Accessibility

Accessibility is the extent to which the land use and transport system enables people or goods to reach activities or destinations.

A highly accessible location is well connected to the destinations that matter for a specified purpose. Which destinations matter, how "well connected" is measured, and for whom: those three choices define an accessibility indicator, and different choices lead to very different maps of the same country.

Four components

Geurs & van Wee (2004) decompose accessibility into four components. Any indicator is, implicitly or explicitly, a statement about all four. An indicator that ignores one of them is making an assumption about it rather than avoiding it.

Component	Question	Typical model input
Land use	What is where, and how much of it?	Jobs, dwellings, schools, hospitals, shops per zone
Transport	What does it cost to get there?	Network, speeds, timetables, fares, congestion
Temporal	When are origins, destinations and the network available?	Opening hours, peak and off peak, service frequency
Individual	Who is travelling, and what are their means and needs?	Car ownership, income, age, mobility impairment

The land use component also carries the competition effect: a hospital within 10 minutes is worth less if 200,000 other people are also within 10 minutes of it. See Accessibility indicators for measures that account for this.

Four measurement perspectives

The same literature distinguishes four families of measures, in increasing order of behavioural realism and data demand.

1. Infrastructure based, the performance of the network itself: average speed, congestion, volume over capacity ratio. Common in transport planning, but it says nothing about what can be reached.
2. Location based, the accessibility of a place: distance to the nearest destination, opportunities within a threshold, potential accessibility. The most widely used family, and the main subject of this wiki.
3. Person based, what an individual can reach given their time budget and fixed commitments, following Hägerstrand's space time geography.
4. Utility based, the economic benefit a person derives from the available set of destinations, typically the logsum of a discrete choice model.

Accessibility indicators works through these families with formulas and guidance on when each is appropriate.

How a location based indicator is built

Most indicators in this wiki are assembled from the same three ingredients.

1. Travel impedance $d_{ij}$, the generalised cost of travelling from origin $i$ to destination $j$, computed over a network (Shortest path and the Dijkstra algorithm) and usually stored as an Origin Destination matrix (trip table).
2. A distance decay function $f(d_{ij})$, converting impedance into a travel potential $p_{ij}$, so that nearer destinations weigh more heavily.
3. An attraction $A_j$, the size or quality of destination $j$.

These combine into an attraction potential per origin destination pair, aggregated over destinations:

• $p_{ij} := f(d_{ij})$
• $pot_{ij} := A_j \cdot p_{ij}$
• $Accessibility_i := \sum\limits_{j} pot_{ij}$

Summation is not the only option. Aggregation can be done by summing (the 1-norm, when all attractions add up), by taking the maximum (the $+\infty$-norm, when only the best destination counts), or by anything in between. See Minkowski distance and p-norms. The choice encodes a behavioural assumption: whether people value having many options or only the best one.

Why this matters for land use

Accessibility is a key factor in the attractiveness of locations in land use modelling. There the causality runs both ways: accessibility drives where activities locate, and the resulting distribution of activities changes accessibility. Models that iterate between the two need indicators that are cheap enough to recompute, a practical constraint that often decides which indicator is used.

Further reading

• Geurs, K.T. & van Wee, B. (2004). Accessibility evaluation of land-use and transport strategies: review and research directions. Journal of Transport Geography 12(2), 127-140. doi:10.1016/j.jtrangeo.2003.10.005
• Geurs, K.T. & Ritsema van Eck, J.R. (2001). Accessibility measures: review and applications. RIVM report 408505 006. PDF

See References for the full list.