Forecasting Future Traffic Flows 23
Zone of origin Zone of destination
1234 ◊◊◊◊
1T 11 T 12 T 13 T 14 ◊◊◊◊
2T 21 T 22 T 23 T 24 ◊◊◊◊
3T 31 T 32 T 33 T 34 ◊◊◊◊
4T 41 T 42 T 43 T 44 ◊◊◊◊
◊ ◊◊◊.
◊ ◊◊◊◊
◊ ◊◊◊◊
Table 2.3Origin-
destination matrix (e.g.
T 14 =number of trips
originating in zone 1
and ending in zone 4)
between origins and destinations, termed an origin-destination matrix. Its layout
is illustrated in Table 2.3.
There are several types of trip distribution models, including the gravity
model and the Furness method.
2.5.2 The gravity model
The gravity model is the most popular of all the trip distribution models. It
allows the effect of differing physical planning strategies, travel costs and trans-
portation systems to be taken into account. Within it, existing data is analysed
in order to obtain a relationship between trip volumes and the generation and
attraction of trips along with impedance factors such as the cost of travel.
The name is derived from its similarity to the law of gravitation put forward
by Newton where trip interchange between zones is directly proportional to the
attractiveness of the zones to trips, and inversely proportional to some function
of the spatial separation of the zones.
The gravity model exists in two forms:
(2.2)
or
(2.3)
where
Tij=trips from zone i to zone j
Aj=trip attractions in zone j
Pi=trip productions in zone i
Fij=impedance of travel from zone i to zone j
The impedance term, also called the deterrence function, refers to the resistance
associated with the travel between zone iand zone jand is generally taken as a
T
APF
ij PF
ji ij
iij
j
=
Â()
T
PA F
AF
ij
ijij
jij
j
=
Â()