Accessibility (transport)

Access to jobs by public transit in Toronto

In transport planning, accessibility refers to a measure of the ease of reaching (and interacting with) destinations^[1] or activities distributed in space,^[2][3] e.g. around a city or country.^[4][5] Accessibility is generally associated with a place (or places) of origin. A place with "high accessibility" is one from which many destinations can be reached, or destinations can be reached with relative ease. "Low accessibility" implies that relatively few destinations can be reached for a given amount of time/effort/cost or that reaching destinations is more difficult or costly from that place.

The concept can also be defined in the other direction, and we can speak of a place having accessibility from some set of surrounding places. For example, one could measure the accessibility of a store to customers as well as the accessibility of a potential customer to some set of stores.

In time geography, accessibility has also been defined as "person based" rather than "place based", were one would consider a person's access to some type of amenity through the course of their day as they move through space.^[6] For example, a person might live in a food desert but have easy access to a grocery store from their place of work.

Accessibility is often calculated separately for different modes of transport.^[7]

Mathematical definition[]

In general, accessibility ${\displaystyle A}$ is defined as:

${\displaystyle A_{i}=\sum _{j}{W_{j}}\times f\left({C_{ij}}\right)}$

where:

• ${\displaystyle i}$ = index of origin locations
• ${\displaystyle j}$ = index of destination locations
• ${\displaystyle W_{j}}$ = a set of weights associated with destinations e.g. the number of jobs in a traffic analysis zone
• ${\displaystyle C_{ij}}$ is a cost of travel from ${\displaystyle i}$ to ${\displaystyle j}$ and
• ${\displaystyle f\left({C_{ij}}\right)}$ is an impedance function on the travel cost giving the utility of a destination.^[8]

Cost metrics[]

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 ${\displaystyle j}$.

Impedance functions[]

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.

Relation to land use[]

Accessibility has long been associated with land-use;^[14][15] as accessibility increases in a given place, the utility of developing the land increases.^[16][2] This association is often used in integrated transport and landuse forecasting models.

In practice[]

Transport for London utilize a calculated approach known as Public Transport Accessibility Level (PTAL) that uses the distance from any point to the nearest public transport stops, and service frequency at those stops, to assess the accessibility of a site to public transport services. Destination-based accessibility measures are an alternate approach that can be more sophisticated to calculate. These measures consider not just access to public transport services (or any other form of travel), but the resulting access to opportunities that arises from it. For example, using origin-based accessibility (PTAL) we can understand how many buses one may be able to be access. Using destination-based measures we can calculate how many schools, hospitals, jobs, restaurants (etc..) can be accessed.^[17]

See also[]

• Availability
• Co-benefits of climate change mitigation
• Exurb
• Forced rider
• Isochrone map
• Mobility aid
• Suburbanization
• Transit desert
• Transport divide
• Urban resilience

References[]