Weighted Benefit, Variable Radius, and Gradual Coverage

The previous chapters have primarily focused on application contexts and modeling approaches where predefined, discrete coverage metrics are appropriate. Examples of this include: a fire department adequately serves/covers those properties that are within 5 min of travel from a station, or a surveillance system monitors/covers the areas that can be viewed by one or more cameras. That is, coverage is defined as being achieved or not, a simple binary yes or no property. The fact that coverage is defined as being provided or not to an area or object conceived of as a demand for service makes many coverage problems relatively simple to construct, especially for problems that are discrete in nature. When both demand objects and potential facility sites are discrete locations and finite in number, it is possible to identify which sites are capable of covering specific demand objects. An important question, however, is whether coverage should be so crisply defined. For example, when demand for service requires five and a half minutes to respond to from the closest fire station, it may not be considered covered according to a desired 5 min service time standard. In reality, demand for service along these lines obviously receives some level of degraded response service, but just not complete coverage characteristics associated with an established service standard. This chapter therefore explores how coverage models have been extended to be more flexible by including multiple levels of coverage, or steps of coverage, as well as defining a range where coverage is gradually degraded or lost. The idea that service/coverage is degraded, lost or not provided is itself of potential concern, and raises issues of equity. Essentially, in a public setting, we should be concerned with treating those demands that are not covered as fairly as possible. How do we identify a facility configuration (solution) that is as equitable as possible? This too is a subject of this chapter. Finally, there are cases when the coverage capabilities at a given location can be a function of investment. That is, we might be able to expand what a facility can cover by enhancing or upgrading associated equipment. For example, a viewshed (or coverage range) of a fire lookout tower might be extended by increasing its height. An emergency broadcast tower, as another example, might be outfitted with a superior transmitter providing a stronger signal, thereby increasing its range of reception. Such enhancements or upgrades likely are more costly, but do represent ways service capabilities may be altered. This chapter also addresses modeling where there may be options for increasing the coverage range of a facility along with making location siting decisions.