Spatial linear network Voronoi analysis to quantify accessibility of police stations in South Africa

Abstract

This study quantifies the overlap between existing police precinct boundaries and theoretically optimal boundaries derived from Voronoi diagrams based on Euclidean and network distances. Spatial similarity measures are used to analyse the relationship between boundary overlap and police station accessibility, hypothesising that reduced overlap corresponds to decreased accessibility. Accessibility, in this mini-dissertation, refers to how easily an individual can reach a police station, with closer points being more accessible. The analysis extends to the potential effects of boundary placement on crime rates, suggesting that greater inaccessibility of police stations may correlate with less crimes reported in that precinct. By quantifying these relationships, this research evaluates the effectiveness of current precinct boundaries and their potential influence on crimes reported. For precincts with low similarity values, indicating low accessibility, we analyse the proportional change in the number of crimes reported after boundary modifications. A decrease in reported crimes within the new boundaries generated by Voronoi models would support our hypothesis. This decrease would suggest that a significant portion of crimes are now being reported to other, nearer, and more accessible police stations.