Park-and-Ride Station Choice Behavior in a Multimodal Network with Overlapping
Routes
A Thesis
SUBMITTED TO THE FACULTY OF THE
UNIVERSITY OF MINNESOTA
BY
Alexander Webb
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF
MASTER OF SCIENCE
Alireza Khani
May 24, 2020
Copyright © 2020 Alexander Webb. All rights reserved.
Acknowledgements
I first would like to thank my advisor, Alireza Khani, for taking a chance on me when I
reached out to merely discuss the prospect of graduate school in the spring of 2018. Without
his continued guidance, support, and encouragement this thesis would not exist. I would
also like to thank the Minnesota Department of Transportation for the grant that helped
fund this project, Brent Rusco and Jim Hendricksen for their support and feedback, and
Eric Lind at Metro Transit for his insights and collaboration. Thank you to my committee:
Jason Cao, Gary Davis, and Alireza Khani. Finally, I would like to thank my parents and
Rosie for encouraging me to pursue my interest in transportation planning, and my friends
in the Transit Research Lab for taking this journey with me.
i
Abstract
The purpose of this thesis is to provide insight into the travel behavior and pref-
erences of park-and-ride (PNR) users in the Twin Cities. From an on-board survey
conducted by Metro Transit in 2016, 1,690 PNR user’s route choices are used to es-
timate a discrete choice model. Precise coordinates of their origin, destination, and
parking location enable the calculation of travel time experienced by each PNR user,
as well as aspects of their transit path, such as walking time, waiting time, and re-
quired number of transfers. Further, attributes of each PNR facility are used to model
preferences for quality of service. A contribution of this thesis is the consideration of
overlapping routes. While previous literature on station choice has investigated the
relationship between routes that share a transit path, no studies specific to PNR choice
have considered the matter. In this study, route overlap is measured using a path size
factor and a nested logit model. The estimated models show significant evidence that
commute time spent in a car is approximately four times more burdensome than the
same amount of time spent in public transit. Evidence is shown that PNR users do not
strictly minimize total travel time in choosing their commute route. Ultimately, the
best-fitting model correctly predicts the PNR choice for 64% of users in a test sample.
This study is extended to define commuter travelsheds for commuters to the Uni-
versity of Minnesota using the previously estimated multinomial logit model. Upon
assigning each Travel Analysis Zone (TAZ) in the Twin Cities metropolitan area to a
given PNR travelshed, the total population served by each PNR facility is inferred. This
analysis may interest planners wanting to measure competition between PNR facilities
as well as their relative attractiveness.
ii
Contents
Contents iii
List of Tables v
List of Figures vi
1 Introduction 1
1.1 Background and Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 Methodology 7
2.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Street Network Shortest Path . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3 Schedule-based Transit Shortest Path . . . . . . . . . . . . . . . . . . . . . 10
2.4 Choice Set Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.5 Model Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3 Results 19
3.1 Model Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.2 Multimodal Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.3 Same Route, Different Station . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4 Application: Commuter Travelshed for the University of Minnesota 26
iii
Contents
4.1 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.2 Data and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.4 PNR Facility Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.5 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
5 Conclusion 37
Bibliography 39
iv
List of Tables
2.1 Explanatory Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.1 Logit Model Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4.1 Travelshed Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
v
List of Figures
1.1 Twin Cities Park-and-Ride facilities . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1 Distance Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 Nested Logit Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.1 Total Travel Time (dashed line shows the mean) . . . . . . . . . . . . . . . . . 23
3.2 Time Ratio for chosen routes (dashed line shows the mean) . . . . . . . . . . . 23
3.3 Walk time on chosen routes (dashed line shows the mean) . . . . . . . . . . . . 24
3.4 Alternative Choice Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4.1 Travelshed for PNR facilities serving the University of Minnesota, West Metro
Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.2 Travelshed for PNR facilities serving the University of Minnesota, East Metro
Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
vi
Chapter 1
Introduction
1.1 Background and Motivation
Since 2014, downtown Minneapolis has lost more than 5,500 parking stalls, and more than
2,400 of those have not been replaced [1]. Practically every major urban center across the
country is taking similar steps to repurpose excess parking infrastructure for other uses.
Not only does the City of Minneapolis intend to continue reducing the number of parking
spaces downtown, the city has outlawed the construction of new drive-throughs [2] and plans
to eliminate the requirement for off-street parking minimums for businesses [3]. Explicitly,
the Minneapolis 2040 plan aims to ”disincentivize driving and driving alone” [4]. These
policy recommendations have been echoed throughout the country and are unambiguous –
a seismic shift in the function of America’s urban centers is upon us.
The Twin Cities metropolitan area offers over 100 park-and-ride (PNR) facilities served
by express bus, heavy rail, and light rail that give commuters an alternative to driving
and parking downtown. Between 2004 and 2015, PNR usage in the Twin Cities grew by
almost 60%, but has decreased slightly since 2015 [5]. As parking becomes more difficult
in downtown Minneapolis and Saint Paul, improving PNR service will be essential to the
region’s pursuit of mobility and environmental goals. The purpose of this thesis is to provide
insight into the travel behavior and preferences of PNR users in the Twin Cities. From an
on-board survey conducted by Metro Transit in 2016, 1,690 PNR user’s route choices are
used to estimate a discrete choice model. Precise coordinates of their origin, destination,
and parking location enable the calculation of travel time experienced by each PNR user,
1
1.2. Literature Review
as well as aspects of their transit path, such as walking time, waiting time, and required
number of transfers. Further, attributes of each PNR facility are used to model preferences
for quality of service. Given the PNR that each user chose to use, a choice set of reasonable
alternatives is generated from the facilities shown in Figure 1.1.
A contribution of this thesis is the consideration of overlapping routes. While previous
literature on station choice has investigated the relationship between routes that share a
transit path, no studies specific to PNR choice have considered the matter. In this study,
route overlap is measured using a path size factor and a nested logit model. Finally, this
thesis will conclude with an application of the estimated choice model to determine PNR
travelsheds for commuters to the University of Minnesota. For each TAZ in the metropolitan
region, commuters will be assigned to the most likely PNR based on the previously estimated
choice model, resulting in a spatial understanding of the areas and populations served by
each PNR facility.
1.2 Literature Review
1.2.1 Findings
Station choice modeling first appeared in academic literature in the mid-1970s, and is now
an established application of discrete choice modelling [6]. Most often, researchers have used
revealed preference data to frame station choice as a utility maximization process. Among
the most common findings in station choice modelling is a negative effect of distance from
origin to station on station choice [7–9]. In the earliest study to report this finding the
researcher created a binary variable indicating if a station was ”local” to a given user,
and found this variable along with access time to be the most influential factors in station
choice [7]. Another study modeled Dutch Railway station choice as a share of postcode area
demand, and not only found a negative effect of access distance, but found a steeper negative
effect of access distance on non-motorized access modes compared to motorized access
2
1.2. Literature Review
Figure 1.1: Twin Cities Park-and-Ride facilities
3
1.2. Literature Review
modes [8]. Finally, a study of commuter train station choice around Montreal validated
these results, showing a negative effect of access time by mode on station choice [9]. Transit
frequency has also commonly been found to have a positive effect on station choice [8,9]. Due
to differences between transit networks, some of these key findings should be interpreted
with caution. For example, studies that found a positive effect of transit frequency on
station choice were conducted on rail transit systems with regular headways. In the Twin
Cities, PNR facilities are largely served by express buses with irregular headways, and
therefore station choice may have a different relationship with transit frequency.
The relatively limited body of literature specific to PNR station choice may offer the
most relevant findings to this study. A study from Perth, Australia used a stated pref-
erence survey to estimate a multinomial logit model for PNR station choice along a rail
network [10]. The findings indicate that quality of facilities and surrounding land-use most
significantly influence PNR station choice. Similar to station choice literature which found
access distance to be significant, this study observed 60% of PNR users boarding at the
nearest station to their origin. These results may not be widely applicable, however, as each
PNR user is assumed to face a choice between exactly two PNR locations. This limitation
is partially addressed by a study of PNR station choice in Toronto, in which train riders
face a choice between the five nearest stations and subway riders choose between the three
nearest stations [11]. The study found that access distance and the direction of the station
from their origin were the strongest predictors of station choice. The study is further lim-
ited by a lack of driving and transit path attributes. A study from Austin, Texas provides
the most relevant framework for analyzing PNR station choice in the United States [12].
The authors used on-board survey data to estimate passenger’s travel path, using a street
network representation to model shortest-path access times, and a schedule-based shortest
path algorithm to model transit paths [13]. Among the findings are preferences for higher
transit frequency, transit in-vehicle time less than ten minutes, and shorter walking times.
This recent study is significant for including detailed transit path information, as well as its
4
1.2. Literature Review
application of choice modelling to a transit system where express buses are the dominant
service.
1.2.2 Methodology
Across the literature, several methodological themes exist. First, most studies define a
choice set such that each user’s station choice is between a fixed number of stations
[8, 10, 11, 14], while a minority of studies define a more flexible choice set [9, 12]. Fixed
choice sets are easy to define and manage, but may also be highly influential in a model’s
understanding of choice behavior. Flexible choice sets are formed using some criteria to
determine which stations are reasonable or unreasonable alternatives for a given user. For
example, one study defines a reasonable alternative path as one whose total travel time
does not exceed the shortest total travel time plus 50 minutes [12]. This type of choice
set definition is preferable to a fixed definition as it does not dictate the size of a choice
set, but rather eliminates extreme alternatives based on observed behavior. Second, most
studies use Euclidean distance to measure the distance between a user’s origin and each
reasonable station [7, 8, 11]. One study improved upon this methodology by using a net-
work representation of the roads in Austin, Texas to approximate each user’s experiences
driving time [12]. A variety of methods are used to estimate transit travel times including a
Google Maps based algorithm [9] and a schedule-based shortest path algorithm proposed by
Khani [13]. These methods are preferable to simple measures of travel time, because they
include more detailed information about the experienced walking time, waiting time, and
number of transfers on a transit path. Finally, the studies reviewed in this chapter were
selected for their application of discrete choice modelling. More specifically, each study
estimates a multinomial logit model, and some estimate a mixed logit or nested logit model
for station choice. The mixed logit model provides a more flexible framework than the
multinomial logit model, allowing random taste variation, unrestricted substitution pat-
terns, and correlation in unobserved factors over time [15]. These benefits only carry the
5
1.2. Literature Review
burden of increased computation time. In the context of station choice, the nested logit
model has only been used for situations where a traveler has a two-stage choice between
stations and station access mode [8]. In this thesis, the nested logit will be adapted to
capture substitution patterns between the different transit modes available throughout the
Twin Cities PNR system.
1.2.3 Route Overlap
Literature on PNR station choice has yet to consider similarities between routes or overlap-
ping routes. When two different routes share part of a transit route, there exists a statistical
correlation between the alternatives that should be accounted for when estimating a discrete
choice model. The most related work in the context of PNR station choice comes from a
study in Brisbane, Australia which uses a modeling framework called Random Regret Min-
imization (RRM) that is notable for its accommodation of the “Compromise Effect” [14].
A compromise alternative is one with generally intermediate performance across several
attributes, in contrast to an alternative with extreme performance. For example, a PNR
facility that is an average driving distance from a user’s origin and provides average transit
speed would be a compromise alternative. The popularity of compromise alternatives has
been well-documented in many decision-making contexts, but is often overlooked in trans-
portation applications [16]. While this framework acknowledges a trade-off relation between
alternatives, it does not explicitly account for or measure route overlap. Outside of PNR
choice literature, a multimodal path size factor has been developed to measure subroute
overlap, and will be adapted for this study. Three different path size factor formulations
are proposed by Hoogendoorn-Lanser and Bovy, each accommodating a slightly different
multimodal path scenario. Ultimately, the study finds that the inclusion of a path size
factor in their discrete choice model significantly improves model performance [17].
6
Chapter 2
Methodology
2.1 Data
2.1.1 On-Board Survey
This study is made possible by an on-board survey conducted by Metro Transit, in which
transit riders were asked to answer questions about the origin and destination of their trip,
access mode, boarding time, transit route(s), trip purpose, and demographic information
[18]. The survey received 30,491 responses between April 2016 and February 2017, of which
4,033 (13.2%) recorded using a designated PNR facility. Only PNR users whose trip origin
was their home or a hotel and whose transit trip started at a PNR facility were ultimately
selected from the survey for further analysis (1,895 users). While each respondent was asked
to record the transit route they took to reach their destination, this information may be
unreliable or incomplete. This study uses the geospatial coordinates of each respondent’s
home, chosen PNR location, and destination to approximate each respondent’s travel time
and route (hereafter referred to as their “observed route”). After calculating a path for each
respondent and cleaning the data, 1,690 respondents with complete information remained
and were used to produce the results of this study.
2.1.2 Demographic Attributes
Previous studies have shown a significant relationship between socio-economic factors and
station choice, such as age and income [12]. This study will consider four individual-specific
attributes when modeling station choice: income, age, gender, and disability status. Each
7
2.1. Data
respondent of the on-board survey reported their household income as one of seven brackets
(e.g. $49,000 - $64,999, $150,000 or more). These brackets have been coded and ordered
for use in the model estimation. Age is reported in a similar fashion, with 5 distinct age
ranges. Finally, disability status is treated as a binary variable, in which each respondent
with a disability that effects their use of transit is marked as having a disability, while all
others are marked as not having a disability.
2.1.3 Park-and-ride Facility Attributes
Model estimation uses several facility-specific attributes from a dataset downloaded from
MN Geospatial Commons [19]. The Twin Cities has three transitways that serve PNR
facilities: the Northstar commuter rail, the Blue Line light rail transit (LRT), and the Red
Line bus rapid transit (BRT). These lines are distinct from standard express bus service in
quality and frequency of service. The Northstar is a commuter train that provides peak-
hour service with irregular headways, while the Blue Line has a ten minute headway for
most of the day, and is used for both commuting and intra-city travel. Finally, the Red Line
is a bus service that acts as an extension of the Blue Line, with 30 minute headways during
peak hours. These transitways first appear in the logit models as explanatory variables,
and later as a nest designation in the nested logit model. Detail is provided later in the
model construction. Another facility-specific variable, Amenities, counts how many of the
surveyed features exist at a given facility. The complete set of amenities is presented below:
• Electric vehicle charging station
• Shelter
• Indoor waiting area
• Lights
• Drop off area
8
2.2. Street Network Shortest Path
• Bench
• Trash
• Public restroom
• Elevator
• Escalator
• Bike racks
• Bike locker
2.2 Street Network Shortest Path
Using the origin coordinates of each survey respondent, the free-flow driving time and dis-
tance to each PNR facility were calculated using the python package Osmnx [20]. This
package uses OpenStreetMap’s API to download street geometries and provides a built-in
function to find the shortest path through the street network between any two coordinate
pairs. In the Twin Cities metropolitan area, OpenStreetMap has complete information
about the classification of each road segment, but for the majority of segments is missing a
speed limit. Thus, it was straightforward to calculate a distance-based shortest path, but
more information was needed to calculate a time-based shortest path. The road classifi-
cation for each road segment was used to approximate speed limits: any segment labeled
’motorway’ received a speed limit of 55 miles per hour, while every other classification was
given a speed limit of 30 miles per hour. Assuming that free-flow travel time is equivalent
to driving at the speed limit, a time-based shortest path was calculated from every origin
location to every PNR facility. In estimating logit models, both driving time and distance
will be tested separately as explanatory variables. If they both prove to be significant pre-
dictors of PNR facility choice, only the more significant one will be included in the final
model due to the close relationship between driving time and distance.
9
2.3. Schedule-based Transit Shortest Path
2.3 Schedule-based Transit Shortest Path
In contrast to the street network shortest path, a transit path depends on both direction
and time of travel. Finding a path through a transit path is a much more complicated
process as a result, and is performed using a previously developed algorithm [13]. Using
General Transit Feed Specification (GTFS) data, a time-expanded network is constructed
from the transit schedule [21,22]. Nodes are used to represent transit stops at a particular
point in time, thus the connection between nodes depends on spatiotemporal proximity. In
the transit network, Node A is connected to node B with a directed link if node B follows
node A in any transit route’s stop sequence. Node A can also be connected to node B if
they are within a tenth of a mile and within a 120 minute time window of each other. In
other words, transit passengers can only make a transfer if it requires less than a tenth of a
mile of walking, and the required waiting or walking time is less than 120 minutes. Given
a transit schedule, the algorithm generates a path through the network in which features
of a transit path can be weighted to mimic rider preferences. A previous study found the
disutility of transferring to be roughly equivalent to 35 minutes of walking time [12]. With
the intention of incorporating this finding as well as maintaining a flexible shortest-path
algorithm, transit paths generated for this study will have a transfer disutility penalty equal
to 15 minutes of walking or waiting time. This has the effect of forcing the algorithm to
avoid paths with a high number of transfers; it does not mean that transit paths with a
transfer are estimated to take longer than actually experienced.
In the context of PNR travel behavior in the Twin Cities, observed transit paths are
fairly predictable. Commuters park adjacent to their boarding stop, board an express bus
or train, and most often require no more than one transfer to reach their destination. Based
on this behavior, the path generated for each user has the following characteristics:
1. Maximum walking distance of 0.25 miles from parking location to initial boarding
stop
10
2.4. Choice Set Generation
2. Maximum walking distance of 1 mile from final egress stop to destination
3. High transfer penalty
In the on-board survey, respondents are asked to provide the hour window in which their
trip began (e.g. 8:00 - 9:00 AM). Travel time is relatively sensitive to departure time for
irregular transit routes, so several precautions were taken to limit inaccuracies in the travel
times associated with generated paths. Each path is generated such that the trip starts
and ends within two hours of the beginning of the stated time window. For a passenger
departing between 8:00 and 9:00 AM, the transit path is constrained to arrive at their
destination by 10:00 AM. Crucially, the shortest-path algorithm has been written in a way
that does not penalize early arrival or late departure. Thus, the assigned transit path is
simply the lowest cost trip within two hours of the surveyed boarding time. Once the path
is generated, the initial transit boarding time is inferred as the arrival time minus the travel
time. The transit path may include in-vehicle time, waiting time at a transfer point, walking
time between transfer points, and walking time from the final egress stop to a destination.
Because the initial departure time is not provided in the survey, waiting time at the initial
boarding stop is not included in total travel time.
Finally, the schedule-based shortest path algorithm is written to find a transit path
backwards through the transit network, as it greatly reduces computational time. In its
simplest form, Dijkstra’s shortest path algorithm finds the travel cost from one node to
every other node in the network. For this study, we are interested in finding the travel cost
from many PNR facilities to one destination. The problem is inverted, thus the algorithm
is inverted as well.
2.4 Choice Set Generation
In generating a choice set for each PNR user, this study solely considers PNR location
alternatives to the observed route. Thus, the option of driving the complete distance from
11
2.4. Choice Set Generation
origin to destination is beyond the scope of this study. To generate the choice set for each
user, an auto path and a transit path are calculated for all 111 PNR locations. Many of
these alternative routes may be unreasonable. In the interest of reducing each user’s choice
set to only include reasonable options, the distribution of observed route travel times was
examined to inform two route-eliminating criteria. For this study, a reasonable route has
the following features:
1. Time criterion: travel time ratio less than a threshold A = 1.657
Time Criterion: ttn,i
ttn,∗
< A (2.1)
2. Distance criterion: distance ratio less than a threshold B = 1.361
Distance Criterion: Xn,i + Yn,i
Zn
< B (2.2)
The first criterion aims to reduce each user’s choice set by eliminating routes with a
particularly long total travel time. The total travel time associated with the route through
PNRi for user n, ttn,i, is equal to the sum of the driving time from origin to PNRi, and the
time spent in transit between PNRi and the destination. For each user, the PNR location
that provides the shortest possible total travel time (and may differ from the user’s observed
route) is identified and assigned the ttn,∗ designation. So, the ratio of ttn,i to ttn,∗ is simply
a measure of how much longer a given route takes compared to the fastest possible route
available to each user. Finally, the threshold A is set to capture 95% of observed route
time ratios, thus eliminating the most extreme 5% of observed routes along with all other
routes with a time ratio greater than A. Similar to the first criterion, the second constrains
the choice set based on the straight-line distance from origin to destination. For each PNR
location alternative i and user n, three straight-line distances are calculated, as shown in
Figure 2.1. Xn,i is the straight-line distance from a user’s origin to a PNR location, while
12
2.5. Model Construction
Figure 2.1: Distance Ratio
Yn,i is the straight-line distance from PNR location to the user’s destination. This criterion
measures how “out of the way” each alternative PNR location is compared to a straight
path from origin to destination, Zn. The threshold B is set to capture 95% of observed
routes, and eliminate all alternative routes with extreme distance ratios. These two criteria
firmly ground each user’s choice set in both time space and Euclidean space, and reduce the
dataset to 1691 users. On average, each user is faced with about 19 reasonable alternatives
to their observed route. Choice set summary statistics are provided in Table 1.
2.5 Model Construction
2.5.1 Multinomial, Nested, and Mixed Logit
This study fits a multinomial logit model, mixed logit model, and nested logit model to the
data, and compares their respective predictive abilities. The base multinomial logit model
frames expected utility as the sum of observed and unobserved components:
Un,i = βxn,i + ϵn,i (2.3)
In Equation (2.3), Un,i is the expected utility that user n derives from alternative i. The
righthand side of the equation shows a vector xn,i of observed variables related to alternative
13
2.5. Model Construction
i, β which is a vector of coefficients to be estimated, and the unobserved random error, ϵn,i.
For this equation, the logit probabilities are:
Pn,i =
eβxn,i∑
i∈I βxn,i
(2.4)
In Equation (2.4), I is the complete set of alternatives faced by user n. This probability
expression assumes that user n will choose the alternative with the highest utility. Fur-
ther, this model assumes proportional substitution patterns across alternatives, known as
the Independence of Irrelevant Alternatives (IIA) property [15]. This assumption may be
unrealistic, and can be overcome in a variety of ways. First, if a relationship is known
between alternatives, they can be nested together in the aptly named nested logit model.
In this model, the alternatives i are partitioned into non-overlapping subsets B1,B2,… ,Bk.
The utility function becomes:
Un,i = Wn,k + Yn,i + ϵn,i (2.5)
In this equation, Wn,k depends on variables that describe nest k. Similarly, Yn,i represents
the variables that describe alternative i [15]. The choice probabilities are an extension of
Equation 4, where the probability of choosing alternative i in nest k is:
Pn,i = Pn,i|BkPn,Bk (2.6)
where:
Pn,Bk =
eWn,k+λkQn,k∑K
l=1 e
Wn,i+λkQn,i
(2.7)
Pn,i|Bk =
e
Yn,i
λk∑
i∈Bk e
Yn,i
λk
(2.8)
Qn,k = ln
∑
i∈Bk
e
Yn,i
λk (2.9)
14
2.5. Model Construction
Figure 2.2: Nested Logit Structure
The nest parameter λk measures the degree of independence in unobserved utility be-
tween alternatives in nest k, and is between 0 and 1 in the context of utility maximization.
When λk = 1, this model reduces to the multinomial logit model, indicating that no cor-
relation exists between alternatives in nest k. Conversely, a small value for λk indicates
correlation in unobserved utility within nest k. One of the most common applications of
the nested logit model is in transportation mode choice, as alternative modes have been
shown to have disproportionate substitution rates [8]. Even more flexible than the nested
logit model is the mixed logit model. While the previous two models are deterministic,
the mixed logit is a simulation-based model that allows for random taste variation across
users, unrestricted substitution patterns, and correlation in the unobserved factors [15].
The mixed logit choice probabilities can be expressed as:
Pn,i =
∫
eβxn,i∑
i∈I βxn,i
f(β)dβ (2.10)
In Equation (2.10), the mixed logit probability is a weighted average of the probability
described in Equation (2.6) evaluated for different values of β, where the values of β are
taken from the density function, f(β). The main distinction here is that β is not treated
as a fixed number, but instead a random variable whose density f(β) is a function of the
mean and covariance of β across the population [15].
All three of these logit models were estimated using the pylogit package in Python
15
2.5. Model Construction
[23]. Three different nesting setups were tested for the nested logit model, and the model
described in Figure 2.2 was ultimately selected. In estimating the simulation-based mixed
logit model, 500 draws were taken from the distribution of the random coefficients. For
all three models, all variables listed in Table 2.1 were initially included as predictors, and
insignificant variables were incrementally eliminated until every remaining variable was
significant at the 0.05 level.
2.5.2 Explanatory Variables
Table 2.1: Explanatory Variables
Variable Description Mean Std.
Dev.
Individual Attributes
Age Survey response category (e.g. 18-24, 55-64) 35-44
Income Survey Response category (e.g. $49,000 - $64,999, $150,000
or more)
$60 -
$100k
-
Disability
status
Survey Response; 1 = disability impacting transit use, 0 =
otherwise
0.04 -
Female Survey Response; 1 = female, 0 = otherwise 0.6 -
Path Attributes
In-transit
time
Total time spent in a bus or train (minutes) 36.6 13.0
In-car time Total time spent driving (minutes) 10.3 12.2
Driving dis-
tance
Total distance driven (miles) 5.9 7.7
Walk time Total time spent walking (minutes) 6.0 4.1
Wait time Total time spent waiting between transfers (minutes) 0.4 1.7
Transfers Number of transfers on a transit path 0.13 0.4
Average
headway
Average time between buses/trains for the route boarded
at a PNR, during the time period of boarding
30.4 24.6
16
2.5. Model Construction
Distance ra-
tio
Measure of how directly a path goes from origin to desti-
nation (see Figure 2)
1.1 0.1
Time ratio Measure of how much longer a given path takes than the
fastest path available for each individual, see Equation (2.1)
1.2 0.2
Park-and-ride Attributes
Lot Capacity Number of parking spaces at a park-and-ride facility 692.9 439.8
# Routes
served
Number of unique transit routes that stop at a given park-
and-ride facility
3 2.3
Structured 1 = facility has a structured parking lot, 0 = otherwise 0.5 -
Transitway 1 = facility is served by Blue Line, Red Line, or Northstar,
0 = otherwise
0.3 -
Amenities Number of amenities available at a facility 6.6 2.6
2.5.3 Path Size Factor
It has been acknowledged that a shortcoming of the multinomial logit model is its failure
to account for overlapping routes, and as a result may produce unrealistic choice proba-
bilities [17]. Introducing a path size factor to the logit model addresses this problem by
measuring the extent to which a given route overlaps with other routes, and adjusting utility
accordingly. For this study, a path size factor is calculated solely for the transit sub-route
of a given path. The factor is calculated as the following [17]:
PSirn =
1
Lir
∑
a∈Air
la
Nna
(2.11)
where Air is the set of legs in a subroute r of path i, Lir is the total length in minutes
of a subroute, and l is the length in minutes of a leg of the subroute. For any leg of a
subroute, a, Nna is the number of distinct routes sharing that leg.
Crucial to the calculation of the path size factor is complete information about the
transit stops passed through on a given transit path. First, Lir is set equal to the difference
between the first boarding time and the final egress time on a transit path. When the
17
2.5. Model Construction
path includes a transfer between transit routes, the access and egress points will not be
connected by a single transit route. Next, Air is found by creating an ordered list of transit
stops that each path passes through. While the time at which the stop was passed through
is critical to determine the order of the stops, the time is not considered when comparing
two transit paths. In other words, two paths that cover the same stretch of road at different
times during the day are considered to be overlapping routes. Once the ordered set of stops
is found for each transit path in the choice set of user n , Nna increases by one for every
occurrence of two consecutive transit stops in the choice set of user n. Finally, the length
of overlap is determined by the length of time scheduled between two consecutive transit
stops. For example, if it a transit route is scheduled to pass through stop B three minutes
after stop A, the length of overlap on that leg of the transit path would be three minutes.
In the Twin Cities, there are examples of routes that share transit stops, but take
different paths in between. An example of this is the 53 and 21 buses, which both run along
Lake Street in Minneapolis and Marshall Avenue in Saint Paul. They diverge at Snelling
Avenue, where the 53 takes the I-94 until it reaches downtown Saint Paul, while the 21
continues along Marshall Avenue until reaching downtown Saint Paul. So, these two bus
routes share a bus stop at Marshall and Snelling Avenues, diverge to take different paths,
and then meet back up in downtown Saint Paul. The path size factor used in this study
would not consider these two routes to overlap between Snelling Avenue and downtown
Saint Paul. While these two bus routes start and end in the same place, they serve different
purposes; the 53 acts as an express bus through Saint Paul while the 21 stops frequently
along a major commercial corridor. For this study, overlapping paths necessarily have road
segments and at least two transit stops in common, but may serve substantially different
sets of transit stops throughout the full length of their routes.
18
Chapter 3
Results
3.1 Model Results
Table 3.1: Logit Model Results
Variable MNL Nested Mixed
transit time -0.092*** -0.054*** -0.11***
in-car time -0.39*** -0.11*** -0.52***
walk time -0.067*** -0.025*** -0.079**
transfers -1.61*** -0.39*** -2.0054***
avg. headway -0.015*** -0.005*** -0.016***
distance ratio -3.81*** - -4.67***
capacity 0.0014*** 0.0009*** 0.002***
transitway 1.53*** - 1.73***
structured 0.47*** -0.32*** 0.56***
# routes available -0.13*** -0.047*** -0.21***
path size 0.56* - -
transitway nest 0.54
bus nest 0.38**
σ in-car time 0.17***
σ walk time 0.20***
σ # routes
available
0.40***
McFadden’s R2 0.598 0.456 0.613
Log-Likelihood -1,280.19 -2,387.82 -1,232.92
19
3.1. Model Results
Predictive Ability 64.3% 53.4% 63.7%
*** p < 0.001, ** p < 0.01, * p < 0.05
Table 3.1 shows the estimation results for the multinomial, nested, and mixed logit models.
Among all of the variables tested, only those that are significant at the 95% were used
to estimate the final models. Based on McFadden’s R2 and log-likelihood measures, the
multinomial and mixed logit models provide a significantly better fit to the data than the
nested logit model. All three models agree on the relative effect of each variable; the sign of
each coefficient is consistent across all three models. The in-transit and in-car coefficients
tell us that PNR users generally choose a larger percentage of their total trip time to be
spent on transit as opposed to in a car. The distance ratio coefficient indicates that PNR
users prefer to be moving in the direction of their destination. Given the insignificance
(and exclusion) of the time ratio coefficient, PNR users are less interested in minimizing
total travel time. In summary of the average behavior, PNR users are more interested in
minimizing driving time and distance traveled than minimizing total travel time.
Coefficients for walk time and transfers offer insight into preferences along a transit
path. Adding a transfer to the transit path has a marginal rate of substitution of 17.5 with
transit time. In other words, PNR users choose to ride transit routes with no transfers
instead of routes that are 17.5 minutes faster but include a transfer. A similar interpreta-
tion can be given for the transitway coefficient: PNR users have no preference between a
Transitway route and an express bus route that is 16.6 minutes faster. This finding alone
emphasizes the success of investing in transitway infrastructure along PNR routes. Finally,
the coefficient found for the number of routes available variable does not lend itself to
an intuitive explanation. The sign is negative, indicating that PNR users have a positive
perception of facilities with fewer transit routes available. It may be the case that this
variable has some unrepresented spatial component. For example, PNR facilties nearest to
downtown Minneapolis may serve the most routes, while those that are farther away serve
20
3.2. Multimodal Behavior
fewer routes. If this is the case, the negative coefficient may reflect the finding that PNR
users perceive transit time more positively than transit time.
The purpose of fitting a nested logit model was to explain differences between service
types based on intuition, however the nest specification ultimately gave a significantly worse
fit to the data than the other models. While further work should be done on mode nesting,
it appears that the effect of transit type is more effectively captured by the transitway
variables in the multinomial and mixed logit models. The variance of every variable was
tested for heterogeneity across users in the mixed logit model, and three were found to
vary significantly. As a result, this variance is reflected in the model by the three sigma
terms. Finally, it is worth noting a few variables that were tested but insignificant across all
models tested. Individual attributes such as income and gender as well as several interaction
terms were found to be insignificant, as was the number of amenities available at each PNR
facility.
All three models presented in Table 3.1 are estimated using a random sample of 70%
of the PNR users and validated against the remaining 30% of PNR users. This process
was repeated for ten random samples and the average predictive ability is reported for each
model. For simplicity of interpretation, the predictive ability is the percentage of observed
routes that have the highest choice probabilities among each user’s choice set of alternatives.
The highest predictive ability indicates that the multinomial logit model correctly identified
the chosen PNR facility for 64.3% of the test sample.
3.2 Multimodal Behavior
Following the results of the logit models, Figure 3.1 contrasts the total travel time for
observed routes and all other routes in choice sets. First, the scale of the distributions are
different because there are a total of 33,822 routes considered while only 1,690 were chosen
by surveyed individuals. Still, only 1.6% of chosen routes exceed 100 minutes of total travel
21
3.2. Multimodal Behavior
time and have an average total travel time of 46.9 minutes. In contrast, 8.6% of non-chosen
routes exceed 100 minutes and have an average total travel time of 63 minutes.
Figure 3.2 shows the time ratio for each surveyed individual, which is a ratio of the travel
time of their chosen route compared to the travel time of the fastest route available. While
a significant proportion have a ratio value of one indicating that they chose the fastest
route available, the overall distribution shows that surveyed individuals are not strictly
time minimizing. On average, they chose a route that is 17% longer than the shortest route
available to them. As discovered from the logit model coefficients, PNR users prefer to
minimize driving time and total distance before minimizing total travel time. In Figure 3.2,
the otherwise smooth distribution appears to be interrupted by a sudden drop around the
1.02 mark. This could be explained by the distribution of PNR facilities throughout the
Twin Cities. PNR facilities are often associated with specific commuter communities, such
as Burnsville, Maple Grove, and Inver Grove Heights. The gap in the figure may reflect
the gap in space between the locally-serving PNR facility for these communities and the
next nearest selection of suburban PNR facilities. In other words, the figure shows that
choice sets are often missing alternatives that are 2-4% longer than the fastest alternative
available.
In both the multinomial and mixed logit model estimations, the Transitway variable
was found to be significantly positive, meaning that PNR users perceive the Transitway
routes to have higher utility than comparable express bus routes. In the multinomial logit
model, the Transitway coefficient has a magnitude equivalent to about 23 minutes of walk
time. This relationship can be further explored by plotting the density curves for walk
time by transit service, as shown in Figure 3.3. We can see that PNR users who chose
to use transitway routes walked on average about three minutes longer than express bus
users. For PNR users, very little walk time is incurred at the start of a transit trip because
the PNR parking facilities usually sit very near to the transit stops. Thus, the density
curves shown in Figure 3.3 mainly capture the walking time between the alighting stop and
22
3.2. Multimodal Behavior
Figure 3.1: Total Travel Time (dashed line shows the mean)
Figure 3.2: Time Ratio for chosen routes (dashed line shows the mean)
23
3.3. Same Route, Different Station
Figure 3.3: Walk time on chosen routes (dashed line shows the mean)
final destination. It can be interpreted that PNR users are less likely to consider taking
an express bus route than a transitway service if the express bus route does not stop very
near to their destination. This could have major implications for transit planners aiming
to serve large areas without expanding the number of transit routes available – transitway
riders are willing to walk further distances to reach their destination from their alighting
stop.
3.3 Same Route, Different Station
To better understand the predictive ability of these models, we can further explore the
nature of the prediction error. Upon estimating the multinomial logit model and calculating
the choice probabilities for each alternative, each user’s set of alternatives is put in one of
two groups: those with the same first transit route as the observed path, and those with a
different first transit route. Across all user choice sets, same-first-transit-route alternatives
24
3.3. Same Route, Different Station
Figure 3.4: Alternative Choice Probabilities
made up about 5% of alternatives, while other alternatives made up the remaining 95%.
Figure 3.4 shows the normalized choice probability densities for these two groups. The
Kolmogorov-Smirnov test gives significant evidence that these density functions come from
different distributions [24]. Further, same route alternatives generally have higher choice
probabilities, and thus higher utility. This means that the multinomial logit model may
be better at predicting a PNR user’s route than their boarding station. To test this, we
compare the observed transit route to the predicted transit route, and find a 75% match
rate, showing a substantial increase over the 64% match rate for station prediction.
25
Chapter 4
Application: Commuter Travelshed for the University of Minnesota
4.1 Objective
This chapter will explore the process of defining commuter travelsheds for commuters to
the University of Minnesota using the multinomial logit model estimated in the previous
section. Travelsheds for each PNR facility are defined analogously to a catchment area in
human geography: the area from which a PNR facility attracts users. Defining these areas
can be useful to planners interested in better understanding which areas are underserved
by PNR facilities in the commuter region. Travelsheds can also inform the expected growth
in usage for each facility over time by associating population growth projections from each
TAZ with a PNR facility. The following chapter will explain the data and methodology
used to calculate travelshed regions, followed by an analysis and discussion of limitations.
Within academic research, few studies describe an approach for delineating travelsheds.
One study estimates travelsheds using a parabolic shape based on the idea of a horizontal
and vertical ”break even” distance [25]. It is first assumed that users of a PNR facility
are drawn from a parabolic region centered around a line drawn from the Central Business
District (CBD) to the PNR facility. The break even distance from the PNR facility is the
point in space at which the options of either using the PNR facility or driving the complete
distance to the CBD would offer the same travel time. This distance has both vertical and
horizontal implications for the shape of the parabolic travelshed region [26]. Outside of this
methodology, no standard approach exists for estimating travelshed regions.
26
4.2. Data and Methods
4.2 Data and Methods
Estimating logit models in the previous chapter relied on a dataset containing origin-
destination coordinate pairs for PNR users, and this portion of the study will require
generating a similar dataset. The Twin Cities Traffic Analysis Zone (TAZ) dataset was
downloaded from Minnesota Geospatial Commons - these 3,030 zones will act as the ori-
gin locations representative of commuters throughout the region [27]. TAZs are defined as
bounded areas, so the coordinate pairs of each TAZ centroid will be used when generating
travel times. Next, the Coffman Union transit station was used as the destination associated
with every TAZ. This destination was chosen because all commuter bus routes that serve
the university pass through the Coffman Union transit station, and it is relatively central
to the University campus. Using TAZs centroids together with the previously estimated
utility model will answer the following question: given a commuter’s origin location, which
PNR commute alternative to the University of Minnesota campus will yield the highest
utility?
For many TAZs, using a PNR facility to reach campus will be unreasonable or may
not be the best transit option. For example, it will be much faster for many commuters
from downtown Minneapolis to take the Green Line train to campus. Similarly, many areas
within City of Minneapolis limits are served by local transit routes that go directly to the
Coffman Union transit station. To most accurately define commuter travelsheds for each
PNR facility, TAZs were only considered if a PNR facility was the fastest transit option
available. In other words, transit travel times were calculated from every TAZ to Coffman
Union, and those for which a local transit route was faster than the fastest PNR option
were removed from the dataset.
27
4.3. Results
4.2.1 Auto and Transit Travel Time
Similar to the initial PNR user driving time estimations, the python package Osmnx was
used to estimate the free-flow shortest-path driving time from every TAZ to every PNR
facility. Time of day was not considered when calculating these estimates, and speed limits
were assigned using the method described in Section 2.2. Transit travel times from every
PNR facility to Coffman Union transit station were found using a schedule-based transit
shortest path, described in Section 2.3. Because the origin-destination pairs are being used
to estimate average commuter behavior to the Universtiy of Minnesota, the transit paths
were identified as the shortest available route that begins and ends between 7 am and 9
am. Using these two travel path components, a total travel time was calculated for every
TAZ and PNR facility pair.
4.2.2 Choice Set Generation
Unlike the choice set generation performed for the initial model estimation in Chapter 2,
only the PNR facilities that directly serve Coffman Union with no required transfers were
considered in the choice set generation for each TAZ. These 21 PNR facilities are listed by
name in Table 4.1. The methodology from Section 2.4 was adopted for each TAZ’s choice
set, eliminating the PNR alternatives that did not meet the Time and Distance criteria.
All PNR alternatives remained in the choice set for all TAZ origins, meaning the two
criteria did not eliminate any alternatives. This is likely an outcome of previously filtering
each choice set to only include direct transit routes to Coffman Union. Three TAZs were
eliminated from the dataset due to missing data, leaving 3,027 TAZs each with 21 PNR
facility alternatives to reach Coffman Union.
28
4.3. Results
Figure 4.1: Travelshed for PNR facilities serving the University of Minnesota, West Metro Area
29
4.3. Results
Figure 4.2: Travelshed for PNR facilities serving the University of Minnesota, East Metro Area
30
4.3. Results
4.3 Results
Figures 4.1 and 4.2 show the Twin Cities Metropolitan Area with TAZs color coded by
which PNR facility a commuter would most likely use if traveling to the University of
Minnesota between 7 and 9 am. Using the multinomial logit model previously estimated
from survey data, the utility of each PNR facility for each TAZ was modeled, translated
to a choice probability, and the PNR facility with the highest probability was selected as
the most likely option. Several findings from the multinomial logit model are apparent
in travelshed patterns. First, travelsheds are largest furthest away from the University of
Minnesota. This reflects the finding that PNR users choose the facility with the shortest
driving distance from their origin because the PNR facilities farthest from the University
often present the travel path that involves the least driving. Second, some of the travelsheds
are composed of non-contiguous TAZs, which may be explained by the use of travel time as
opposed to distance. Due to varying driving speeds by road classification, some TAZs are
closer in travel time to a given PNR facility than other TAZs that are closer in space. In the
center of Minneapolis, grey TAZs are those for which using a PNR facility was slower than
taking a local transit route to reach Coffman Union. Similar to the shaping of travelsheds,
the grey region is defined by transit speed as opposed to transit distance.
Table 4.1: Travelshed Results
Name ID Employed
pop. 2020
Employed
pop. 2030
Change (%) Attractiveness
Grace Church 59 245,967 257,932 4.9 88.1
Burnsville Transit
Station
101 173,785 188,695 8.6 79.3
I-35W & 95th Ave 36 172,595 188,081 9 93.4
Maple Grove Tran-
sit Station
47 171,473 189,867 10.7 81.2
Hwy 61 & Co Rd C 32 139,569 150,804 8 76.3
31
4.3. Results
Southdale Transit
Center
99 130,935 139,531 6.6 80.6
SouthWest Station 104 89,409 95,680 7 76.1
Co Rd 73 & I-394
South
4 84,628 90,787 7.3 49.3
Cedar Grove Tran-
sit Station
109 82,684 89,974 8.8 70.2
Louisiana Ave
Transit Center
97 74,003 77,590 4.8 44.5
South Bloomington
Transit Center
100 62,712 68,169 8.7 73.5
General Mills Blvd
& I-394
24 62,039 65,513 5.6 41.4
Park Place & I-394 27 56,489 58,703 3.9 73.9
East Creek Station 70 33,503 38,269 14.2 61.9
SouthWest Village 67 30,959 34,346 10.9 42.3
Plymouth Road
Park & Ride
98 16,705 17,987 7.7 0.0
Southbridge Cross-
ing
61 7,312 8,026 9.8 38.2
Marschall Road
Transit Station
87 6,769 7,731 14.2 37.9
Eagle Creek Transit
Station
108 5,560 6,200 11.5 34.3
Station 73 105 4,662 5,008 7.4 0.0
Chanhassen Tran-
sit Station
79 4,006 4,351 8.6 0.0
*PNR 98, 105, and 79 have a choice probability between zero and a tenth of a percent,
and appear as zero due to rounding.
32
4.4. PNR Facility Comparison
4.4 PNR Facility Comparison
A significant body of literature exists on the optimal placement of PNR facilities – that
is, if a transit provider were to create a new PNR facility or move an existing one, where
should it be placed? A related question has been less-often explored in academic literature
but remains of interest to planners: which PNR facilities are providing the least value
and can thus be eliminated? Table 4.1 lists each PNR facility that serves the University of
Minnesota, as well as some information that may inform the answer to that question. Based
on official employed population projections for each TAZ, the total employed population
that is served by each PNR facility is shown for both 2020 and 2030, calculated as:
Empj =
∑
i∈I
Empi ∗ P (ij) ∀j ∈ J (4.1)
where ”Emp” is an abbreviation of ”Employed Population Served”, J is the set of all
PNR facilities, I is the set of all TAZs, and P (ij) is the probability that a commuter from
TAZ i would choose to use PNR facility j. These projections can be used to estimate the
potential volume of ridership for each PNR facility. Similarly, employed population growth
can be used to predict the change in ridership for each PNR facility. It should be noted
that these population numbers represent the whole of the population, while this application
only considers PNR routes to the University of Minnesota. If a planner is only interested
in forecasting ridership to the University, these employed population numbers should be
multiplied by some estimated proportion of the total employed population that commutes
to the University of Minnesota. Estimating total PNR ridership for a given facility will
require further study. Many PNR facilities that have attractive service to the University
of Minnesota have relatively unattractive service to downtown Minneapolis. It is easy to
see that, depending on the destination of a PNR user, the attractiveness of each PNR
facility will change significantly. If this method is used for PNR demand forecasting, a
planner should be equipped with information about the proportions of employees who work
33
4.4. PNR Facility Comparison
in various employment hubs throughout the metropolitan area. Simply, they could con-
sider employees as working in one of three locations: the University of Minnesota campus,
downtown Minneapolis, and downtown Saint Paul.
In addition to considering the total employed population served, the logit choice prob-
abilities can help us understand the relative attraction of each PNR facility given a desti-
nation. In Table 4.1, ”Attractiveness” records the following measure:
Attractivenessj =
∑n
i∈I P (ij) ∗ zij∑
i∈I zij
∀j ∈ J (4.2)
zij = 1 : P (ij) > P (ik) ∀k ∈ J zij = 0 : otherwise (4.3)
where J is the set of all PNR facilities, I is the set of all TAZs, P (ij) is the probability
that a commuter from TAZ i would choose to use PNR facility j, and zij is a binary variable
indicating if j is the highest probability alternative for commuters from TAZ i. The Attrac-
tiveness measure for each PNR facility can be interpreted as the average choice probability
among TAZs within its travelshed. A higher value means that the PNR alternative is rel-
atively more attractive compared to other alternatives in the choice set. Similarly, a low
probability means that the PNR facility did not stand out from other alternatives and was
selected somewhat agnostically. For example, if a choice set consists of three alternatives
and each has a choice probability of one third, the PNR user will randomly choose between
the alternatives.
Some trends emerge when comparing PNR Attractiveness and Employed Population
Served. First, PNR Attractiveness has a statistically significant positive relationship with
Employed Population Served. This trend is particularly evident at the extremes, where
highly attractive facilities serve a large population while the least attractive facilities serve
relatively few. This trend is a combination of more attractive facilities drawing more users,
and the effects of some TAZs having higher populations than others. In between, variation
34
4.5. Limitations
within the trend may give reason to investigate the overall success of a given PNR facility.
PNR 100 and 24 serve a very similar number of employed individuals, but PNR 100 has
an Attractiveness score of 73.5 which dwarfs the 41.4 rating for PNR 24. This means that
PNR 100 is a clear choice for its users while PNR 24 is competing closely with other PNR
facilities for its users. The importance of understanding these numbers in context cannot
be understated. PNRs can differentiate themselves in unobserved ways - the availability of
land, service to marginalized communities, or service to underserved destinations. These
numbers can, however, serving as a starting point to understand where a surplus or deficit
of PNR service exists throughout the metropolitan area.
4.5 Limitations
While this travelshed analysis can paint in broad strokes the behavior we would expect to
see from commuters to the University of Minnesota, analysis is limited in several ways by
the aggregate nature of the data. First, it is assumed that all commuters are traveling to
Coffman Union station. While this point is central to much of the university campus, it
may not capture the full extent of many commutes. For example, walk time from the final
alighting stop to any destination is effectively ignored in travel time calculations by setting
the transit stop as the destination itself. Second, assigning the entire employed population
from each TAZ to a PNR facility may not have a strong relationship with the number of
expected commuters to the university, as university employees are not uniformly distributed
throughout the metropolitan area. Lastly, some TAZs were eliminated from travelsheds
because it would be faster for a commuter from that TAZ to ride transit without driving at
all. This measure was likely unable to identify all of the TAZs from which its residents ride
local transit instead of using a PNR facility. This comes about because comparing local
transit to PNR routes based solely on travel time ignores the disutility of driving compared
to not driving. Even if a PNR facility can offer the fastest commute time for a commuter,
35
4.5. Limitations
it may be preferable to ride transit the whole distance and avoid driving all together. Thus,
some of the travelsheds generated for each PNR facility will include too many TAZs.
36
Chapter 5
Conclusion
Among the models tested, the multinomial and mixed logit models were found to most
accurately reveal PNR user preferences from the Metro Transit On-Board Survey data.
The model shows that PNR users choose travel paths with a high proportion of time spent
on transit, and PNR locations with a small distance ratio, where distance ratio measures
how “out of the way” a PNR location is when travelling from origin to destination. The
models further indicate that PNR users are not necessarily looking to use the PNR lot
that minimizes their overall travel time. It may be incorrect to draw the conclusion that
PNR users do not value shortening travel time, but instead that additional travel time is
not as burdensome as some other factors, such as transferring between transit routes. This
outcome is most likely a result of the choice set definition, where some alternative routes
may in practice be unreasonable despite their competitive travel time. One particularly
meaningful comparison is that of the coefficients of driving time and transferring. The
multinomial logit model shows that adding a transfer to a transit path has the disutility
equivalent to an additional 17.5 minutes of transit time. PNR users also exhibited facilities
preferences – structured lot facilities were preferred to surface parking facilities, and facilities
that served more unique transit routes were perceived negatively. Lastly, the presence of
a Transitway route in the multinomial logit model made a PNR location more attractive,
meaning Transitway routes were sought out in higher proportion than their representation
in user’s choice sets.
This study joins a small body of literature on PNR location choice, and is innovative
in its inclusion and analysis of overlapping routes. First, a nested logit model was esti-
37
mated to capture substitution rates between transitway routes and express bus service.
This model gave an inferior fit to the data compared to the multinomial and mixed logit
models. Second, a sub-route path size factor for the transit leg of each path was calculated,
and found to be significant in the multinomial logit model estimation. This model suc-
cessfully predicted the PNR location choice of 64.3% of users when tested on a sample set
of PNR users, and was used to generate travelsheds for each PNR facility that serves the
University of Minnesota. The centroids of all 3,030 TAZs in the Twin Cities metropolitan
area were used to represent commuters to the University, and were assigned to the PNR
facility with the highest choice probability among their choice set alternatives. In addition
to creating a spatial representation of the areas served by each PNR facility, this simulation
provided the total employed population served by each PNR facility as well as a measure of
attractiveness for each PNR facility. While this application outlines the methodology for
generating travelsheds, future work should include information about the spatial distribu-
tion and proportion of commuters to the University of Minnesota to produce more refined
results.
38
Bibliography
[1] Emma Nelson. It’s not your imagination — parking is disappearing in Minneapolis.
Star Tribune, 2017.
[2] Peter Cox. Minneapolis bans new drive-thrus. MPR News, 2019.
[3] Minneapolis Department of Community Planning and Economic Development.
Minneapolis 2040, Pedestrian-Oriented Building and Site Design.
[4] Minneapolis Department of Community Planning and Economic Development.
Minneapolis 2040, Clean environment.
[5] Emma Pickett. 2018 Annual Regional Park-and-Ride System Report. Technical
report, Metro Transit, January 2019.
[6] Marcus A. Young and Simon P. Blainey. Development of railway station choice
models to improve the representation of station catchments in rail demand models.
Transportation Planning and Technology, 41(1):80–103, 2018.
[7] Cheryl Rosen Kastrenakes. Development of a Rail Station Choice Model for NJ
Transit. Transportation Research Record, 1(1162):16–21, 1988.
[8] Ghebreegziabiher Debrezion, Eric Pels, and Piet Rietveld. Modelling the joint access
mode and railway station choice. Transportation Research Part E: Logistics and
Transportation Review, 45(1):270–283, 2009.
[9] Vincent Chakour and Naveen Eluru. Analyzing commuter train user behavior: A
decision framework for access mode and station choice. Transportation Research
Record, 15(1):74–83, 2014.
[10] Doina Olaru, Brett Smith, Jianhong (Cecilia) Xia, and Ting (Grace) Lin. Travellers’
Attitudes Towards Park-and-Ride (PnR) and Choice of PnR Station: Evidence from
Perth, Western Australia. Procedia - Social and Behavioral Sciences,
162(Panam):101–110, 2014.
[11] Mohamed Salah Mahmoud, Khandker Nurul Habib, and Amer Shalaby.
Park-and-Ride Access Station Choice Model for Cross-Regional Commuting.
Transportation Research Record: Journal of the Transportation Research Board,
2419(1):92–100, 2014.
39
Bibliography
[12] Hao Pang and Alireza Khani. Modeling park-and-ride location choice of
heterogeneous commuters. Transportation, 45(1):71–87, 2018.
[13] Alireza Khani, Mark Hickman, and Hyunsoo Noh. Trip-Based Path Algorithms
Using the Transit Network Hierarchy. Networks and Spatial Economics,
15(3):635–653, 2014.
[14] Bibhuti Sharma, Mark Hickman, and Neema Nassir. Park-and-ride lot choice model
using random utility maximization and random regret minimization. Transportation,
pages 1–16, 2017.
[15] Kenneth E Train. Discrete choice methods with simulation. Cambridge university
press, 2009.
[16] Caspar G. Chorus and Michel Bierlaire. An empirical comparison of travel choice
models that capture preferences for compromise alternatives. Transportation,
40(3):549–562, 2013.
[17] Sascha Hoogendoorn-Lanser and Piet Bovy. Modeling overlap in multimodal route
choice by including trip part-specific path size factors. Transportation Research
Record, 1(2003):74–83, 2007.
[18] Metro Transit. 2016 On-Board Survey.
[19] MN Geospatial Commons. Park and Ride Lots.
[20] Geoff Boeing. Osmnx: New methods for acquiring, constructing, analyzing, and
visualizing complex street networks. Computers Environment and Urban Systems,
65:126–139, 07 2017.
[21] MN Geospatial Commons. Metro Transit Schedule Data - General Transit Feed
Specification (GTFS).
[22] MN Geospatial Commons. Minnesota Valley Transit Authority - General Transit
Feed Specification (GTFS).
[23] Timothy Brathwaite and Joan L. Walker. Asymmetric, closed-form, finite-parameter
models of multinomial choice. Journal of choice modelling, 29(C):78–112, 2018.
[24] Frank J. Massey Jr. The kolmogorov-smirnov test for goodness of fit. Journal of the
American Statistical Association, 46(253):68–78, 1951.
[25] Bilal Farhan and Alan T Murray. A GIS-based approach for delineating market areas
for park and ride facilities. Transactions in GIS, 9(2):91–108, 2005.
[26] Jose Holguin-Veras, Jack Reilly, Felipe Aros-Vera, et al. New York City park and ride
study. Technical report, University Transportation Research Center, 2012.
40
Bibliography
[27] MN Geospatial Commons. Transportation Analysis Zones (Official TAZ System
w/3,030 Zones) with Current Forecasts.
41