Join Potential Path Area (jPPA) can be used to identify spatial-temporal overlap between individuals’ paths and the public bus transportation system. Using the jPPA implementation defined in this study presents a proof-of-concept method for finding the spatial-temporal overlap in GPS data of individuals and the public bus system in an urban environment. Vadan A, Stanley K. Identifying bus ridership with joint Potential Path Area. Presentation at the University of Saskatchewan's Undergraduate Student Research Assistant Poster Competition; August 2019; Saskatoon, SK.

1. Identifying bus ridership with joint Potential Path Area
Antoniu Vadan, Kevin Stanley
University of Saskatchewan, Department of Computer Science
Introduction
The Space-Time Prism
“The space-time prism is the envelope of all possible space-time paths between
known locations and times” [4]. We use the concept of the space-time prism
(STP) to determine if a study participant is riding the bus at a given time
(Figure 1). An STP is typically defined by two anchors in space and time. These
anchors are data points where the location of an individual is known. The
volume of an STP is not only determined by the distance between anchors, but
also by the upper bound on participant speed during that time interval. The
anchors and the speed limit therefore define a prism which spans all possible
space-time paths between the anchors [4] (Note: if the assumed upper bound on
speed limit is too low, then it is possible for no STP to exist between the two
anchors. To deal with this case, we use A* pathfinding to linearly interpolate
location for any time between when the two anchors are recorded). The
underlying concept of this study is that if the STPs of a participant’s path
intersect with the GPS traces of a bus for a long enough duration of time, then
the participant is likely to be on that bus.
Results
Problem
Do bus riders change their movement behaviours as a result of a change in
the public transportation network? To be able to answer this question, a
quantitative method of measuring bus ridership is required.
Conclusion and future work
Acknowledgements
Using jPPA and spatial-temporal overlap between people and buses to
identify bus ridership is possible. Further work needs to verify the
correctness of this approach and to analyze the changes in behaviour of
public transportation users after a change in environment.
We would like to thank Luana Fragoso for implementing the trip detection algorithm.
x
y
t
Figure 1: A space time prism as an intersection of cones originating at the anchor points.
Reproduced from https://images.app.goo.gl/kUsginXmhoQYWny86
Joint Potential Path Area
Joint potential path area is defined to be the spatial overlap of two or more STPs.
Thus, it represents the region in which two or more agents have the potential to
meet in space and time [3].
At any given time τ between two space-time anchors recorded at locations ai and
ai+1 at times ti < τ < ti+1, the accessibility space of an individual is defined by the
overlap of two discs [3].
Disc 1 (Di,τ): Centered at ai with radius !" = $%&'× ) − +"
Disc 2 (Di+1,τ): Centered at ai+1 with radius !",- = $%&'× +",- − )
ri,τ
Di,τ
GA
τ
Di+1,τ
PPA
ai
ai+1
a)
ai
ai+1
bj
bj+1
GAB
τ
b)
Figure 2: a) The accessibility space ./
0 of participant A whose trip begins at point ai and ends at
point ai+1. The union of ./
0 for all τ such that ti < τ < ti+1 represents the Potential Path Area
(PPA) - an ellipse [3]. b) The spatial overlap ./
01 between the potential paths of participant A
and B at time τ (joint Potential Path Area). Mathematically, ./ = 2" ∩ 2",- and 445 = ∪ ./
for all ti < τ < ti+1. Figure reproduced from [3].
References
[1] B. Chaix, J. Méline, S. Duncan, C. Merrien, N. Karusisi, C. Perchoux, A. Lewin, K.
Labadi and Y. Kestens, "GPS tracking in neighborhood and health studies: A step forward for
environmental exposure assessment, a step backward for causal inference?," Health & Place,
vol. 21, pp. 46-51, 2013
[2] R. Brondeel, B. Pannier and B. Chaix, "Using GPS, GIS, and Accelerometer Data to
Predict Transportation Modes," Medicine & Science in Sports & Exercise, 2015.
[3] J. A. Long, S. L. Webb, T. A. Nelson and K. L. Gee, "Mapping areas of spatial-temporal
overlap from wildlife tracking data," Movement Ecology, vol. 3, no. 38, 2015.
[4] H. J. Miller, "Time geography and space-time prism," The International Encyclopedia of
Geography, 2017.
Figure 5 depicts an
example of a participant
trip. The assumed
maximum speed of the
participant is 2m/s,
causing PPA to exist
only between data
points that are at least
within 600m of each
other. This is a result of
time intervals between
data points being at least
5 minutes long. The
location of the majority
of the points in the
middle of the trip were
interpolated using the
A* pathfinding
algorithm.
Figure 6 is an example of a
participant’s path closely
following that of a bus
without intersecting it until
the participant begins
walking (large red region). At
that point in time, we can
conclude that the bus is
accessible to the individual.
While this example shows
that the colocation in time of
a participant and a bus is
identifiable, it also
exemplifies the possibility of
misinterpreting the case in
which the participant travels
near the bus for the
participant riding the bus.
Methods
We use seven features to define bus GPS data.
The participant data is provided by INTERACT, a Canadian collaboration of
scientists and urban planners evaluating the effects of changes in urban
environments on the health and equity of community members (Figure 3).
Figure 3: Heatmap of participant data in Victoria, BC.
Type of data Definition
Route ID A unique route identifier
Trip ID A unique trip identifier
Service ID A unique service identifier
Time The departure time from a specific stop
on a trip
Stop sequence Identifies the order of stops on a
particular trip
Easting The distance from the western edge of a
UTM zone
Northing The distance from the southern edge of a
UTM zone
Figure 4: Steps to compute the jPPA
Figure 5: Potential Path Area example
Figure 6: Joint Potential Path Area example
The PPAs were computed individually for participants and buses.
The overlaps of PPAs represents the jPPA (Figure 4).
GPS data has been previously used to study variables from the realm of
people’s exposure to and interaction with the environment [1]. An
environmental variable that has been found to be challenging to identify
is transportation mode [2]. An approach that has the potential to help in
decoding the intricacies of identifying transportation mode is Join
Potential Path Area (jPPA). Originally proposed to analyze human
spatial behaviours and previously used to find wildlife inter-individual
interaction, jPPA can be used to identify spatial-temporal overlap
between individuals’ paths and the public bus transportation system.
Using the jPPA implementation defined in [3] this study presents a
proof-of-concept method for finding the spatial-temporal overlap in
GPS data of individuals and the public bus system in an urban
environment. The study uses participant data from individuals in
Victoria, BC, Canada, as basis for identifying changes in individuals’
bus ridership behaviours in Saskatoon, SK, Canada. Specifically, the
study aims to better understand the change in bus ridership within the
context of metropolitan infrastructural changes.
Abstract