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regional network of public transport in Montreal at two dates [MOR 06]. The set is
composed of the persons' residences. By comparison, the dispersion of residents
taking public transportation does not evolve between 1987 and 1998, while those of
individuals not taking any transport evolved considerably. This type of insight,
essentially spatial, allows us to question the adequacy of the offer of transportation
in a context of deployment of peri-urban places of residence for persons working in
Montreal.
The indicators used to describe the transformation of a spatial organization can
also be the result of statistical modeling. If we consider, for example, the gravity
model
5
(presented in Chapter 2) that consists of modeling the intensity of exchanges
between places in proportion to the masses of places and in inverse proportion to the
distance between them [HAG 65, TAY 77]. It can be used diachronically to show,
for example, the evolution of the parameter associated with the distance, called the
distance friction, at several dates. Thus, if it is used to model the commuting
characterizing an urban area, the model will be expressed as:
F
i,i,t
=k(t) M
it
.M
i't
/D
b(t)
ii't
where F
i,i't
is the value of the commuting flow between the municipalities i and i' at
the date t, M
it
and M
i't
are, respectively, the active population residing in
the municipality i and the jobs of the municipality i' at the date t, and D
ii'
is the
distance separating the two municipalities. All the quantities are likely to evolve in
time. The two parameters k(t) and b(t) represent the mobility rate (the share of
effective exchanges among the exchanges theoretically possible) and the distance
friction (the dissuasive effect of the distance). The variation of the distance friction
during time b(t1), b(t2), b(t3), etc. gives a new image of the exchanges' follow-up
over time: it allows us to assess the role of the distance in the change and approach
that of the range of a labor center's attraction area. A similar approach can be
developed from Clark's model (also presented in Chapter 2), which allows the
decrease of cities' density to be modeled as a function of the distance to the center
[MAT 00]. In this case, it is the population that is modeled for a set of municipalities
in the region of the Rhone valley in France (around Valence):
P(i,t) = a
t
exp(-b
t
x
i
)
5 In its most general form, the gravity model is written: Fi,i′=k Mi.Mi′/D
b
ii
' where Fi,i′ is the
value of the exchange between the places i and i′, Mi (respectively, Mi′) are the weights
associated with each of the places assessing the emitting capacity of i (respectively, receiving
i′) and Dii′ is the distance between the two places.
