Exercise 4 Trip distribution

Work trips
1 2 3 4 5 6 Oi
1 636
2 898
3 1,274
4 4,301
5 5,416
6 5,575
Dj 9050 2,715 2,715 905 905 1,810 18,100

Service / Other trips

1 2 3 4 5 6 Oi
1 142
2 2,557
3 1,843
4 6,220
5 7,833
6 8,063
Dj 13,440 1,460 1,470 1,840 2,150 2,430
22,790

The results from the trip production- and attraction-calculations are presented in the two tables a
Below you fin the cost matrix for this town expressed in generalized cost (time + cost)

Cost matrix (generalized cost)

1 2 3 4 5 6
1 7 12 14 20 23 27
2 12 5 13 15 17 23
3 14 13 5 20 17 13
4 20 15 20 8 13 15
5 23 17 17 13 8 14
6 27 23 13 15 14 10
For the work trips you shall use a double constrained gravity model with a deterrence-function lik
For the service / other trips you shall use a single constrined gravity model with a deterrence fun
and a = 0,2

Work trips
beta= 0.4

1 2 3 4 5 6 Sum
1 4,155.4 1,004.8 944.8 273.0 258.2 484.3 7,120.5
2 3,349.5 1,426.2 973.2 306.3 291.4 516.4 6,863.0
3 3,149.2 973.2 1,426.2 273.0 291.4 648.8 6,761.8
4 2,730.5 919.0 819.1 393.9 324.4 612.7 5,799.7
5 2,582.0 874.2 874.2 324.4 393.9 629.8 5,678.5
6 2,421.6 774.6 973.2 306.3 314.9 720.6 5,511.2

Basic single constrained model

1 2 3 4 5 6 Sum
1 371 90 84 24 23 43 636
2 438 187 127 40 38 68 898
3 593 183 269 51 55 122 1,274
4 2,025 682 607 292 241 454 4,301
5 2,463 834 834 309 376 601 5,416
6 2,450 784 984 310 319 729 5,575
8,340 2,759 2,906 1,027 1,051 2,017
1.09 0.98 0.93 0.88 0.86 0.90

1. iteration
1 2 3 4 5 6 Sum
1 403 88 79 21 20 39 650
2 476 184 119 35 33 61 907
3 644 180 251 45 47 110 1,278
4 2,197 671 568 257 207 408 4,308
5 2,672 821 779 273 324 539 5,407
6 2,658 771 920 273 274 654 5,550
9,050 2,715 2,715 905 905 1,810
1.00 1.00 1.00 1.00 1.00 1.00

2. iteration
1 2 3 4 5 6 Sum
 1 394 86 77 21 19 38 636
2 471 182 118 35 33 60 898
3 642 180 250 45 47 109 1,274
4 2,194 670 567 257 207 407 4,301
5 2,677 822 780 273 324 540 5,416
6 2,670 775 924 274 276 657 5,575
9,047 2,714 2,716 905 906 1,811
1.00 1.00 1.00 1.00 1.00 1.00
Dj 9050 2715 2715 905 905 1810

1-5 6 - 10 11 - 15 16 - 20 21 - 25 26 - 30 Sum
432 1,632 5,289 4,508 3,531 2,708 18,100
4 8 13 18 23 28
1,729 13,056 68,752 81,152 81,209 75,821 321,720

Trips-cost distribution
Work trips
6,000
Number of trips

5,289
5,000
4,508

4,000
3,531

3,000 2,708

2,000
1,632

1,000
432

-
1-5 6 - 10 11 - 15 16 - 20 21 - 25 26 - 30
Cost intervals
 1,632

1,000
432

-
1-5 6 - 10 11 - 15 16 - 20 21 - 25 26 - 30
Cost intervals
 26,659

nted in the two tables above

time + cost)
 deterrence-function like a power-function; F = c ij-b and b= 0,7
el with a deterrence function like a exponential function; F = exp(- a cij)

Service / other trips

alfa = 0.1

1 2 3 4
1 6,674.1 439.7 362.5 249.0
2 4,048.1 885.5 400.6 410.6
3 3,314.3 397.9 891.6 249.0
4 1,818.9 325.8 198.9 826.8
5 1,347.5 266.7 268.5 501.5
6 903.2 146.4 400.6 410.6

Basic single constraint matrix

1 2 3 4
1 117 8 6 4
2 1,622 355 161 165
3 1,034 124 278 78
4 2,632 471 288 1,196
5 2,672 529 533 995
6 2,217 359 983 1,008
10,294 1,846 2,249 3,445
Dj 13,440 1,460 1,470 1,840

0.98 1-5 6 - 10 11 - 15 16 - 20
0.99 633 5,423 10,905 4,343
1.00 4.0 8.0 13.0 18.0
1.00 2,532 43,388 141,766 78,181
1.00
1.00

Trip-cost distribution
Service / other trips (single constrain
Number of trips

12,000
10,905

10,000
 Trip-cost distribution
Service / other trips (single constrain

Number of trips
1.00 12,000
1.00 10,905
1.00 10,000
1.00
1.00 8,000
1.00
6,000 5,423
4,343
4,000

2,000
633
-
17.8 1-5 6 - 10 11 - 15 16 - 20
Cost intervals

Making the model double constrained by adjusting the attractions p

Corrected attractions:
1 2 3 4
15722 1708 1720 2152

Basic single constraint matrix

1 2 3 4
1 117 8 6 4
2 1,622 355 161 165
3 1,034 124 278 78
4 2,632 471 288 1,196
5 2,672 529 533 995
6 2,217 359 983 1,008
10,294 1,846 2,249 3,445
2,708 Dj 15,722 1,708 1,720 2,152
1.53 0.92 0.76 0.62

1. iteration
1 2 3 4
1 179 7 5 3
2 2,477 328 123 103
3 1,579 115 213 49
4 4,020 436 220 747

26 - 30
 5 4,081 489 407 621
6 3,386 332 752 630
26 - 30 15,722 1,708 1,720 2,152
Dj 15,722 1,708 1,720 2,152
1.00 1.00 1.00 1.00

2. iteration
1 2 3 4
1 129 5 3 2
2 1,989 264 99 83
3 1,349 98 182 41
4 3,899 423 214 725
5 4,284 514 427 652
6 3,767 370 837 701
15,418 1,673 1,761 2,204
Dj 15,722 1,708 1,720 2,152
1.02 1.02 0.98 0.98

3. iteration
1 2 3 4
1 131 5 3 2
2 2,029 269 96 81
3 1,376 100 177 40
4 3,976 432 208 708
5 4,369 524 417 637
6 3,842 377 817 684
15,722 1,708 1,720 2,152
Dj 15,722 1,708 1,720 2,152
1.00 1.00 1.00 1.00

4. iteration
1 2 3 4
1 129 5 3 2
2 2,001 265 95 80
3 1,364 99 176 40
4 3,962 430 208 706
5 4,375 525 418 638
6 3,871 380 823 690
15,703 1,705 1,723 2,155
Dj 15,722 1,708 1,720 2,152
 1.00 1.00 1.00 1.00

1-5 6 - 10 11 - 15 16 - 20
441 3,442 8,816 5,282
4.0 8.0 13.0 18.0
1,765 27,538 114,603 95,077

Trip-cost distribution
Service / other trips (doble constraint)
Number of trips
10,000
9,000
8,000
7,000
6,000
5,000
4,000
3,000
2,000
1,000
-
1-5 6 - 10 11 - 15 16 - 20 21 - 25
Cost intervals
 5 6 Sum
215.6 163.3 8,104.2
392.8 243.6 6,381.2
392.8 662.3 5,907.8
585.9 542.2 4,298.5
966.1 599.2 3,949.5
530.2 893.9 3,284.9

5 6 Sum
4 3 142
157 98 2,557
123 207 1,843
848 785 6,220
1,916 1,188 7,833
1,301 2,194 8,063
4,349 4,474 26,658
2,150 2,430 22,790

21 - 25 26 - 30 Sum
3,133 2,220 26,658
23.0 28.0 15.0
72,062 62,157 400,087

stribution
her trips (single constraint)

10,905
stribution
her trips (single constraint)

10,905

4,343
3,133
2,220

11 - 15 16 - 20 21 - 25 26 - 30
Cost intervals

y adjusting the attractions proportionally

5 6 SUM
2515 2843 26659

5 6 Sum
4 3 142
157 98 2,557
123 207 1,843
848 785 6,220
1,916 1,188 7,833
1,301 2,194 8,063
4,349 4,474 26,658
2,515 2,843 26,659
0.58 0.64

5 6 Sum
2 2 197 142 0.72
91 62 3,184 2,557 0.80
71 131 2,157 1,843 0.85
490 498 6,412 6,220 0.97
1,108 755 7,462 7,833 1.05
753 1,394 7,246 8,063 1.11
2,515 2,843 26,659
2,515 2,843 26,659
1.00 1.00

5 6 Sum
2 1 142 142 1.00
73 50 2,557 2,557 1.00
61 112 1,843 1,843 1.00
476 484 6,220 6,220 1.00
1,163 793 7,833 7,833 1.00
837 1,551 8,063 8,063 1.00
2,611 2,990 26,658
2,515 2,843 26,659
0.96 0.95

5 6 Sum
2 1 144 142 0.98
70 47 2,592 2,557 0.99
58 107 1,859 1,843 0.99
458 460 6,242 6,220 1.00
1,120 753 7,821 7,833 1.00
807 1,474 8,001 8,063 1.01
2,515 2,843 26,659
2,515 2,843 26,659
1.00 1.00

5 6 Sum
1 1 142 142 1.00
69 47 2,557 2,557 1.00
58 106 1,843 1,843 1.00
456 458 6,220 6,220 1.00
1,122 755 7,833 7,833 1.00
813 1,486 8,063 8,063 1.00
2,520 2,852 26,658
2,515 2,843 26,659
 1.00 1.00

21 - 25 26 - 30 Sum
4,804 3,873 26,658
23.0 28.0 17.2
110,493 108,435 457,912

on
s (doble constraint)

1 - 15 16 - 20 21 - 25 26 - 30
Cost intervals
Exercise 4 Trip distribution

Work trips
1 2 3 4 5 6
1
2
3
4
5
6
Dj 9050 2,715 2,715 905 905 1,810

Service / Other trips

1 2 3 4 5 6
1
2
3
4
5
6
Dj 13,440 1,460 1,470 1,840 2,150 2,430
22,790

The results from the trip production- and attraction-calculations are presented in the two ta
Below you fin the cost matrix for this town expressed in generalized cost (time + cost)

Cost matrix (generalized cost)

1 2 3 4 5 6
1 7 12 14 22 23 27
2 12 5 13 15 17 23
3 14 13 5 20 17 13
4 22 15 20 8 13 16
5 23 17 17 13 8 14
6 27 23 13 16 14 10

a) For the work trips you shall use a double constrained gravity model with a deterrence-func
b) For the service / other trips you shall use a single constrained gravity model with a deterre
and a = 0,2
 c) Adjust the zonal attractions so they match the sum of zonal productions. Then use a doubl

d) For the service / other trips there exist an observed trip-cost distribution (table 1, figur 1). W

1-5 6 - 10 11 - 15 16 - 20 21 - 25 26 - 30 Sum
698 6,000 9,490 4,990 3,590 1,990 26,758
Avg.int.cost 4.0 8.0 13.0 18.0 23.0 28.0
Trips*cost 2,792 48,000 123,370 89,820 82,570 55,720 402,272

Table 1: Observed trip cost distribution for service / other trips

Observed trip-cost distribution

Service / other trips
Nuber of trips

10,000 9,490
9,000
8,000
7,000
6,000
6,000
4,990
5,000
4,000 3,590
3,000
1,99
2,000
1,000 698

-
1-5 6 - 10 11 - 15 16 - 20 21 - 25 26 -
Cost intervals

Figur 1 Observed trip-cost distribution service / other trips

 Oi
636
898
1,274
4,301
5,416
5,575
18,100

Oi
142
2,557
1,843
6,220
7,833
8,063 26,659

presented in the two tables above

cost (time + cost)

with a deterrence-function like a power-function; F = c ij-b and b= 0,7

y model with a deterrence function like a exponential function; F = exp(- a cij)
ons. Then use a double constraint model. Can you investigate the differences in the model properties ?

ion (table 1, figur 1). Which deterrence function and what parameter will give you "the best fit" ?

Avg.cost

15.0

3,590

1,990

21 - 25 26 - 30
model properties ?

e best fit" ?