = 2,000 × ((1,151 × 0.95) /
((1,151 × 0.95) + (693 × 1.3) + (5,892 × 0.85) + (486 × 0.95)))
T21 = 2,000 × (1,093 / 7,464)
T21 = 293
T22 = 2,000 × ((693 × 1.3) /
((1,151 × 0.95) + (693 × 1.3) + (5,892 × 0.85) + (486 × 0.95)))
T22 = 2,000 × (901 / 7,464)
T22 = 241
T23 = 2,000 × ((5,892 × 0.85) /
((1,151 × 0.95) + (693 × 1.3) + (5,892 × 0.85) + (486 × 0.95)))
T23 = 2,000 × (5,008 / 7,464)
T23 = 1,342
T24 = 2,000 × ((486 × 0.95) /
((1,151 × 0.95) + (693 × 1.3) + (5,892 × 0.85) + (486 × 0.95)))
T24 = 2,000 × (462 / 7,464)
T24 = 124
T31 = 3,000 × ((1,151 × 0.80) /
((1,151 × 0.80) + (693 × 0.85) + (5,892 × 1.3) + (486 × 1)))
T31 = 3,000 × (921 / 9,655)
T31 = 286
T32 = 3,000 × ((693 × 0.85) /
((1,151 × 0.80) + (693 × 0.85) + (5,892 × 1.3) + (486 × 1)))
T32 = 3,000 × (589 / 9,655)
T32 = 183
T33 = 3,000 × ((5,892 × 1.3) /
((1,151 × 0.80) + (693 × 0.85) + (5,892 × 1.3) + (486 × 1)))
T33 = 3,000 × (7,660 / 9,655)
T33 = 2,380
T34 = 3,000 × ((486 × 1) /
((1,151 × 0.80) + (693 × 0.85) + (5,892 × 1.3) + (486 × 1)))
T34 = 3,000 × (486 / 9,655)
T34 = 151
T41 = 2,200 × ((1,151 × 0.65) /
((1,151 × 0.65) + (693 × 0.95) + (5,892 × 1) + (486 × 1.3)))
T41 = 2,200 × (748 / 7,930)
T41 = 208
T42 = 2,200 × ((693 × 0.95) /
((1,151 × 0.65) + (693 × 0.95) + (5,892 × 1) + (486 × 1.3)))
T42 = 2,200 × (658 / 7,930)
T42 = 183
T43 = 2,200 × ((5,892 × 1) /
((1,151 × 0.65) + (693 × 0.95) + (5,892 × 1) + (486 × 1.3)))
T43 = 2,200 × (5,892 / 7,930)
T43 = 1,634
T44 = 2,200 × ((486 × 1.3) /
((1,151 × 0.65) + (693 × 0.95) + (5,892 × 1) + (486 × 1.3)))
T44 = 2,200 × (632 / 7,930)
T44 = 175
Observe that the computed attractions approximately equal the given attractions.
A total convergence would be expected in another iteration.
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