Methodology
This is a summary of the accessibility indicators used in Conveyal. For more details, please see Conway, Matthew Wigginton, Andrew Byrd, and Marco van der Linden (2017). “Evidence-Based Transit and Land Use Sketch Planning Using Interactive Accessibility Methods on Combined Schedule and Headway-Based Networks”
Spatial resolution
As a shared geographic foundation for regions, spatial datasets, and accessibility indicators, Conveyal uses a regular grid of cells. Conveyal supports up to 5 million such cells, reflecting a much finer resolution than typical regional travel demand models. To counter the effects of the "modifiable areal unit problem" and in response to systematic bias we observed when using the center points of polygons defined by roads, the Conveyal team made an intentional methodological choice to default to calculations on regular grids whose geometry is independent of roads and land parcels.
Opportunity datasets from uploaded point or polygon files, as well as LODES imports, are resampled into this standardized regular grid. For example, if a large traffic analysis zone in an uploaded shapefile has 10 thousand jobs, those jobs are dispersed throughout the grid cells intersecting that zone, according to the areal proportion of the intersection of each cell with the zone.
Zoom levels
The grid cells are spaced at one-unit steps in Web Mercator projection, which is commonly used in web mapping. This approach helps accelerate map display, while eliminating the complexity of switching to different local projections. The resolution of each cell depends on its latitude and the selected Web Mercator Zoom level. At any given zoom level, the cell size will be largest at the equator and decrease toward the poles.
Use higher zoom levels with caution. They yield higher-resolution results but require substantially more computation.
Conveyal's current methods are not designed for polygons averaging less than one opportunity per grid cell. Processing low density layers at high zoom levels may yield unexpected results; contact your support team for more information.
| Zoom level | Cell width (at equator) | Cell width (at 45° lat.) | Width of square region with 5 million cells (at 45° lat.) |
|---|---|---|---|
| z9 | 306 m (1002 ft.) | 216 m (709 ft.) | 483 km (302 mi.) |
| z10 | 153 m (501 ft.) | 108 m (355 ft.) | 241 km (150 mi.) |
| z11 | 76 m (251 ft.) | 54 m (177 ft.) | 121 km (75 mi.) |
Accounting for variability
The default methods in Conveyal's routing engine (R5) assume perfect reliability of transit operations. Vehicles operate on-time; passengers have full information about all schedules in the system, choose routes to minimize their total travel time, and can board any vehicle (unimpeded by crowding or lack of accessibility features). Even with these assumptions, travel times by transit can be highly variable depending on when travelers start their journeys and the timetables of routes they use. To account for this variability, we calculate the distribution of travel times experienced in a given departure window, then allow selecting specific values from this distribution according to a parameter we call the time percentile (discussed below). This percentile ranges from 0 to 100 and represents how reliably a destination is reachable for travelers starting journeys in the selected departure window.
In general, this approach allows us to more appropriately characterize travel times between origin-destination pairs served by many alternative routes (e.g. a corridor with many overlapping bus services) than blanket half-headway assumptions. Note, however, that it assumes travelers have perfect knowledge of schedules in the network and act accordingly to minimize their travel time. In some cases, this assumption may not be appropriate. Travelers without access to complete schedule information may be inclined to board the first vehicle that arrives, even if others would allow them to arrive at their destination sooner.
We use the median or other percentile travel time, rather than the mean, because it can handle travel times that are infinite or undefined (for example, because the only route to a particular destination uses a bus that stops running before the end of the time window). For more details, please see Conway, Matthew Wigginton, Andrew Byrd, and Marco van der Linden (2017). “Evidence-Based Transit and Land Use Sketch Planning Using Interactive Accessibility Methods on Combined Schedule and Headway-Based Networks.”
Compared to mean accessibility
Others calculate the accessibility at each departure time and take a mean of accessibility, as is done by the University of Minnesota Accessibility Observatory. Conveyal does not use this approach because we choose to treat the travel time to each opportunity independently. Consider a situation of a small town situated between two major cities each with 500,000 jobs, with hourly train service to each city. Suppose that we’re interested in the number of jobs reachable in one hour, given departure during a time window of 8:00 to 9:00 AM. Further suppose that, due to how the train schedules are written, it is possible to commute to all jobs in the first city in under an hour if you leave between 8:00 and 8:15, and all the jobs in the second city are accessible if you leave between 8:30 and 8:45, and at other times no jobs are accessible. This corresponds to hourly trains to each city, leaving at 8:15 in one direction and 8:45 in the other, and needing 45 minutes to travel to the respective city. Using the average of accessibility, this location would have an accessibility of 250,000, because ¼ of the time 500,000 jobs are accessible in the first city, ¼ of the time 500,000 jobs are accessible in the second city, and ½ of the time no jobs are accessible. Thus the accessibility value would be 250,000 even though there is no job that can be reached in an average travel time of less than 60 minutes.
Time percentile
As mentioned above, the time percentile parameter represents how reliably people can reach destinations during a departure time window. For most analyses, the default time percentile value of 50 is acceptable. You may also want to consider 25th or 75th percentile travel times, depending on whether users are likely to use schedules or start trips randomly. The interpretation of the travel time percentile depends on whether the transit network has frequency-/headway-based routes, as opposed to routes with fully specified exact timetables.
Exact timetables
Assuming all transit service operates in accordance with fully specified timetables, the time percentile can be interpreted as how inclined travelers are to adjust their departure time based on transit schedules. Low time percentile values imply travelers are flexible and start their journeys at times that minimize their waiting and overall travel time, which is appropriate for passengers accustomed to coordinating their activities with published transit schedules (e.g. commuter rail riders). Higher time percentile values are appropriate for passengers who expect “turn-up-and-go” service (e.g. users in dense areas with frequent service).
Networks with frequency-based routes
Some routes, whether in baseline networks (built from uploaded GTFS) or in Conveyal modifications, may have frequencies/headways defined, but not explicit timetables. When frequency-based routes are present, the variability in travel time distributions discussed above is compounded by uncertainty that arises from the interactions of simulated schedules for these routes with each other and the fully specified exact timetables. Our methods combine the variability (the ride and wait time will vary depending on the rider's departure time choices) and uncertainty (specific actual departure times will be realized on any given day, but we don't know which ones the transit operator will choose) in a single travel time distribution. Choosing a lower percentile when frequency-based routes are present thus jointly represents a better departure time choice by the passenger and simulated schedules that yield shorter waiting times.
Conveyal's routing engine allows you to understand this uncertainty by simulating feasible timetables for all headway-based routes. For example, if the Red Line is set to depart Airport Station every ten minutes, without explicit timetables, one simulated timetable could include departures at 7:00, 7:10, 7:20…, and another simulated timetable could include departures at 7:02, 7:12, 7:22… The number of simulated schedules parameter in the analysis settings determines how many simulated timetables are used, rounding up to an integer number of schedules per minute in the departure window. For more details on this parameter, see our recent paper ("Half-(head)way there").
Uncertainty introduced by frequency-based routes can sometimes lead to results that do not match initial expectations. You may want to consider developing exact timetables to eliminate uncertainty, or using the phasing feature to reduce it through the use of timed transfers.
Example
Consider travelers with the following hypothetical journey:
- Walk 10 minutes from their origins to a stop served by a single route
- Wait at the stop
- Board the first vehicle of the route that arrives at the stop, and ride it for 30 minutes
- Alight directly at their destinations
These travelers have at least 40 minutes of travel time, plus a waiting time that varies depending on when they begin their journey with respect to the route’s timetable.
Say these travelers want to begin their journeys sometime between 7:00 and 8:40 AM (a departure window of 100 minutes), and that they will only consider their destination reachable if their door-to-door travel time is less than 45 minutes. If the route departs the stop once per hour, at 7:00 and 8:00, there will only be five minutes of the departure window for which the destination is reachable. Travelers can start their journeys between 7:45 and 7:50, arriving at the stop between 7:55 and 8:00 to board the 8:00 departure. The destination will only be considered reachable at time percentiles up to the 5th (5 of the 100 possible departure minutes in the departure window). That level of reliability may be acceptable for travelers who are willing to coordinate their travel with schedules for services with low frequency.
If instead, the route departs the stop every 10 minutes, starting at 7:00, there will be fifty minutes of the departure window for which the destination is reachable (beginning trips between 7:05 and 7:10, or between 7:15 and 7:20, or between 7:25 and 7:30, etc.). The destination will be considered reachable at time percentiles up to the 50th.
Finally, if the route departs every 5 minutes, the destination will be reachable within the 45-minute cutoff 100% of the time. Even if travelers just miss a vehicle, the next one will depart in 5 minutes, and they will arrive at their destination without exceeding the time cutoff.