==Decay vs. Cut-offs==
One major distinction in measuring accessibility is how parameters are set for determining if a destination is accessible. One method is to create a time cut-off. For example, one can ask how many jobs can be reached in 30 minutes using transit from a given location? Or, how many household/job combinations are there within 30 minutes of each other along a transit line or in a transit system? The alternative is to use a decay function. A decay function weights destinations based on how far they are, so that
a farther locations are given less weight than closer ones.
Time cut-offs are useful because they are slightly easier to calculate. Some tool is needed to figure out how far one can go on a system in the specified amount of time, and then all points corresponding to a destination within that area are counted up. They also tend to be easier to communicate to the public or to decision makers.
The idea that there are 10,000 jobs accessible in 30 minutes from a given area, or that a new line or faster service will increase the number of jobs available in 30 minutes of travel is easy to understand.Time cut-offs suffer a few disadvantages however. A large employment center just outside of the time range is completely disregarded. So if there are 1,000 jobs available in 30 minutes but 2,000 jobs available in 31 minutes, the analysis will ignore the jobs just outside the cut-off. Cut-offs also don't discriminate between where destinations are located within a region. For example, this type of analysis will provide the same results is all of the jobs are five minutes away or thirty minutes way, although being five minutes away clearly provides better access. Some of these disadvantages can be over come by conducting multiple analyses with different cut-offs, such that instead of having one number for a certain distance, the change as one gets farther away can be observed.
[[File:Decay function.png|thumb|A decay function showing the change in weighted values for different modes and destination as travel time increases<ref>"Operationalizing Accessibility: Tools and Practices." State Smart Transportation Initiative. 30 March 2017. http://www.ssti.us/Events/operationalizing-accessibility-part-1-tools-and-practices/</ref>]]
Decay functions offer a more fine-tuned assessment of accessibility by weighting destinations based on how far away they are. A job that is five minutes away contributes more to accessibility than one that is thirty minutes away, and a job that is thirty minutes away contributes about the same as one that is thirty-one minutes away. Decay functions usually have a cut-off, somewhere around the 60
or 90 minute mark, where destinations are considered so inaccessible that they can no longer greatly contribute.Using decay is challenging for a number of reasons. A meaningful and reliable decay function has to be developed. The computation effort of calculating the exact distance to each location and weighting the location is large and complicated. Finally, because location are weighted, the final output is unit-less; it cannot be explained as number of jobs within 30 travel time. This may allow for internal comparisons but may be difficult to understand conceptually for public presentations. One solution to improve presentation is developing a clear scale and creating references are explanations for various points on the scale. (ex. a 1-100, where 80-100 is excellent accessibility, etc.)
==First and Last Mile==