The sequence involved in the Furness method is:
(1) The origin growth factor is calculated for each row of the trip interchange
matrix using the following formula(2.11)
(2) Check whether the origin growth factors are within approximately 5% of
unity. If they are, the procedure is not required. If they are not, proceed
to the next step
(3) Multiply the cells in each column ofTtijby its origin growth factor Gtti¢to
produce the first version of the revised matrix Ttij¢
(4) The destination growth factor is calculated for each column of the trip
interchange matrix using the following formula:(2.12)
(5) Check whether the destination growth factors are within approximately 5%
of unity. If they are, the procedure is not required. If they are not, proceed
to the next step
(6) Multiply the cells in each row of the first version ofTtij¢by its destination
growth factor Gtti¢to produce the second version ofTtij¢
(7) Recalculate the origin growth factor:(2.13)
(8) Proceed back to point 2.
(9) Repeat the process until both the origin or destination growth factors being
calculated are sufficiently close to unity (within 5% is usually permissible).GO Titt¢¢= ijij t
GD Tttj¢¢= j Âi ijt
GO Titt¢= ijij t
28 Highway Engineering
Example 2.4 – Furness method of trip distribution
Table 2.6 gives the matrix of present flows to and from four zones within a
transportation study area. It also provides the total number of trips predicted
to start from zone i, and the total number of trips predicted to terminate in
zone j. Calculate the final set of distributed flows to and from the four zones.Solution
Table 2.7 gives the origin and destination growth factors.
Table 2.8 multiplies all the trip cells by the appropriate origin growth
factors and a new set of destination growth factors are estimated. These are
well outside unity.
Table 2.9 multiplies all trip volumes in Table 2.8 by the amended destina-
tion growth factors to give a new matrix. From these a new set of origin
growth factors are estimated. The factors are still not within 5% of unity.
Tables 2.10 to 2.13 repeat the above sequence until the factors are seen to
be within 5% of unity.
Contd