The Diurnal Cycle of Regional Commuter Systems: North Wales, 1991

Places of household residence and places of commuter destination are considered in a contiguous system of subareas constituting a region. An intrahousehold distribution of household members, by subarea of their commuting destination, is considered for each subarea of residence. A household composition matrix is constructed in reference to the average number of commuters to subareas of destination, per household at a subarea of residence, across all subareas. The matrix is a linear transformation from the spatial distribution of households onto the spatial distribution of daytime population, over all subareas of the region. Diurnal population change throughout the region is rendered by this transformation. A linear optimization model extending this transformation formalizes general conditions that relate the diurnal population system to household choice of residence and work. Further, the division of the region into subareas is assumed to be such that the average household in each subarea contains at least one person who remains in the subarea during day and night. Under these conditions, the diurnal system is shown to be analogous to the Leontief input‐output model. An example of eleven counties of North Wales, along with an exogenous area of northwestern England, drawn from the 1991 census of the United Kingdom, illustrates the formal relationships.