assignment 1 (1)
DESCRIPTION
cven3301 assignment 1TRANSCRIPT
Question 1Given data:
Household Household Size Income Zone (Node)1 1 1 1 120000 A2 5 2 1 100000 C3 4 2 2 60000 B4 3 1 1 40000 B5 2 2 1 80000 A6 5 3 2 50000 C7 4 2 2 80000 C8 1 1 1 70000 A9 2 1 1 40000 B
10 6 3 3 50000 C11 2 2 1 40000 A12 5 2 1 50000 B13 2 2 1 80000 A14 3 2 2 100000 B15 5 2 2 120000 C
Workplace Number of Employe Yearly Profit Zone (Node)1 10 5 800000 E2 20 3 500000 D3 7 5 1200000 E4 20 10 2200000 E5 10 2 400000 D6 5 1 400000 D7 5 0 500000 E8 8 4 500000 E9 6 5 700000 D
10 5 2 400000 D
Given production and attraction equations:Production: #trips = 2/9 H.H.SIZE + 4/11 NUM.ADULTS + 2/15 NUM.VEH + 1/75000 INCOME Attraction: #trips = 2/5 NUM.EMPLOY. + 1/12 PARK.SIZE + 1/3,000,000 PROFIT
Number of Adults (>18)
Number of Vehicles
Parking Lot Size (in # spots)
Subbing in gives:Production: Attraction
1 2.3333333333333 1 4.683333333332 3.2666666666667 2 8.416666666673 2.6666666666667 3 3.616666666674 1.6666666666667 4 9.566666666675 2.4 5 4.36 3.1333333333333 6 2.216666666677 2.9333333333333 7 2.166666666678 1.6666666666667 8 3.79 1.4666666666667 9 3.05
10 3.4666666666667 10 2.311 1.866666666666712 2.613 2.414 315 3.6666666666667
10.666666666667 20.2833333333
11.4 23.7333333333
16.466666666667
Total production = 38.533333333333 Total attraction = 44.0166666667
Total at Node A (1, 5, 8, 11, 13) =
Total at Node D (2, 5, 6, 9, 10) =
Total at Node B (3, 4, 9, 12, 14) =
Total at Node E (1, 3, 4, 7, 8) =
Total at Node C (2, 6, 7, 10, 15) =
Question 2Given data:
A B C D E
9 14 16 21 17
f(cij) A B C Tij = Ki Oi Dj f(cij)D 20 20 45E 35 20 15
Calculate KiKi A B C
0.000985 0.001316 0.000833
Calculate TijTij A B C TargetD 3.724138 7.736842 12.6 20E 5.275862 6.263158 3.4 17Target 10 12 17 37/39
Check TijTij A B C SumD 3.044719 6.486486 11.63245 21.16366E 6.955281 5.513514 5.367546 17.83634Sum 10 12 17 39
Check # trips leaving match # trips producedf(cji) D EA 16 43B 21 21C 35 19
Calculate new KiKi D E
0.001002 0.001015
Calculate # tripsTji D E Target SumA 3.03006 6.679188 10 9.709248B 6.186373 5.074112 12 11.26048C 11.78357 5.246701 17 17.03027Target 20 17 37Sum 21 17 37
Production(#trips)
Attraction(#trips)
Ki = 1/∑j Dj f(cij)
Question 3Given data:
D EBUS IVTT OVTT COST IVTT OVTT COSTA 11 10 1.8 25 15 2B 19 15 1.7 20 10 2C 25 10 2 18 5 1.5
D EAUTO IVTT OVTT COST IVTT OVTT COSTA 15 2 5 22 3 12B 21 2 7 17 3 8C 24 2 7 12 3 4
Calculate U(BUS) = - 0.2*IVTT - 0.5*OVTT - COSTU(BUS) D EA -9 -14.5B -13 -11C -12 -7.6
Calculate P(BUS) = e^U(BUS)/(e^U(BUS)+e^U(AUTO))P(BUS) D EA 0.268941 0.916827B 0.141851 0.71095C 0.450166 0.331812
Calculate U(AUTO) = 1 - 0.2*IVTT - 0.5*OVTT - COSTU(AUTO) D EA -8 -16.9B -11.2 -11.9C -11.8 -6.9
Calculate P(AUTO) = e^U(AUTO)/(e^U(AUTO)+e^U(BUS))P(AUTO) D EA 0.731059 0.083173B 0.858149 0.28905C 0.549834 0.668188
Tji D E (from previous question and rounded to integer)A 3 7B 5 4C 12 5
Calculate T(BUS) = P(BUS)*TjiT(BUS) D E
A 1 7 (rounded to nearest integer)B 1 3C 5 2
Calculate T(AUTO) = P(AUTO)*TjiT(AUTO) D EA 2 1B 4 1C 6 4
Question 4.a)Given data:Tij D E For n iterations: Xi = (1/n)*X + (1-1/n)*Xold)A 10 20 For free flow, all X=0B 15 15C 20 5
Calculate cost of each path and use all or nothing to Calculate cost of each link apply method of successive averageX Iteration 1 Cost 1 Iteration 1A-1 0 0 Cost X Xold XiB-1 0 0 A-1-D 0 10 0 10B-2 0 0 A-1-3-D 1 0 0 0C-2 0 0 A-1-2-3-D 6 0 0 01-2 0 22-1 0 1 B-1-D 0 15 0 151-3 0 1 B-1-3-D 1 0 0 02-3 0 4 B-1-2-3-D 2 0 0 01-D 0 0 B-2-1-D 1 0 0 03-D 0 0 B-2-1-3-D 2 0 0 02-E 0 0 B-2-3-D 4 0 0 03-E 0 0
C-2-1-D 1 20 0 20C-2-1-3-D 2 0 0 0C-2-3-D 4 0 0 0
A-1-3-E 1 20 0 20A-1-2-3-E 6 0 0 0A-1-2-E 2 0 0 0
B-1-3-E 1 0 0 0B-1-2-3-E 6 0 0 0B-1-2-E 2 0 0 0B-2-1-3-E 2 0 0 0B-2-3-E 4 0 0 0B-2-E 0 15 0 15
C-2-1-3-E 2 0 0 0C-2-3-E 4 0 0 0C-2-E 0 5 0 5
Re-calculate with new cost functions For n iterations: Xi = (1/n)*X + (1-1/n)*Xold)X Iteration 2 Cost 2 Iteration 2A-1 30 30 Cost X Xold XiB-1 15 15 A-1-D 75 0 10 5B-2 15 15 A-1-3-D 111 0 0 0C-2 25 25 A-1-2-3-D 36 10 0 51-2 0 22-1 20 61 B-1-D 60 0 15 7.51-3 20 81 B-1-3-D 96 0 0 02-3 0 4 B-1-2-3-D 62 0 0 01-D 45 45 B-2-1-D 121 0 0 03-D 0 0 B-2-1-3-D 157 0 0 02-E 20 20 B-2-3-D 19 15 0 7.53-E 20 20
C-2-1-D 131 0 20 10C-2-1-3-D 167 0 0 0C-2-3-D 29 20 0 10
A-1-3-E 131 0 20 10A-1-2-3-E 56 0 0 0A-1-2-E 52 20 0 10
B-1-3-E 116 0 0 0B-1-2-3-E 41 0 0 0B-1-2-E 37 0 0 0B-2-1-3-E 177 0 0 0B-2-3-E 39 0 0 0B-2-E 35 15 15 15
C-2-1-3-E 187 0 0 0C-2-3-E 49 0 0 0C-2-E 45 5 5 5
For n iterations: Xi = (1/n)*X + (1-1/n)*Xold)X Iteration 3 Cost 3 Iteration 3A-1 30 30 Cost X Xold XiB-1 7.5 7.5 A-1-D 52.5 10 5 6.666667B-2 22.5 22.5 A-1-3-D 93.5 0 0 0C-2 25 25 A-1-2-3-D 118.5 0 5 3.3333331-2 15 172-1 10 31 B-1-D 30 15 7.5 101-3 10 41 B-1-3-D 71 0 0 02-3 22.5 49 B-1-2-3-D 69.5 0 0 01-D 22.5 22.5 B-2-1-D 76 0 0 03-D 22.5 22.5 B-2-1-3-D 117 0 0 02-E 30 30 B-2-3-D 94 0 7.5 53-E 10 10
C-2-1-D 78.5 20 10 13.33333C-2-1-3-D 119.5 0 0 0C-2-3-D 96.5 0 10 6.666667
A-1-3-E 81 0 10 6.666667A-1-2-3-E 106 0 0 0A-1-2-E 77 20 10 13.33333
B-1-3-E 58.5 0 0 0B-1-2-3-E 83.5 0 0 0B-1-2-E 54.5 0 0 0B-2-1-3-E 104.5 0 0 0B-2-3-E 81.5 0 0 0B-2-E 52.5 15 15 15
C-2-1-3-E 107 0 0 0C-2-3-E 84 0 0 0C-2-E 55 5 5 5
Question 4.b)Given data:Tij D E For n iterations: Xi = (1/n)*X + (1-1/n)*Xold)A 14 28 For free flow, all X=0B 21 21C 28 7
Calculate cost of each path and use all or nothing to Calculate cost of each link apply method of successive averageX Iteration 1 Cost 1 Iteration 1A-1 0 0 Cost X Xold XiB-1 0 0 A-1-D 0 14 0 14B-2 0 0 A-1-3-D 1 0 0 0C-2 0 0 A-1-2-3-D 6 0 0 01-2 0 22-1 0 1 B-1-D 0 21 0 211-3 0 1 B-1-3-D 1 0 0 02-3 0 4 B-1-2-3-D 2 0 0 01-D 0 0 B-2-1-D 1 0 0 03-D 0 0 B-2-1-3-D 2 0 0 02-E 0 0 B-2-3-D 4 0 0 03-E 0 0
C-2-1-D 1 28 0 28C-2-1-3-D 2 0 0 0C-2-3-D 4 0 0 0
A-1-3-E 1 28 0 28A-1-2-3-E 6 0 0 0A-1-2-E 2 0 0 0
B-1-3-E 1 0 0 0B-1-2-3-E 6 0 0 0B-1-2-E 2 0 0 0B-2-1-3-E 2 0 0 0B-2-3-E 4 0 0 0B-2-E 0 21 0 21
C-2-1-3-E 2 0 0 0C-2-3-E 4 0 0 0C-2-E 0 7 0 7
Re-calculate with new cost functions For n iterations: Xi = (1/n)*X + (1-1/n)*Xold)X Iteration 2 Cost 2 Iteration 2A-1 42 42 Cost X Xold XiB-1 21 21 A-1-D 105 0 14 7B-2 21 21 A-1-3-D 155 0 0 0C-2 35 35 A-1-2-3-D 48 14 0 71-2 0 22-1 28 85 B-1-D 84 0 21 10.51-3 28 113 B-1-3-D 134 0 0 02-3 0 4 B-1-2-3-D 86 0 0 01-D 63 63 B-2-1-D 169 0 0 03-D 0 0 B-2-1-3-D 219 0 0 02-E 28 28 B-2-3-D 25 21 0 10.53-E 28 28
C-2-1-D 183 0 28 14C-2-1-3-D 233 0 0 0C-2-3-D 39 28 0 14
A-1-3-E 183 0 28 14A-1-2-3-E 76 0 0 0A-1-2-E 72 28 0 14
B-1-3-E 162 0 0 0B-1-2-3-E 55 0 0 0B-1-2-E 51 0 0 0B-2-1-3-E 247 0 0 0B-2-3-E 53 0 0 0B-2-E 49 21 21 21
C-2-1-3-E 261 0 0 0C-2-3-E 67 0 0 0C-2-E 63 7 7 7
For n iterations: Xi = (1/n)*X + (1-1/n)*Xold)X Iteration 3 Cost 3 Iteration 3A-1 42 42 Cost X Xold XiB-1 10.5 10.5 A-1-D 73.5 14 7 9.333333B-2 31.5 31.5 A-1-3-D 130.5 0 0 0C-2 35 35 A-1-2-3-D 163.5 0 7 4.6666671-2 21 232-1 14 43 B-1-D 42 21 10.5 141-3 14 57 B-1-3-D 99 0 0 02-3 31.5 67 B-1-2-3-D 96.5 0 0 01-D 31.5 31.5 B-2-1-D 106 0 0 03-D 31.5 31.5 B-2-1-3-D 163 0 0 02-E 42 42 B-2-3-D 130 0 10.5 73-E 14 14
C-2-1-D 109.5 28 14 18.66667C-2-1-3-D 166.5 0 0 0C-2-3-D 133.5 0 14 9.333333
A-1-3-E 113 0 14 9.333333A-1-2-3-E 146 0 0 0A-1-2-E 107 28 14 18.66667
B-1-3-E 81.5 0 0 0B-1-2-3-E 114.5 0 0 0B-1-2-E 75.5 0 0 0B-2-1-3-E 145.5 0 0 0B-2-3-E 112.5 0 0 0B-2-E 73.5 21 21 21
C-2-1-3-E 149 0 0 0C-2-3-E 116 0 0 0C-2-E 77 7 7 7