Adaptive zoning and its effectiveness in spatial economic activity simulation

Spatial interaction models commonly partition the study area into a number of zones and model the interaction between all zone pairs. For many applications this implies that the computational demands, both in terms for processing time and memory allocation, are quadratic to the number of zones. These practical implications compel modellers to reduce the number of zones and trade accuracy for efficiency. This paper presents an approach to modelling spatial interaction to reduce the computational demands while maintaining accuracy. The main idea is to create for each zone a set of clustered zones that it interacts with. The degree of clustering of interacting is governed by the error caused by aggregation. Areas with strong spatial interaction are modelled at high detail whereas the precision for weak interactions is lower. For the same number of zones the interaction will be based on a considerably smaller number of zone-pairs. In a typical model where interaction diminishes with distance, each zone interacts with small zones close by and increasingly large aggregated zones at further distances. The new adaptive zoning approach is applied on a doubly constrained distribution model of commuting in England. The case highlights the model modifications necessary to work with the adaptive zoning systems as well as the tradeoff in efficiency and accuracy that it entails. It appears that the number of zone pairs can be reduced by 95% whilst maintaining a fine granularity.