Highway Engineering

Assuming Equation 2.2 is used, the rows will sum correctly but the columns

will not. The first iteration of the corrective procedure involves each value ofTij

being modified so that each column will sum to the correct total of attractions.

(2.5)

Following this initial procedure, the rows will no longer sum correctly. There-

fore, the next iteration involves a modification to each row so that they sum to

the correct total of trip productions.

(2.6)

This sequence of corrections is repeated until successive iterations result in

changes to values within the trip interchange matrix less than a specified per-

centage, signifying that sufficient convergence has been obtained. If Equation

2.3 is used, a similar corrective procedure is undertaken, but in this case the

initial iteration involves correcting the production summations.

2.5.3 Growth factor models

The cells within a trip matrix indicate the number of trips between each origin-

destination pair. The row totals give the number of origins and the column totals

give the number of destinations. Assuming that the basic pattern of traffic does

not change, traffic planners may seek to update the old matrix rather than

compile a new one from scratch. The most straightforward way of doing this is

by the application of a uniform growth factor where all cells within the existing

matrix are multiplied by the same value in order to generate an updated set of

figures.

(2.7)

where

Ttij¢=Trips from zone ito zone jin some future forecasted year t¢

Tijt =Trips from zone ito zone jin the present year under observation t

Gtt¢=Expected growth in trip volumes between year tand year t¢

One drawback of this approach lies in the assumption that all zones will grow

at the same rate. In reality, it is likely that some will grow at a faster rate than

others. An approach that allows for such situations is the singly-constrained

growth factor approach, which can be applied to either origin or destination

data, but not both. The former application is termed the origin constrained

growth factor method where a specific growth factor is applied to all trips orig-

inating in zone i (see Equation 2.8 below), while the latter is termed the desti-

TTGijt¢¢=¥ijttt

¢=

Â

T

P

ij T

i

ij

i

¢=

Â

T

A

ij T

j

ij

j

26 Highway Engineering