A simple model for predicting the number of servers necessary to cover a region

A simple regression model is developed to estimate the number of servers necessary to cover a region. Data for the model were obtained within a research design that included five replications of 180 experimental conditions. A total of 300 rectangular regions were generated, and a set covering location problem was solved for each region using three distance metrics. Statistical results established coverage radius, compactness, and the number of nodes in the region to be significant factors. The resulting regression model was applied to a South Carolina county. Its estimates are seen to be very close to the number of units needed to cover. The model is shown to be a convenient technique for quickly estimating the number of servers while exhibiting an error distribution that is conservatively biased towards overestimation. This last property is desirable for public emergency services.