Question

4. (10 points) Using Microsoft Excel spreadsheet, solve the trip distribution problem to obtain O/D trip tables by the following doubly constrained Gravity model. - Trip Productions and Attractions ? Zone 1 2 3 4 1 2 3 4 T O 200 560 450 610 1,820 Ti Di 160 380 500 780 - Travel Impedance Matrix ($c_{ij}$) ? Zone 1 2 3 4 1 3 11 18 22 2 12 3 13 19 3 15.5 13 5 7 4 24 18 8 5 - Travel Impedance Function ? $f(c_{ij}) = c_{ij}^{1.5}e^{-0.05c_{ij}}$ - Doubly Constrained Gravity Model $T_{ij} = A_i \cdot O_i \cdot B_j \cdot D_j \cdot f(c_{ij})$ where $A_i = \frac{1}{\sum_{j=1}^4 [B_j \cdot D_j \cdot f(c_{ij})]}$ $B_j = \frac{1}{\sum_{i=1}^4 [A_i \cdot O_i \cdot f(c_{ij})]}$ Criterion of Convergence (COC) Stop iteration, if for each $O_i$ or $D_i$, $COC = (T_i - O_i)^2$ or $(T_i - D_i)^2 < 0.01.$

          4. (10 points) Using Microsoft Excel spreadsheet, solve the trip distribution problem to obtain O/D trip
tables by the following doubly constrained Gravity model.
- Trip Productions and Attractions
?
Zone
1
2
3
4
1
2
3
4
T
O
200
560
450
610
1,820
Ti
Di
160
380
500
780
- Travel Impedance Matrix ($c_{ij}$)
?
Zone
1
2
3
4
1
3
11
18
22
2
12
3
13
19
3
15.5
13
5
7
4
24
18
8
5
- Travel Impedance Function
?
$f(c_{ij}) = c_{ij}^{1.5}e^{-0.05c_{ij}}$
- Doubly Constrained Gravity Model
$T_{ij} = A_i \cdot O_i \cdot B_j \cdot D_j \cdot f(c_{ij})$
where
$A_i = \frac{1}{\sum_{j=1}^4 [B_j \cdot D_j \cdot f(c_{ij})]}$
$B_j = \frac{1}{\sum_{i=1}^4 [A_i \cdot O_i \cdot f(c_{ij})]}$
Criterion of Convergence (COC)
Stop iteration, if for each $O_i$ or $D_i$, $COC = (T_i - O_i)^2$ or $(T_i - D_i)^2 < 0.01.$

4. (10 points) Using Microsoft Excel spreadsheet, solve the trip distribution problem to obtain O/D trip
tables by the following doubly constrained Gravity model.
- Trip Productions and Attractions
?
Zone
1
2
3
4
1
2
3
4
T
O
200
560
450
610
1,820
Ti
Di
160
380
500
780
- Travel Impedance Matrix (cij)
?
Zone
1
2
3
4
1
3
11
18
22
2
12
3
13
19
3
15.5
13
5
7
4
24
18
8
5
- Travel Impedance Function
?
f(cij) = cij^1.5e^-0.05cij
- Doubly Constrained Gravity Model
Tij = Ai · Oi · Bj · Dj · f(cij)
where
Ai = (1)/(∑j=1^4 [Bj · Dj · f(cij)])
Bj = (1)/(∑i=1^4 [Ai · Oi · f(cij)])
Criterion of Convergence (COC)
Stop iteration, if for each Oi or Di, COC = (Ti - Oi)^2 or (Ti - Di)^2 < 0.01.

Added by Ashley B.

Question

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