Highway Engineering

vidual row does not sum to give the correct number of trips produced by each.
(It should be noted that the overall number of productions and attractions are
equal at the correct value of 121 000.)
In order to produce a final matrix where both rows and columns sum to their
correct values, a remedial procedure must be undertaken, termed the row-
column factor technique. It is a two-step process.
First, each row sum is corrected by a factor that gives the zone in question
its correct sum total (Table 2.20).
Second, because the column sums no longer give their correct summation,
these are now multiplied by a factor which returns them to their correct indi-
vidual totals (Table 2.21).
This repetitive process is continued until a final matrix is obtained where the
production and attraction value for each zone is very close to the correct row
and column totals (Table 2.22).

Forecasting Future Traffic Flows 39

Origin

Destination zone

Correct Row

zone A B C D E F G Total total factor

A5 905 1019 1 713 740 958 525 10 861 22 000 2.026

B 2053 2446 8 060 1 547 1 391 581 16 078 11 500 0.715

C 1388 9 587 4 791 1 201 1 861 633 19 461 17 500 0.899

D 1150 15 569 2361 5 418 3 947 1 094 29 540 14 500 0.491

E 1183 7 113 1409 12 898 2 818 4 498 29 919 26 500 0.886

F 500 2 088 712 3 066 920 2 970 10 256 17 500 1.706

G 200 638 177 622 1 074 2 174 4 886 11 500 2.354

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

Table 2.20Row correction of initial gravity model trip matrix

Origin

Destination zone

zone A B C D E F G Total

A011 962 2064 3 470 1 499 1 941 1 064 22 000

B 1468 0 1750 5 765 1 107 995 415 11 500

C 1249 8 621 0 4 308 1 080 1 673 569 17 500

D 565 7 642 1159 0 2 660 1 938 537 14 500

E 1048 6 301 1248 11 424 0 2 496 3 984 26 500

F 853 3 562 1216 5232 1 569 0 5 068 17 500

G 472 1 501 417 1 464 2 529 5 117 0 11 500

Total 5654 39 589 7854 31 663 10 443 14 160 11 636

Correct

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

Column

factor 1.145 1.033 1.035 0.984 1.044 0.929 0.885

Table 2.21Column correction of gravity model trip matrix