Accessibility (transport)

Travel cost metrics (${\displaystyle C_{ij}}$ in the equation above) can take a variety of forms such as:

• Euclidean Distance
• Network distance
• Travel time[2][1]
• Monetary cost or fare[9]
• Comfort or subjective ease of travel[10]
• Internal and/or external costs[11]

Cost metrics may also be defined using any combination of these or other metrics. For a non-motorized mode of transport, such as walking or cycling, the generalized travel cost may include additional factors such as safety or gradient. The essential idea is to define a function that describes the ease of travelling from any origin ${\displaystyle i}$ to any destination ${\displaystyle j}$.

The function on the travel cost ${\displaystyle f\left({C_{ij}}\right)}$ determines how accessible a destination is based on the travel cost associated with reaching that destination. Two common impedance functions are "cumulative opportunities" and a negative exponential function. Cumulative opportunities[12][8] is a binary function[13] yielding 1 if an opportunity can be reached within some threshold and 0 otherwise. It is defined as:

${\displaystyle f(C_{ij})={\begin{cases}1~~{\text{if}}&C_{ij}\leq \theta \\0~~{\text{if}}&C_{ij}>\theta \end{cases}}}$

where ${\displaystyle \theta }$ is the threshold parameter.

A negative exponential[12] impedance function can be defined as:

${\displaystyle f(C_{ij})=e^{-\beta C_{ij}}}$

where ${\displaystyle \beta }$ is a parameter defining how quickly the function decays with distance.