Representing Service Variation in Accessibility Measures

By Matthew Wigginton Conway 04 May 2015

Accessibility analysis is the central feature of our Transport Analyst tool. We typically think of accessibility as a single number for a location—how many jobs are accessible within an hour from each location in a city? However, transit systems contain variation, so wrapping accessibility up into a single number is an oversimplification.

How much variation there is depends primarily on the frequency of the service. For example, the user experiences of an hourly commuter train and of a frequent subway are significantly different. In the former case, the user will likely look at a schedule and time their trip so as to catch the train when it arrives, whereas in the latter the user will likely turn up at the station with the assumption that a train will arrive shortly, not bothering to check a schedule. As Jarrett Walker astutely points out, “frequency is freedom.” Frequent services allow users to make and change plans freely, without being constrained in their mobility by the transit schedule.

Guaranteed (dark green) and possible (light green) mobility from Downtown Seattle.

These different experiences of transit demand different measures of accessibility. In the case of the frequent subway, we want to know about the “guaranteed” accessibility—the number of jobs, for example, that you are guaranteed to be able to reach in a specified amount of time, if you leave your house at any time between, say, 7 and 9 AM. We might also be curious about the average or expected accessibility, which is the number of jobs you can reach with an average travel time of m minutes. In the case of infrequent commuter rail, we are more interested in the “possible” accessibility—the number of jobs you could reach within a specified amount of time, given that you left you house at a particular but unspecified time, in order to catch the train without waiting. These are different concepts, but we can (and should) compute them all.

Let’s make this a bit more concrete. Downtown Seattle has high-frequency transit service; generally there’s a bus coming pretty soon. The map above shows where you can go via transit within 60 minutes from downtown during the morning rush; the dark green areas are areas that you can always get to within 60 minutes (your guaranteed mobility). This encompasses most of the core metropolitan region of Seattle; the blue dot is placed on the origin of the search, which is in the heart of downtown. The light green areas, on the other hand, are areas that you can get to if you time your trip perfectly (your possible mobility). Note that this area is not a huge amount larger than the area you can always get to.

Guaranteed (dark green) and possible (light green) mobility from Woodinville.

Now consider this map. It shows the same thing, but from a location in suburban Woodinville, Washington, northeast of Seattle and on the other side of Lake Washington. The first thing one notices, of course, is that the reachable areas are much smaller because transit service is not so dense. But also notice that the area of possible mobility (light green) is many times larger than the area of guaranteed mobility (dark green). This is because service is less frequent in suburban areas, and there is much more variation in travel time depending on when you leave. Users of suburban transit are therefore more likely to look at a schedule and time their trip in order to experience the maximum possible mobility.

Plots of accessibility and variation from Downtown Seattle (left) and Woodinville, WA (right).

So far, we’ve only looked at maps of mobility, how far you can go in a given amount of time. We can also see this in plots of accessibility, or what you can access in a given amount of time. On the left we have the accessibility to jobs for a person in Downtown Seattle, and on the right we have accessibility to jobs for a person in Woodinville. The plots show how many jobs you can reach within a certain number of minutes. Let’s ignore the absolute values for the moment, and look at the variation. The upper boundary of the shaded area in each plot represents how many jobs you could access if you were to time your trip and leave at the best possible moment between 7 and 9 AM (the possible accessibility), whereas the lower boundary represents the number of jobs you could reach if you just missed your transit vehicle (the guaranteed accessibility). Notice that in downtown, these numbers are very close to each other, whereas in Woodinville there is a large spread. Downtown, the number of jobs available doesn’t depend much on when you leave your house. In Woodinville, it matters a huge amount.

In the literature, accessibility analysis using averages is referred to as continuous accessibility; minima and maxima over a continuous time range are also present in the literature.

In order to efficiently calculate these measures of accessibility, we run the range RAPTOR algorithm to compute the travel time from the origin to all destinations for every minute in the time window, and then compute summary statistics. The Minnesota Accessibility Observatory used similar methodology in their Access Across America study, which, like our tools, used OpenTripPlanner. We are now optimizing the algorithms to compute these measures of accessibility and integrating them back into the OpenTripPlanner codebase.

These types of accessibility represent qualitatively different experiences of transit, and thus should be used in different situations. When analyzing an urban core service intended for spontaneous use, either guaranteed or average accessibility is the right metric to use because it represents how people use the service. In suburban and commuter systems where people are likely to time their trips to meet the transit schedule, possible accessibility may be a better measure. One thing that possible accessibility does not capture (and guaranteed accessibility does) is the number of trips available; it would not show a change between an hourly service and a half-hourly service. Even though people would time their trips for both, the half-hourly service is arguably more useful because there are more possible departure and arrival times.

Map data © OpenStreetMap; transit data © King County Metro