Highway Engineering

As illustrated by Equations 2.2 and 2.3, the gravity model can be used to dis-
tribute either the productions from zone ior the attractions to zone j.If the cal-
culation shown in Example 2.1 is carried out for the other five zones so that T 2 j,
T 3 j,T 4 j,T 5 j and T 6 jare calculated, a trip matrix will be generated with the rows
of the resulting interchange matrix always summing to the number of trips pro-
duced within each zone because of the form of Equation 2.2. However, the
columns when summed will not give the correct number of trips attracted to
each zone. If, on the other hand, Equation 2.3 is used, the columns will sum
correctly whereas the rows will not. In order to generate a matrix where row and
column values sum correctly, regardless of which model is used, an iterative cor-
rection procedure, termed the row–column factor technique, can be used. This
technique is demonstrated in the final worked example in section 2. It is
explained briefly here.

Forecasting Future Traffic Flows 25

Example 2.3 Contd

Table 2.5 details the sequence involved in the calculation of all five trip

volumes,T 12 ,T 13 ,T 14 ,T 15 ,T 16.

TP AF 12 1 2 12 AFjj 1

10000 2114 2597

8143

=¥ ¥[]()∏¥()

=¥∏()

=

Â

Generalised cost

Zone (travel time in mins.) Productions Attractions

110000 15 000

257500 45 000

31015000 25 000

41512500 12 500

520 8 000 15 000

625 5 000 20 000

Table 2.4Trip

productions, attractions

and travel times

between zones

Zone Aj Ci, j Fi, j AjFi, j T1, j

115000

245000 5 0.047 2114 0.814 8143

325000 10 0.013 315 0.121 1212

412500 15 0.006 73 0.028 280

515000 20 0.003 51 0.020 195

620000 25 0.002 44 0.017 170

S 2597 1.000 10 000

AF

F

jij

ij

j

Â()

Table 2.5Estimation of

trip volumes between

zone 1 and zones 2 to 6