The Lowry Model

Author: Dr. Jean-Paul Rodrigue

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1. Concepts

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 assumes 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 and residential.

Basic sector. Employment that meets non-local demand. It produces good and services, which are exported outside the urban area. It generates a centripetal flow of capital into the city generating growth and surpluses. Most industrial sector employment is within this category. It is generally assumed that this sector is less constrained by urban location problems since the local market is not the main concern. This consideration is an exogenous element of the Lowry model and must be given.

Retail sector (non-basic sector). This employment meets the local demand. It does not export any finished goods and services and use the region as its main market area. It accounts mostly for services such as retailing, food and construction. Since this sector strictly serves the local / regional demand, location is an important concern. Employment levels are also assumed to be linked with the local population. This consideration is an endogenous element of the Lowry model.

Residential sector. The number of residents is related to to the number of basic and retail jobs available. The choice of a residential area is also closely linked to the place of work. This consideration is an endogenous element of the Lowry model.

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 three assumptions:

• The residential sector, and thus urban land use, is a function of employment. This function is calculated assuming 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. The retail employment is thus the result of a multiplier effects on the basic sector.
• The location of the population is a function of the costs involved to go to their place of work, a gravity-based friction of distance function.

2. Data Process Structure

The model aims to establish a representation of the residential structure, 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 first sub-model establish the impacts of the basic employment over the non-basic employment and over the population.
• The second sub-model establish the distribution of the population in function of attractivity and transport costs. This is done by a gravity-type spatial interaction model.

The two sub-models require a set of basic data and resolve the problem as follows:

1. The spatial distribution of basic employment is assumed as given.
2. The location of the basic workers is determined according to a location-probability matrix, itself the result of a least friction of distance function.
3. Calculation of the residential sector per zone according to the population per worker multiplier.
4. 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 multiplier.
5. The location of non-basic workers is determined according to a location-probability matrix.
6. Revision of the total population according to the population per worker multiplier.
7. 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.
8. The above processes (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.

3. Variables and Model

The model can be singly constrained, that is the only constraint is the fixed location of basic employment, as it is the case for the below set of equations. 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:

• Tij = Interaction from residential zone i to work zone j (work-related travel).
• Sij = Interaction from residential zone i to service zone j (service-related travel).
• 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.

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, current economic changes are in the service (non-basic) sectors, forming the foundation of urban productivity and dynamics in many metropolitan areas. Under such circumstances the model is likely the be inaccurate in the major service-oriented metropolitan areas of today. A way to overcome this issue is to consider some non-basic service employment as basic. The Lowry model does not consider movements of freight in urban areas, which are very significant and have impacts on the friction of distance.

• Click here to download an operational basic Lowry model (MS Excel format).