Question

Calculate the future trip distribution based on the (a) uniform (b) average (c) Fratar (d) furness growth factor models using the existing trip matrix as presented in Table 6.72. The future trip productions and attraction for zone 1, 2, 3 and 4 are (90, 45), (70, 48), (52, 82) and (42, 66), respectively.

1. Calculate the future trip distribution based on the (a) uniform (b) average (c) Fratar (d) furness growth factor models using the existing trip matrix as presented in Table 6.72. The future trip productions and attraction for zone 1, 2, 3 and 4 are (90,45), (70, 48), (52,82) and (42, 66), respectively. TABLE 6.72 10+ lus islas 30 24 41 44 139

NOTE: PLEASE DETERMINE THE (c) Fratar AND (d) furness growth factor models using the existing trip matrix ONLY!!

Answer 1

Answer:

Given table:

Table 6.72
	1	2	3	4	P
1	10	4	15	16	45
2	5	8	14	13	40
3	8	7	5	6	26
4	7	5	7	9	28
	30	24	41	44	139

(c)

Fratar :

i\j	1	2	3	4	P	Pi	Fi	Li
1	10	4	15	16	45	90	2	0.58
2	5	8	14	13	40	70	1.75	0.56
3	8	7	5	6	26	52	2	0.57
4	7	5	7	9	28	42	1.5	0.58
aj	30	24	41	44
Aj	45	48	82	66
Fj	1.5	2	2	1.5
Lj	0.37	0.33	0.86	0.87

$L_{i}=\frac{P}{2T_{ij}^{b}\times F_{j}}$

$L_{i}=\frac{P_{1}}{T_{11} F_{1}+T_{12} F_{2}+T_{13} F_{3}+T_{14} F_{4}}$

Sample Calculations,

$L_{i}=\frac{45}{10\times 1.5+4\times1.75+15\times2+16\times1.5}$

L; = 0.58

Similarly,

$L_{j}=\frac{a_{j}^{b}}{2T_{ij}^{b}\times F_{j}}$

$L_{j}=\frac{30}{10\times 2+4\times1.75+15\times2+16\times1.5}$

$L_{j}=0.37$

1st Iteration:

i\j	1	2	3	4	P	Pi	Fi	Li
1	14	7	43	35	99	90	0.90	1.58
2	6	12	35	24	77	70	0.90	1.10
3	11	13	14	13	51	52	1.01	0.98
4	7	7	15	15	44	42	0.95	1.05
aj	38	39	107	87
Aj	45	48	82	66
Fj	1.18	1.23	0.76	0.75
Lj	0.69	0.62	1.69	1.66

$T_{ij}^{n}=T_{ij}^{b}\times F_{i}\times F_{j}\times \left ( \frac{L_{i}+L_{j}}{2} \right )$

$T_{ij}^{n}=10\times 2\times 1.5\times \left ( \frac{0.58+0.37}{2} \right )$

$T_{ij}^{n}=14$

Sample Calculation:

$L_{i}=\frac{P}{2T_{ij}^{b}\times F_{j}}$

$L_{i}=\frac{P_{1}}{T_{11} F_{1}+T_{12} F_{2}+T_{13} F_{3}+T_{14} F_{4}}$

$L_{i}=\frac{45}{10\times 1.8+4\times1.23+15\times0.76+16\times0.75}$

L; = 0.58

Similarly,

$L_{j}=\frac{a_{j}^{b}}{2T_{ij}^{b}\times F_{j}}$

$L_{j}=\frac{30}{10\times 0.90+4\times0.90+15\times1.01+16\times0.95}$

$L_{j}=0.69$

2nd iteration can be done in the similar way.

(d).

Furness growth factor:

i\j	1	2	3	4	P	Pi	O.G.F
1	10	4	15	16	45	90	2
2	5	8	14	13	40	70	1.75
3	8	7	5	6	26	52	2
4	7	5	7	9	28	42	1.5
aj	30	24	41	44
Aj	45	48	82	66
D.G.F	1.5	2	2	1.5

It's a column operation problem.

1st iteration is given by,

i\j	1	2	3	4	P	Pi	O.G.F
1	15	28	30	24	77	90	1.16
2	8	16	28	70	72	70	0.97
3	12	14	10	9	45	52	1.15
4	11	10	14	14	29	42	0.85
aj	46	48	82	67
Aj	45	48	82	66
D.G.F	0.97	1	1	0.98

$D.G.F=\frac{A_{j}}{a_{j}}=\frac{45}{46}=0.97$

$O.G.F=\frac{P_{i}}{P}=\frac{90}{77}=1.16$

$T_{ij}=T_{11}=10\times 1.5=15$,

$T_{12}=4\times 2=8$ etc...

2nd iteration can be done in the similar way.