Highway Engineering

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()