The Mathematical Representation of a Model of the Relationship Between Transport and Land Use.

This paper contains the mathematical description of a model that represents the relationships between transport and the spatial distribution of population, housing, jobs, employment, shopping and land. This paper complements the verbal description of the model elsewhere (Mackett, 1979b), and is intended for the reader interested in the detailed workings of the model. In the model, transport costs are measured in generalised costs units for the public and private modes. The demolition and building of housing are calculated within the model, taking any exogenous information into account. Economic activity is divided into twelve sectors which are allocated to three groups according to the degree of locational response to changes in transport costs. In the model a distinction is made between infrastructure, for example, houses and jobs, and the allocation of peoole to them. The allocation procedure ensures that those who have not moved retain the same residential or employment location over time. The distinction between infrastructure and activities means that inequalities in their provision, for example, vacant houses and jobs, are included. Land availability is taken into account in the location of activities. The equation system is solved using iterative techniques. After convergence a vide range of information is obtained, including the spatial distribution of population, housing and jobs, accessibility indicators, modal splits and time and money expenditure on travel.