Adaptive zoning and its effectiveness in spatial economic activity simulation

In modelling spatial economic interactions such as embodied in the movements of people and goods, the study area is usually subdivided into geographic units, i.e. zones, to represent the origin, destination and any stop-over locations. In most cases, model precision tends to improve as the study area is subdivided into increasingly small zones. Smaller zones however come at the cost of increased run-time. In practice the modeller often has to compromise on the resolution or the geographic coverage, which impinges upon model accuracy and applicability. Current trends in spatial economic interactions are calling for larger study areas and finer spatial details: As transport and telecommunications improve, the realm of spatial interaction continues to expand. Furthermore, the rapid expansion in e-monitoring of the movements of goods and people is offering ever-increasing spatial detail. The combined impact is a strong need to expand spatial model coverage whilst capturing local details. This paper reports on the development of an innovative zoning. The basic idea is to use more detailed zoning where interaction is stronger, e.g. at shorter distance or between higher density areas. Instead of a single zonal division for the whole study area, the zoning scheme consists of one specific zonal division for each respective location (atomic zone) in the study area, adapted to the interaction flows to and from that location. Incorporating this adaptive zoning scheme improves the scaling behaviour of spatial interaction and choice models, as the number of interactions per zone is no longer equal to the number of zones, but - depending on the precise nature of the interaction - logarithmic to it instead. The adaptive zoning scheme will require models to be adjusted to the new geographical representation. This paper will therefore detail the required modifications to a typical doubly-constrained spatial interaction model. Application on commuting patterns in England demonstrates that the adoptive zoning scheme can reduce the number of spatial interactions by as much as 95% whilst maintaining a fine granularity.