function of the cost of travel, travel time or travel distance between the two
zones in question. One form of the deterrence function is:
Fij=C-aij (2.4)The impedance function is thus expressed in terms of a generalised cost func-
tion Cijand the aterm which is a model parameter established either by
analysing the frequency of trips of different journey lengths or, less often, by
calibration.
Calibration is an iterative process within which initial values for Equation 2.4
are assumed and Equation 2.2 or 2.3 is then calculated for known productions,
attractions and impedances computed for the baseline year. The parameters
within Equation 2.4 are then adjusted until a sufficient level of convergence is
achieved.24 Highway Engineering
Example 2.3 – Calculating trip distributions using the gravity model
Taking the information from an urban transportation study, calculate the
number of trips from the central business zone (zone 1) to five other sur-
rounding zones (zone 2 to zone 6).
Table 2.4 details the trips produced by and attracted to each of the six
zones, together with the journey times between zone 1 and the other five
zones.
Use Equation 2.2 to calculate the trip numbers. Within the impedance
function, the generalised cost function is expressed in terms of the time taken
to travel between zone 1 and each of the other five zones and the model para-
meter is set at 1.9.Solution
Taking first the data for journeys between zone 1 and zone 2, the number of
journeys attracted to zone 2,A 2 , is 45 000. The generalised cost function for
the journey between the two zones is expressed in terms of the travel time
between them: 5 minutes. Using the model parameter value of 1.9, the deter-
rence function can be calculated as follows:This value is then multiplied by A 2 :Summing (Aj¥F 1 j) for j= 2 Æ6 gives a value of 2114 (see Table 2.5)
This value is divided into A 2 , and multiplied by the number of trips pro-
duced by zone 1 (P 1 ) to yield the number of trips predicted to take place from
zone 1 to zone 2, i.e.AF^212 ¥=^2114
F^12
=∏ 15 ()^19. = 0. 047
Contd