=Paper=
{{Paper
|id=Vol-2323/SKI-Canada-2019-7-5-2
|storemode=property
|title=Correlation of Public Transit Accessibility Measures with Actual Ridership
|pdfUrl=https://ceur-ws.org/Vol-2323/SKI-Canada-2019-7-5-2.pdf
|volume=Vol-2323
|authors=Sarah Bree,Ehab Diab,Scott Bell
}}
==Correlation of Public Transit Accessibility Measures with Actual Ridership==
https://ceur-ws.org/Vol-2323/SKI-Canada-2019-7-5-2.pdf
Spatial Knowledge and Information Canada, 2019, 7(5), 2
Correlation of Public Transit Accessibility
Measures with Actual Ridership
SARAH BREE EHAB DIAB SCOTT BELL
Geography and Planning Geography and Planning Geography and Planning
University of Saskatchewan University of Saskatchewan University of Saskatchewan
sarah.bree@usask.ca ehab.diab@usask.ca scott.bell@usask.ca
citizens (Ding 2018; Kim 2018). One
ABSTRACT method to assess planned changes to transit
systems is to develop service metric models.
Transit accessibility measures are important These models estimate how the service
tools used by planners to understand the metrics change when model inputs change
effects of changes to the public transit (i.e. transit system configuration).
system. However, it is not clear how existing
accessibility measures (models) described in Accessibility is a key measure of public
the literature correlate with actual public transit system performance. It refers to the
transit ridership data. Public transit ease with which locations can be accessed
systems vary dramatically according to the from other locations (Morris, Dumble, &
regions they serve, and no single model has Wigan, 1979). Several researchers examined
been identified that accurately measures the concept of accessibility. For example,
accessibility across the spectrum. This paper Thill and Kim (2005) and Lei (2010)
evaluates several transit system accessibility proposed several options to calculate
models by correlating the accessibility accessibility based on distance to service
metric they produce with actual ridership using gravity functions.
data, using the City of Saskatoon as a case
study. The results show that frequency Luo and Wang (2003) proposed the Two
based models result in higher correlation Step Floating Catchment Area model
than coverage based models and a distance (2SFCA) to estimate geographical
decay function based on the distance from accessibility of medical services. Their
demand location to service location further model considered supply of surrounding
increases the correlation. This paper services at a particular demand location,
provides transportation planners a better and the total demand on the services by
understanding of the correlation between surrounding locations. Subsequently,
different transit accessibility measures and McGrail and Humphreys (2009) examined
actual transit ridership. the use of the 2SFCA model in rural
Victoria, Australia, and Dai (2010)
examined the use of the 2SFCA model for
1. Introduction estimating access to health care in Detroit,
Michigan.
Saskatoon is continuously improving its
transit system, including the planned
Luo and Qi (2009) proposed an enhanced
introduction of a Bus Rapid Transit (BRT)
2SFCA (E2SFCA) model that applies a
system with an estimated cost of between 90
distance-decay to both steps of the original
and 150 million dollars (City of Saskatoon, 2SFCA model. They proposed discrete
2018). Successful implementation of such weightings that change in a stepwise fashion
an infrastructure project requires that costs
at defined distances. Langford et. al. (2012)
and impacts be accurately estimated and proposed a transit-enhanced E2SFCA model
reported to planners, decision makers, and
2 Correlation of Transit Accessibility Measures with Transit Ridership
for estimating geographical access into
transit systems, which is described in more
detail later in this paper. Recently, Walk
Score (Seattle WA) introduced Transit
Score to quantify local accessibility to
transit (Walk Score, 2018).
This paper evaluates several transit system
accessibility models by correlating the
accessibility metric they produce with actual
public transit ridership data for Saskatoon.
2. Data and Methods
Saskatoon Transit’s General Transit Feed Figure 2. Percentage of transit users by DA from
Specification (GTFS) data was accessed on Statistics Canada (2016).
June 1, 2018. This dataset includes the
location of every stop, route, departure 2.1 Service Area Partitioning
direction, and the time of every weekly
departure. At that time, Saskatoon Transit A transit system serves a geographical area.
operated 41 bus routes serving 1465 stops The smallest geographical sub-areas for
(Figure 1), with 261,868 weekly departures. 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 (Openshaw, 1983).
To overcome the MAUP issue, a grid of
100m by 100m cells was overlayed on the
bounding box containing all Saskatoon DAs.
Figure 1. The June 1, 2018 Saskatoon Transit
and intersections computed for each DA. In
System Configuration.
many cases the grid cells were bisected by
Population data and transit ridership data DA boundaries. That is, while there are
per Dissemination Area (DA) was obtained many grid cells within DAs, the grid cells
from the latest Statistics Canada Data along the DA boundaries are usually clipped
Census Population CSV per Dissemination into smaller, non-square shapes. This
Area report (2016). The percentage of operation resulted in 21,807 grid cells, each
riders in each DA is illustrated in Figure 2. with an internal centroid.
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
Correlation of Transit Accessibility Measures with Transit Ridership 3
computed for each grid cell. The average
𝑊𝑗𝑘 = 1⁄√1 + 𝑥(𝑑𝑗𝑘 ⁄𝑑𝑝𝑎𝑠𝑠 )𝑛
value of for the grid cells within a DA was
then used to compute an accessibility
measure for the DA as a whole. with x=1, n=6 and dpass=250m. For this
paper, each of the model types described
above was run with and without distance
2.2 Service Models decay weighting. Distance decay was
calculated with dpass=250m and the network
Transit access depends on the level of distance djk from the service location j to
service. In this paper, a unit of service is the demand location k.
defined as a departure, on a route, in a
specific direction. In the analysis, the term
route implies a route-direction 2.3 Transit Enhanced Two Step
combination. Service parameters can be Floating Catchment Area Model
evaluated in different ways by different (E2SFCA)
models. In this paper we consider five
model types: The E2SFCA model, proposed by Langford
et. al. (2012), is similar to the Filtered
1. Stop Model. This model counts the Frequency Model with distance decay. The
total number of stops within a service provided at service location j
demand location. depends upon the demand location k.
2. Coverage Model. This model counts Therefore the service provided by service
the total number of routes serving all location j to demand location k is denoted
stops within a demand location. The Sjk. Using the Filtered Frequency Model
service provided by each stop is with distance decay weighting, the
determined by the number of accessibility measure at location k is given
different routes served. by:
3. Frequency Model. This model 𝐴𝑘 = ∑ 𝑊𝑗𝑘 𝑆𝑗𝑘
counts the departures from all stops 𝑗∈{𝐵𝑗𝑘 }
within a demand location over some
time interval (e.g., 1 hour).
4. Filtered Coverage Model. In this where Bjk denotes the set of filtered service
model, departures on the same locations j that fall within demand location
route from stops farther away from k's catchment buffer. The E2SFCA model
the demand location are filtered (i.e., differs from the Filtered Frequency Model
not considered). by using a service-to-demand ratio Rjk in
5. Filtered Frequency Model. In this place of the service Sjk such that:
model departures on the same route
from stops farther away from the 𝐴𝑘 = ∑ 𝑊𝑗𝑘 𝑅𝑗𝑘
demand location are filtered (i.e., 𝑗∈{𝐵𝑗𝑘 }
not considered).
where:
Each one of the model types described
𝑅𝑗𝑘 = 𝑆𝑗𝑘 ⁄𝐷𝑗
above involves service locations at different
distances from the demand location. In
each case, a weighting Wjk based on the Dj is the demand at service location j and is
distance between service location j (bus the sum of the weighed populations P of
stop) and demand location k (grid cell locations k that fall within location j’s
centroid) can be applied to the score catchment buffer:
contributed by each stop. Langford (2012)
suggested a Butterworth filter given by: 𝐷𝑗 = ∑ 𝑊𝑘𝑗 𝑃𝑘
𝑘∈{𝐵𝑘𝑗 }
4 Correlation of Transit Accessibility Measures with Transit Ridership
The DA data from Statistics Canada includes
In addition to the five model types described transit ridership estimates. Because of
in Section 2.2, this paper also considered widely varying DA populations, transit
Langford’s Transit Enhanced 2SFCA model ridership as a percentage of DA population
described above. However, as shown in the was computed and used for correlation with
results (Section 3), Langford’s model the accessibility measures. The percentage
performed poorly. Based on that poor of transit users by DA ranges from 0% in
performance, another model, dubbed the many smaller sized and less populated DAs
E2SFCA-2 model, was also considered. to a maximum of 46.8%. To protect
individual’s privacy, the transit ridership
In the E2SFCA-2 model, the demand (i.e., estimates are intentionally coarse. The data
the population surrounding the service reports a population of 246,376 with 24,980
location) was treated as a potential supply of transit users. A Pearson's correlation
transit riders and was used to increase the coefficient was computed to quantify the
service as shown in equation below. relationship between ridership percentage
and each accessibility measure for
Saskatoon at the DA level.
𝑅𝑗𝑘 = 𝑆𝑗𝑘 √𝐷𝑗
3. Results
2.4 Walk Score’s Transit Score
Each of the five models identified in Section
Walk Score's Transit Score is a filtered 2.2 was run twice: once with dpass=250 m
frequency model that uses departures per and once with no distance decay. Z-scores
week as its service metric (Walk Score, were calculated to allow visual comparison
2018). All departures on a route are ignored between figures. Figures 4 to 10 show the
except for those from the stop located results with distance decay applied. Table 1
closest to the demand location. The score is shows the correlation results for all models.
computed for demand locations on a 500 As seen in the table, the best performance
foot grid. A distance decay, as shown in was obtained with the E2SFCA-2 (figure 10).
Figure 3, is then applied to the service
scores. Distances are computed using the
road network. Once computed, a log of the
score is taken (Figure 4). Table 1: Pearson's r correlation results
Model Fig. Distance Pearson’s
Decay
(dpass)
E2SFCA 250 0.036
Filtered Coverage 0.327
Transit Score 4 Walkscore 0.336
Filtered Coverage 5 250 0.342
Stop Count 0.345
Stop Count 6 250 0.349
Coverage 0.361
Coverage 7 250 0.364
Frequency 0.395
Filtered Frequency 0.398
Frequency 8 250 0.401
Filtered Frequency 9 250 0.418
E2SFCA-2 10 250 0.431
Figure 3. Butterworth distance decay functions
and the Walk Score distance decay function.
2.5 Correlation with Transit Ridership
Correlation of Transit Accessibility Measures with Transit Ridership 5
Figure 4. Walk Score’s Transit Score Figure 7. Coverage
Figure 5. Filtered Coverage Figure 8. Frequency
Figure 6. Stop Count Figure 9. Filtered Frequency
6 Correlation of Transit Accessibility Measures with Transit Ridership
4. Conclusion
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,
Figure 10 .E2SFC-2 improved performance even more. The
E2SFCA algorithm resulted in the worst
A Pearson's r-value of 0.431 (the best performance when treating population as a
obtained result) is not an especially strong demand that reduced accessibility.
correlation. However, it should be noted Conversely, that model performed best
that there is a relationship between transit when modified to treat population as a
service supply and demand. While the supply.
demand for transit is influenced by its
supply, transit supply itself is adjusted by It should be noted that many factors beyond
transit agencies in response to demand physical accessibility have an impact on
changes over time (to provide an efficient transit ridership. Therefore, generating
service). In other words, demand and transit statistical models to isolate such impacts is
accessibility measures should be correlated. the next step of this research. Although
transit system accessibility may be good in
In every case, a model with distance decay low population locations (e.g., centers of
resulted in a better correlation. This work, study, and employment), the transit
confirms that distance to a bus stop is an ridership data collected by Statistics Canada
important factor in accessibility. However, links the users to their home DAs.
filtering the service when computing service Therefore, perhaps using origin and
levels has a mixed result. It improved the destination data could be recommended for
performance of the Frequency Model but future research.
decreased the performance of the Coverage
Model. Based on preliminary results, investing in
higher frequency service rather than
As expected, the E2SFCA model performed expanded coverage might result in greater
poorly (Table 1), indicating no correlation transit ridership gains per dollar spent.
between the model and actual transit Saskatoon’s proposed BRT system
ridership. Therefore, the E2SFCA was rerun prioritizes frequency over coverage.
with a modification that is labeled E2SFCA-
2 in Table 1 and it resulted in the best Future work based on the results of this
performance of all the models considered. paper include treating population as a
The choice of √𝐷𝑗 was arbitrary and future supply rather than a demand. Factors such
work is required to determine how to best as the catchment buffer size and distance
consider population demand in scenarios decay parameters could also be varied. A
such as urban transit systems. model tuned to maximize performance for a
particular transit system could be used to
predict ridership changes in that system
Correlation of Transit Accessibility Measures with Transit Ridership 7
when the system is reconfigured, such as Routes and Schedules”. International
Saskatoon’s proposed BRT configuration. Journal of Geographical Information
Science 24 (2): 283-304. ISSN: 1365-8816.
DOI: 10.1080/13658810902835404
Acknowledgements
Litman, Todd. 2012. “Evaluating Public
The authors would like to thank the Interact Transit Benefits and Costs: Best Practices
Team (https://teaminteract.ca) for Guidebook”.
inspiration and funding; and Michael Bree http://library.usask.ca/scripts/remote?URL
=http://www.deslibris.ca/ID/230688
for help with Python.
Luo, W., and F. Wang. 2003. “Measures of
References Spatial Accessibility to Health Care in a GIS
Environment: Synthesis and a case study in
City of Saskatoon, and Robert Dudiak. 2018. the Chicago region”. Environment and
“Transit Plan” Technical Report. City of Planning B: Planning and Design 30 (6):
Saskatoon. 865-884. ISSN: 02658135
https://www.saskatoon.ca/engage/transit-
plan Luo, Wei, and Yi Qi. 2009. “An Enhanced Two-
Step Floating Catchment Area (E2SFCA)
Dai, Dajun. 2010. “Black Residential Method for Measuring Spatial Accessibility
Segregation, Disparities in Spatial Access to to Primary Care Physicians”. Health and
Health Care Facilities, and Late-Stage Place 15 (4): 1100-1107. issn: 1353-8292
Breast Cancer Diagnosis in Metropolitan
Detroit”. Health and Place 16 (5). ISSN: McGrail, Matthew R., and John S. Humphreys.
1353-8292. 2009. “Measuring Spatial Accessibility to
Primary Care in Rural Areas: Improving
Ding, Jishiyu, Yi Zhang, and Li Li. 2018. “A the Effectiveness of the Two-Step Floating
New Accessibility Measure of Bus Transit Catchment Area Method”. Applied
Networks”. IET Intelligent Transport Geography 29 (4): 533-541. ISSN: 0143-
Systems 12 (7): 682-688. ISSN: 1751-956X. 6228
DOI: 10.1049/iet-its.2017.0286
Morris, J., Dumble, P., and Wigan, M. 1979.
Kim, Hyun, and Yena Song. 2018. “An “Accessibility indicators for transport
Integrated Measure of Accessibility and planning”. Transportation Research Part A:
Reliability of Mass Transit Systems”. General, 13(2), 91-109
Transportation 45, no. 4 (July): 1075-1100.
ISSN: 1572-9435. DOI: 10.1007/s11116-018- Openshaw, S., 1983. The Modifiable Areal Unit
9866-7 Problem. Norwick: Geo Books.
https://doi.org/10.1007/s11116-018-9866-7 ISBN 0860941345. OCLC 12052482
Langford, M., R. Fry, and G. Higgs. 2012. Thill, Jean-Claude, and Marim Kim. 2005.
“Measuring Transit System Accessibility “Trip Making, Induced Travel Demand, and
using a Modified Two-Step Floating Accessibility”. Journal of Geographical
Catchment Technique”. International Systems 7 (2): 229-248. ISSN: 1435-
Journal of Geographical Information 5930.DOI: 10.1007/s10109-005-0158-3
Science 26 (2): 193-214. DOI:
10.1080/13658816.2011.574140 Walkscore. 2018. “Walkscore’s Transit Score
https://doi.org/10.1080/13658816.2011.574 Methodology”.
140 https://www.walkscore.com/transit-score-
methodology.shtml.
Lei, T. L., and R. L. Church. 2010. “Mapping
Transit-Based Access: Integrating GIS,