Transit accessibility measures are important tools used by planners to understand the effects of changes to the public transit system. However, it is not clear how existing accessibility measures (models) described in the literature correlate with actual public transit ridership data. Public transit systems vary dramatically according to the regions they serve, and no single model has been identified that accurately measures accessibility across the spectrum. This paper evaluates several transit system accessibility models by correlating the accessibility metric they produce with actual ridership data, using the City of Saskatoon as a case study. The results show that frequency based models result in higher correlation than coverage based models and a distance decay function based on the distance from demand location to service location further increases the correlation. This paper provides transportation planners a better understanding of the correlation between different transit accessibility measures and actual transit ridership.
Saskatoon is continuously improving its
transit system, including the planned
introduction of a Bus Rapid Transit (BRT)
system with an estimated cost of between 90
and 150 million dollars
Accessibility is a key measure of public
transit system performance. It refers to the
ease with which locations can be accessed
from other locations
This paper evaluates several transit system accessibility models by correlating the accessibility metric they produce with actual public transit ridership data for Saskatoon.
Specification (GTFS) data was accessed on June 1, 2018. This dataset includes the location of every stop, route, departure direction, and the time of every weekly departure. At that time, Saskatoon Transit operated 41 bus routes serving 1465 stops (Figure 1), with 261,868 weekly departures.
Population data and transit ridership data
per Dissemination Area (DA) was obtained
from the latest Statistics Canada Data
Census Population CSV per Dissemination
Area report (2016). The percentage of
riders in each DA is illustrated in Figure 2.
A transit system serves a geographical area.
The smallest geographical sub-areas for
which statistics such as population and
transit ridership are available are DAs. The
most recent data from Statistics Canada
(2016) defines 362 DAs for Saskatoon.
However, the DAs are not uniform: they
range in size from 0.022 km2 to 40.121 km2.
Some DAs are convex with externally
located centroids. This is a typical
Modifiable Areal Unit Problem (MAUP)
issue, in which results can be skewed
depending on the boundaries that are drawn
to aggregate the data
Next, 400m network-constrained buffers were calculated around each bus stop. Buffers that intersected a grid cell were considered within the grid cell's catchment area. Accessibility measures were then computed for each grid cell. The average value of for the grid cells within a DA was then used to compute an measure for the DA as a whole. accessibility
models. model types: Transit access depends on the level of service. In this paper, a unit of service is defined as a departure, on a route, in a specific direction. In the analysis, the term route implies a route-direction combination. Service parameters can be evaluated in different ways by different
In this paper we consider five 1. Stop Model. This model counts the total number of stops within a demand location. 2. Coverage Model. This model counts the total number of routes serving all stops within a demand location. The service provided by each stop is determined by the number of different routes served.
This model counts the departures from all stops within a demand location over some time interval (e.g., 1 hour).
Model. In this model,
departures on the same route from stops farther away from the demand location are filtered (i.e., not considered). 5. Filtered Frequency Model. In this model departures on the same route from stops farther away from the demand location are filtered (i.e., not considered).
model types described above involves service locations at different distances from the demand location. In each case, a weighting Wjk based on the distance between
service location j (bus
stop) and demand location
k (grid cell
centroid) can
be
applied to the
score
contributed by each stop.
with and without distance decay weighting.
Distance decay was calculated with dpass=250m and the network distance djk from the service location j to the demand location k. 2.3
Therefore the service provided by service location j to demand location k is denoted Using the Filtered Frequency Model distance decay weighting, the accessibility measure at location k is given =
∑ ∈{ } where Bjk denotes the set of filtered service locations j that fall within demand location k's catchment buffer. The E2SFCA model differs from the Filtered Frequency Model by using a service-to-demand ratio Rjk in place of the service
Sjk such that: =
∑ ∈{ } = ⁄ where: Dj is the demand at service location j and is the sum of the weighed populations P of locations k that fall within location j’s catchment buffer: =
∑ ∈{ } In addition to the five model types described in Section 2.2, this paper also considered Langford’s Transit Enhanced 2SFCA model described above. However, as shown in the results (Section 3), Langford’s model performed poorly. Based on that poor performance, another model, dubbed the E2SFCA-2 model, was also considered. In the E2SFCA-2 model, the demand (i.e., the population surrounding the service location) was treated as a potential supply of transit riders and was used to increase the service as shown in equation below.
= √
Walk Score's Transit Score is a filtered
frequency model that uses departures per
week as its service metric
The DA data from Statistics Canada includes transit ridership estimates. Because of widely varying DA populations, transit ridership as a percentage of DA population was computed and used for correlation with the accessibility measures. The percentage of transit users by DA ranges from 0% in many smaller sized and less populated DAs to a maximum of 46.8%. To protect individual’s privacy, the transit ridership estimates are intentionally coarse. The data reports a population of 246,376 with 24,980 transit users. A Pearson's correlation coefficient was computed to quantify the relationship between ridership percentage and each accessibility measure for Saskatoon at the DA level.
Each of the five models identified in Section 2.2 was run twice: once with dpass=250 m and once with no distance decay. Z-scores were calculated to allow visual comparison between figures. Figures 4 to 10 show the results with distance decay applied. Table 1 shows the correlation results for all models. As seen in the table, the best performance was obtained with the E2SFCA-2 (figure 10). A Pearson's r-value of 0.431 (the best obtained result) is not an especially strong correlation. However, it should be noted that there is a relationship between transit service supply and demand. While the demand for transit is influenced by its supply, transit supply itself is adjusted by transit agencies in response to demand changes over time (to provide an efficient service). In other words, demand and transit accessibility measures should be correlated. In every case, a model with distance decay resulted in a better correlation. This confirms that distance to a bus stop is an important factor in accessibility. However, filtering the service when computing service levels has a mixed result. It improved the performance of the Frequency Model but decreased the performance of the Coverage Model.
As expected, the E2SFCA model performed poorly (Table 1), indicating no correlation between the model and actual transit ridership. Therefore, the E2SFCA was rerun with a modification that is labeled E2SFCA2 in Table 1 and it resulted in the best performance of all the models considered. The choice of √ was arbitrary and future work is required to determine how to best consider population demand in scenarios such as urban transit systems.
This paper examined accessibility models by correlating their scores with actual ridership data. Accessibility scores were computed for 362 DAs in Saskatoon and correlated with ridership as a percentage of the DA population using Pearson's r. In all cases, incorporating distance decay resulted in improved model performance. Service frequency, as a service metric, performed better than coverage, and a filtered frequency model, in which all but the closest departure locations were discarded, improved performance even more. The E2SFCA algorithm resulted in the worst performance when treating population as a demand that reduced accessibility. Conversely, that model performed best when modified to treat population as a supply.
It should be noted that many factors beyond physical accessibility have an impact on transit ridership. Therefore, generating statistical models to isolate such impacts is the next step of this research. Although transit system accessibility may be good in low population locations (e.g., centers of work, study, and employment), the transit ridership data collected by Statistics Canada links the users to their home DAs. Therefore, perhaps using origin and destination data could be recommended for future research.
Based on preliminary results, investing in higher frequency service rather than expanded coverage might result in greater transit ridership gains per dollar spent. Saskatoon’s proposed BRT system prioritizes frequency over coverage.
Future work based on the results of this paper include treating population as a supply rather than a demand. Factors such as the catchment buffer size and distance decay parameters could also be varied. A model tuned to maximize performance for a particular transit system could be used to predict ridership changes in that system when the system is reconfigured, such as Saskatoon’s proposed BRT configuration.
The authors would like to thank the Interact Team (https://teaminteract.ca) for inspiration and funding; and Michael Bree for help with Python. Dai,
Dajun. 2010. “Black Residential Segregation, Disparities in Spatial Access to Health Care Facilities, and Late-Stage Breast Cancer Diagnosis in Metropolitan Detroit”. Health and Place 16 (5). ISSN: 1353-8292.