Highway Engineering

trips were attracted to zone A. Equation 2.3 is used to estimate what propor-

tion of this total amount sets out from each of the other six zones, based on

the relative number of trips produced by each of the six zones and the time taken

to travel from each to zone A. These computations are given in Table 2.18.

When an identical set of calculations are done for the other six zones using

the gravity model, the initial trip matrix shown in Table 2.19 is obtained.

It can be seen from Table 2.19 that, while each individual column sums to

give the correct number of trips attracted for each of the seven zones, each indi-

38 Highway Engineering

Zone Aj Pi Tij Fij Pi¥Fij

A 6475 22 000

B to A 11 500 10 0.010 115.0 0.317 2053.0

C to A 17 500 15 0.004 77.78 0.214 1388.5

D to A 14 500 15 0.004 64.44 0.178 1150.5

E to A 26 500 20 0.003 66.25 0.183 1182.7

F to A 17 500 25 0.002 28.00 0.077 499.80

G to A 11 500 32 0.001 11.23 0.031 200.50

S=362.7 S= 1 S= 6475

APF

PF

ji ij

Âj()iij

PF

PF

iij

Âj()iij

Table 2.18Gravity model computations for Zone A

Destination zone

Origin zone A B C D E F G Total

A5 905 1019 1 713 740 958 525 10 861

B 2053 2446 8 060 1 547 1391 581 16 078

C 1388 9 587 4 791 1 201 1861 633 19 461

D 1150 15 569 2361 5 418 3947 1 094 29 540

E 1183 7 113 1409 12 898 2818 4 498 29 919

F 500 2 088 712 3 066 920 2 970 10 256

G 200 638 177 622 1 074 2174 4 886

Total 6475 40 900 8125 31 150 10 900 13 150 10 300 121 000

Table 2.19Initial output from gravity model

Destination zone

Origin zone A B C D E F G

A101 515202532

B10751 01522

C15781 41626

D1 558 61018

E201014 6 16 12

F251 5161016 12

G322 226181212

Table 2.17Interzonal

travel times