Jean-Paul Rodrigue (2017), New York:
Routledge, 440 pages.
Author: Dr. Jean-Paul Rodrigue
The Lowry model was one of the first transportation / land use model
to be developed in 1964 for the Pittsburgh region. Even if its formulation
is rather simple, it depicts well the relationships between transportation
and land use. Its premises were expended by several other models, known
as "Lowry-type" models. The core assumption of the Lowry model
that regional and urban growth (or decline) is a function of
the expansion (or contraction) of the basic sector. This employment
is in turn having impacts on the employment of two other sectors; retail
Basic sector. Employment that meets non-local demand. It
produces good and services, which are exported outside the urban
area. It generates a centripetal capital flows into the city,
which results in economic growth and surpluses. Most industrial sector employment is within
this category. This sector is usually less
constrained by urban market accessibility considerations since the local market is
not the main outlet of the output. The basic sector is an exogenous element
of the Lowry model and must be provided.
Retail sector (non-basic sector). This employment is to
local demand such as retailing, food and construction. It does not export any finished goods and services
and use the region as its main market area. Since this sector
strictly serves the local / regional demand, location is an important
consideration. Employment levels are also assumed to be linked with the
local population through a multiplier effect. The retail sector is an endogenous element
of the Lowry model.
Residential sector. The number of residents is related to
the number of basic and retail jobs available. The choice of
a residential area is also closely linked to the place of work,
so the model tries to minimize commuting distances.
This consideration is an endogenous element of the Lowry
Employment in the basic sector influences the spatial distribution
of the population and of service employment. This level of influence
is related to transport costs, or the friction of distance. The
higher the friction of distance, the closer places of employment (basic
and non-basic) and residential areas are. Overall, the Lowry model has
2. Data Process Structure
The model aims to represent the residential structure and the
of employment and of services in an urban area. With an exogenous
spatial distribution of the basic sector employment and a set of
transport costs between zones, the model calculates total population
and employment by zone. It is composed of an
economic sub-model and a
spatial allocation sub-model, which are
subject to constraints.
- The residential sector, and thus urban land use, is a function
of employment. This function is calculated assuming the multiplier
effects of basic and non-basic employment. Each job is thus linked
to a number of people.
- The total employment is a function of the employment in the
basic sector and retail employment the result of multiplier
effects of basic sector employment.
- The location of the population is a function of the costs involved
to go to their place of work, commonly taking the form of a gravity-based friction of distance
The two sub-models require a set of basic data that is used to
solve the model in a series of steps:
- The economic sub-model provides the impacts of basic employment
on non-basic employment and the total population.
- The spatial allocation sub-model provides the distribution of the population
in function of attractiveness and transport costs. This is done by
a gravity-type spatial interaction model.
The Lowry model can be singly constrained, that is the only constraint
is the fixed location of basic employment. It can also be doubly constrained, where
the location of basic employment and housing are fixed. The singly constrained
Lowry model is solved according to these equations:
- The spatial distribution of basic employment is considered given.
- The location of the basic sector workers is determined according to
a location-probability matrix, itself the result of a least friction
of distance function.
- Calculation of the residential popualtion per zone according to
the population per worker multiplier.
- Calculation of the number of non-basic workers per zone to service
the population. This is the result of a non-basic worker per capita
- The location of non-basic workers is determined according to
a location-probability matrix.
- Recalculation of the total population according to the population
per worker multiplier.
- Calculation of the total number of workers and the total population.
This is the summation of the basic and non-basic employment and
of the basic and non-basic related population.
- Steps 4 to 7 are repeated until a convergence
is reached, that is an optimization of the equation system of the
model following a set of constrains such as density limitations.
The Lowry model has obviously several limitations. It is notably
a static model, which does not tell anything about the evolution
of the transportation / land use system. Furthermore, recent economic
changes are in the service (non-basic) sectors, forming the foundation
of urban productivity and dynamics in many metropolitan areas,
cannot be effectively represented. Under
such circumstances the model is likely to be inaccurate in major
service-oriented metropolitan areas. A way to overcome this
issue is to consider some non-basic service employment as basic.
Lowry model does not consider movements of freight in urban areas, which
are very significant and have impacts on the friction of distance.
- Tij = Interaction from residential zone i to work zone j (work-related
- Sij = Interaction from residential zone i to service zone j
- Pi = Total population of a zone i.
- Ei, EBi and ESi = Total employment, employment in the basic
(B) and service (S) sectors for zone i.
- dij = Euclidean distance between zone i and j (in km).
- Alpha = population over basic employment multiplier.
- Beta = service employment over population multiplier.
- Lambda: Friction factor for residential interactions.
- Micron: Friction factor for services interactions.
- WTTRij and WTTSij = Willingness to travel for Residential (R)
or Services (S) between zone i and j.
- LPRij and LPSij = Locational probability for Residential (R)
or Services (S) between zone i and j.
- Click here to download
an operational basic Lowry model (MS Excel format).