A Random Utility Maximization (RUM) based Measure of Accessibility to Transit: Accurate Capturing of the First-Mile Issue in Urban Transit

Abstract

The paper presents a random utility-based measure of accessibility to explain the first-mile issue in urban transit. A discrete access stop/station location choice model is used to calculate the expected maximum utility of transit access choices as the measure of the proposed access to transit measurement approach. It captures the effects of changes in various personal, socio-demographic, transportation and land-use variables on access to urban transit that are overlooked by conventional approaches of accessibility measurements (count-based cumulative opportunities measures and gravity-based measures). The proposed accessibility to transit measurement approach is empirically measured for the Greater Toronto Area and is integrated into an operational tool programmed in a GIS based traffic assignment software, TransCAD 7.0. This allows comparing it against the conventional measures and the results reveal that the conventional measures have the tendency to over-estimate access to transit.

Full text

A Random Utility Maximization (RUM) based Measure of Accessibility to Transit:
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Accurate Capturing of the First-Mile Issue in Urban Transit
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Md Sami Hasnine, MASc
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PhD Candidate
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Department of Civil Engineering
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University of Toronto
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35 St George Street
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Toronto, ON, M5S1A4
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Email: sami.hasnine@mail.utoronto.ca
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Ana Graovac, MASc
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Transportation Consultant at Arup,
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2 Bloor St E, Toronto, ON M4W 1A8
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Email: ana.graovac@arup.com
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Felipe Camargo, MSc
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Associate, Transportation Consultant at Arup,
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2 Bloor St E, Toronto, ON M4W 1A8
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Email: Felipe.Camargo@arup.com
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Khandker Nurul Habib, Ph.D., PEng
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Associate Professor
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Department of Civil Engineering
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University of Toronto
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35 St George Street
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Toronto, ON, M5S1A4
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Tel: 416-946-8027; Email: khandker.nurulhabib@utoronto.ca
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Total Number of Words: 5996+ (6) Figures/Tables (1500) = 7496
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Paper Submitted to the TRB Public Transportation Planning and Development Committee (AP025) for
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Consideration of Presentation at the 97th Annual Meeting.
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ABSTRACT
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The paper presents a random utility-based measure of accessibility to explain the first-mile issue in
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urban transit. A discrete access stop/station location choice model is used to calculate the expected
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maximum utility of transit access choices as the measure of the proposed access to transit measurement
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approach. It captures the effects of changes in various personal, socio-demographic, transportation and
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land-use variables on access to urban transit that are totally overlooked by conventional approaches of
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accessibility measurements (count-based cumulative opportunities measures and gravity-based
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measures). The proposed accessibility to transit measurement approach is empirically measured for the
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Greater Toronto Area and is integrated into an operational tool programmed in a GIS based traffic
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assignment software, TransCAD 7.0. This allows comparing it against the conventional measures and
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the results reveal that the conventional measures have the tendency to over-estimate access to transit.
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Key Words: Accessibility to transit, discrete choice model, station/stop locaiton choice, random utility
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maximization
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1. INTRODUCTION
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Public transport system is considered one of the key agents in achieving the objectives of sustainability
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in urban transportation and so investment in public transit is widely touted by planners and policy
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makers (Albacete et al. 2017). However, investments in transit infrastructure alone cannot increase the
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chance of transit being a dominant travel mode. Many other factors affect the choice of using transit by
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urban dwellers. Among these, accessibility to transit is one of the most crucial ones (Al Mamun and
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Lownes 2011, Foda and Osman 2010). A transit stop/station is the first point of access for the travelers
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to the transit service. This access to the first transit stop is well known as the “first-mile” problem.
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Measuring access to transit is a necessary measure of transit accessibility.
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Accessibility refers to the ease of getting a service, with minimum time, cost and inconvenience. In our
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context, accessibility to transit means be the ease of getting into a transit service (Hansen 1959). In
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general, three types of accessibility measures are commonly found in the literature:
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 Count-based opportunities measures,
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 Gravity-based measures and
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 Utility-based measures
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In the count-based measures, a count of available opportunities near the origin (define by a range of
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areas) of the trip is used as a measure of accessibility to the opportunities. This is a straightforward and
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easy measure of accessibility. For access to transit measurement, the count-based measure of
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accessibility is the total number of transit stop/stations from the origin and within a certain distance
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range. For example, the number of bus stops within 30 minutes walking time can be a measurement of
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access to bus services. The first issue related to this measurement is that the threshold/range of walk
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time is needed to be defined, often arbitrarily. Finally, the implicit assumption of this count-based
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measurement is that all transit stops/stations within the range/threshold are equally attractive. Thus, the
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differences in travel impedances among the alternative locations within the range is overlooked in the
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count-based measures (El-Geneidy et al 2016, Geurs and van Wee 2004, Vickerman, 1974).
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A gravity-based measurement of accessibility discounts the opportunities that are in farther away
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locations from the origin by using a travel impedance measure. Typically, the denominator of an
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aggregate trip distribution gravity model is used to define the travel impedance measure for this
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approach (Niemeier 1997, Handy and Niemeier 1997). Gravity-based measures overcome the
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limitation of count-based measures by accommodating travel impedance and differentiating
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opportunities that are apart from each other, but it does not recognize the user’s perspectives in
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measuring attractiveness (Hanson and Schwab 1987). For example, in measuring access to bus
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services, a closer stop will have more attraction than a distance stop in a gravity-type measure, but it
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implicitly assumed that users of all categories and contexts would have the same perception of
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accessibility to any particular stop. This is problematic as travel impedance can widely vary in
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perception by the different traveler for different travel contexts.
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Both count- and gravity-based measurement of accessibility are reactive measure, as these
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measurements will tell about the status of accessibility without necessary giving a straightforward way
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of forecasting the changes in accessibility for changing conditions of transportation or land use system.
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In addition, both measures completely overlook the travel context (e.g. direction of a trip) in
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quantifying accessibility and thus have the potential of over-estimating accessibility. For example, not
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all transit stops/stations near the traveler’s origin may be feasible for a traveler unless they serve the
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traveler in the direction of her/his final destination. There may be just one or two stops/stations near the
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origin where the traveler can choose to get to the final destination. Thus, the connections between
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individual choices, transit network, and land-use attributes are often neglected in the count and gravity-
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based measures (Bhat et al 1998).
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In contrast, a utility-based measure considers the individual traveler’s perspective of ease in accessing
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to a service. Application of a discrete location choice model can be used to quantify the expected
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maximum utility of choosing a particular location. Such expected maximum utility of choice can be
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used as a quantitative measurement of accessibility to the service (Ben-Akiva and Lerman 1985). It is a
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proactive measure of accessibility as it allows for forecasting future accessibilities for any potential
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changes in transportation or land use system. In the context of transportation policy evaluation, it
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provides a method to translate accessibility to performance measures (Handy and Niemeier 1997). The
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concept of using the discrete choice model to quantify accessibility of not a brand-new idea, however,
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interestingly, very few studies implemented this method for the case of measuring accessibility to
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transit.
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This study contributes to the literature by presenting a GIS based tool of quantifying accessibility to
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transit that uses a discrete transit access stop/station location choice model for the utility-based
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accessibility measurement. For the empirical investigation, the paper uses the latest (2011) household
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travel survey data of the Greater Toronto and Hamilton Area (GTHA) to estimate a discrete choice
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model of walk access to transit stop/station location as a function of socioeconomic, land use and
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transportation related variables. The resulting utility-based accessibility to transit measurement is
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integrated into a tool, which is a GIS-based traffic assignment software platform, TransCAD 7.0
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(Caliper 2017) and named as ‘accessibility Toolkit’. The tool is used to empirically compare the results
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of three alternative approaches of access to transit measurements for the Greater Toronto Area. In
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addition, the estimated empirical model of access to transit stop/station choice model reveals
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behavioural insights into transit accessibility in Toronto.
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The rest of the paper is organized as followings: the next sections presents a brief literature review on
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measruing accessibility. This section is followed by the secions presenting discussions on the study
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area and data for empieirical; econometric methods; empirical model of transit access station/stop
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location choice; developlment of the accessibiliy toolkit and empirical comparisons of alternatove
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accessibility measurements. The paper conclude with a summary of key findings and recommedations
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for future research.
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2. LITERATURE REVIEW
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Spatial distribution of the opportunities (i.e., destinations), travel time, travel cost, activity type and
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destination choices all are crucial in measuring accessibility. In the past literature, different researchers
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proposed different types of accessibility measures. Handy and Niemeier (1997) proposed three
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different forms of accessibility measures: cumulative opportunities measures, gravity-based measures
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and utility-based measures. Curtis and Scheurer (2010) categorized accessibility into seven classes such
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as spatial separation, contour measures, gravity measures, competition measures, time-space measures,
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utility measures and network measures. Geurs and van Wee (2004) proposed four main categories with
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some subcategories such as infrastructure based measures, location based measures (contour measure,
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potential measure, adaptive potential measure, and balancing factors), person based measures, and
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utility-based measures (log-sum benefit measure, space-time measure, and balancing factor benefit
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measure).
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Most of the these measures are for broad and general contexts of urban accessibility. Also, only a few
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of those investigated transit accessibility in particular and none of those investigated the concept of
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‘accessibility to transit’ by focusing on user’s perspective. Two notable studies that used user’s
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perspective through the concept of utility-based measure of accessibility to opportunities in general are
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Niemeier (1997), and Handy and Niemeier (1997). Niemeier (1997) estimated a random utility
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maximizing (RUM) multinomial logit model of mode and destination choice for the morning
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commuting trips considering transit as one of the modes. Travel survey data from the Puget Sound
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Region were used in this study. The denominator of the multinomial logit model of mode-destination
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choices, which is also known as log-sum or social welfare, is treated as the accessibility measure.
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Importantly, this research showed the utility-based accessibility measure has the capability of capturing
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the response to the changes in various transportation policies.
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Handy and Niemeier (1997) presented two case studies. In the first case study, they estimated a series
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of gravity models and accessibility measures based on a cumulative opportunity count approach. A
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gravity model was estimated to compare the accessibility between older and newer neighbourhoods.
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Then they developed a cumulative opportunity measure to get the number of supermarkets available
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within a certain travel time threshold for the same neighbourhoods. Finally, a time discounted gravity-
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based measure is used to get the supermarket accessibility. In the second case study, they estimated a
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joint mode-destination model to measure the accessibility of different income group and results are
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compared. They showed that the discrete choice model provides a better measurement of accessibility
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as it captures user’s perception and handles the random heterogeneity in traveler’s choice making
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behaviour.
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Bhat et al (1998) estimated a discrete location choice model to replace the conventional gravity model
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based accessibility measurement approach. The models were estimated for two trip purposes: home
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based work trips and home based shopping trips. This study presented the empirical models for
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accessibility measurement but did not present any specific evaluation of accessibility measurements.
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Srour et al (2002) used accessibility indices (accessibility to jobs, retail employment, and park space)
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as an explanatory variable in the property valuation and residential choice model and found that these
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accessibility measures had significant explanatory power in defining property valuation and residential
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choice.
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In this paper, we are interested in the measurement of transit accessibility. Specifically, the focus of
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this paper is measuring accessibility to the transit services
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. Moreover, we recognize that it is important
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to capture user’s perspective in measuring accessibility to transit service and so, we would develop
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RUM based discrete choice model to estimate accessibility. Moreover, it is also a matter of importance
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that we compare the results of such utility-based accessibly measure against conventional count and
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gravity-based measures. Considering the focus on discrete choice model based measurement of
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accessibility, we now present a review of studies that investigated the choices of transit stop/station
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location.
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Transit access stop/station location choice model is well established in the literature. A few studies
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were particularly interested that include park and ride, and kiss and ride station location choice models
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(Lythgoe and Wardman 2004, Mahmoud et al 2014, Chen et al. 2015, Weiss and Habib 2017). There
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are also some studies that focused on joint mode and access station choice model (Debrezion et al
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2009, Chakour and Eluru 2014). Several studies dealt with specific type of transit service, e.g. railway
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station location model (Debrezion et al 2007, Givoni and Rietveld 2014). For brevity of the
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presentation, we present the review of relevant studies in a tabular form in Table 1. All of these access
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stop/station choice models use transit level of service variables and land use attributes only.
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Socioeconomic variables were used only in the joint mode and departure time choice models.
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Interestingly, none of these studies dealt with access to transit by walking. Some of these studies
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focused on cross regional commuters or rail users and so park and ride was considered the only option
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of accessing to the transit services. Others investigated mode and destination choice jointly considering
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walk access to transit services as exogenous.
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As such, there is a clear gap of research related to transit stop/station location choice model for the
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people who access transit stop/station by walk. For a better understanding of the evidence based policy
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investigation and measuring accessibility to transit by walking, it is evident that we need a transit
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stop/station location choice model that can accommodate socio-economic, land-use and transit service
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related variables. This paper presents such a model along with its usage of measuring accessibility to
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transit and relative performances against conventional count and gravity-based measures. For the
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Distinction is made between accessibility to transit and accessibility by transit. The former is a part of the latter.

empirical investigation, it considers the Greater Toronto and Hamilton Area (GTHA) as the study area.
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Table 1: Summary of Recent Studies on Transit Access Stop/station choice
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Authors Name
Modelling Structure
Variables used
Weiss, A., and
Habib, K. N.
(2017).
Mixed logit
Drive time from home to transit station, transit walk, wait,
transfer and in vehicle travel time, travel cost (fare and drive
cost), parking cost at the station, parking lot capacity,
washroom, the frequency of trains per hour, station-home-
work angle.
Chen et al. (2015)
Mixed logit
Access time, parking related variables: capacity, search time,
availability, fee, fine, the frequency for illegal parking
inspection.
Mahmoud et al.
(2014)
Multinomial Logit
Distance, angle between origin, destination, and station,
capacity of parking capacity, types of station, parking lot
capacity, station type (regional, local), distance interacted
with mobility tool, restroom and kiosk facilities
Givoni, M., and
Rietveld, P.
(2014)
Nested logit
Total travel time to the destination by rail, Total travel time
to the destination by public transport, total travel distance,
quality of parking spot, taxi distance, bicycle distance,
walking distance, and other distance.
Chakour, V., and
Eluru, N. (2014)
Binary logit and
Multinomial logit with
latent segmentation
Individual and socioeconomic variables (age, gender,
vehicle ownership), travel time by different modes, average
travel times to viable stations, parking and fare information.
Debrezion et al
(2009)
Nested Logit
Driving/transit distance, car parking facilities, transit
frequencies, travel time, rail service quality index.
Debrezion et al
(2007)
Multinomial Logit
Transit frequency, travel distance, parking facility at the
station, status of the station (intercity or others)
Lythgoe, W.F.,
and Wardman, M.
(2004)
Hierarchical Logit
Share at each station, generalized cost, distance, the
proportion of newly generated trips from all trips from the
station.
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3. STUDY AREA AND DESCRIPTIVE STATISTICS
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The GTHA consists of the city of Toronto and five regional municipalities. As per 2016 census data, its
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population is around 7 million which is around 20% of total population of Canada (Statistics Canada
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2016). The GTHA is served by 9 local transit systems and Toronto Transit Commission (TTC) is the
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largest among them. TTC’s public transit fleet is composed of bus, streetcar, and subway. The subway
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network is well-connected with bus and streetcar to provide better connectivity within the city of
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Toronto. The other eight local transit agencies offer the only bus based public transit system. The
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regional transit agency of GTHA, the GO transit, offers connectivity between downtown Toronto
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(Union Station) and other municipalities in GTHA. GO transit provides rail and bus services within the
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GTHA. It is connected with the local transit agencies to provide seamless access to transit in the
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GTHA.
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For the empirical investigation, data for the recent household travel survey of the Greater Toronto and
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Hamilton Area (GTHA) is used. This household level survey collects detailed personal, household and
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single-day travel information of a random 5% random sample of the household in the GTHA (Data
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Management Group 2011). This study is focused on accessibility to transit by walk access. As such, we
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extracted a subset of the trips by public transit with walk access. General Transit Feed Specification
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(GTFS) data, land use information and other relevant data are fused with this dataset. After cleaning for
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missing information, a total of 77,523 trip records is retained for the modelling exercise. For generating
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alternative stop/station locations and the corresponding level of service attributes (travel time, distance)
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a Google Application-Programming Interface (API) based algorithm-TILOS (Tool for Incorporating
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Level of Service attributes) is used (Hasnine et al 2017). Based on the origin, destination, and departure
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time information, TILOS generates a maximum of four alternative access stations (including the chosen
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one) and the corresponding route level travel information. The level of service (LOS) attributes include
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total travel time, distance, the number of transfer, in vehicle travel time, access time, access distance,
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wait time, egress time, longitude and latitude of access and egress stations, and stations types (regional
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or local).
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Table 2 presents the summary statistics of the variables in the dataset that are used for empirical
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investigation. The average size of a household is 3.21 and the average number of cars in a household is
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1.041. A preliminary analysis of the sample statistics shows that the average age of the sample is 39.42.
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Around 57% of the individual in the data set posses a driving license. Female travelers consist of
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(56.5%) of the sample data set. The level of service information (e.g., travel time, distances) for four
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access stations for every traveler is generated. The average travel time of walking to a transit
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stop/station in the GTHA is 6.143 minutes. The average walking distance to access stop/station is 0.865
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km. To better represent the trip context, we calculated the angle between origin, destination and access
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stop/station (as shown in Figure 1) of the trips in the data set. It is found that the average angle is
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81.708 degree. In the past literature, it is found that this angle has significant explanatory power for
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access stop/station location choice (Mahmoud et al 2014, Chen et al. 2015, Weiss and Habib 2017).
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Figure 2 shows the spatial distribution of travelers’ origin, destinations and access stations/stops in the
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data set.
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TABLE 2. Summary Statistics of the Selected Variables
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Continuous Variables
Mean
Standard
Deviation
Number of person in the household
3.208
1.500
Number of vehicle in the household
1.041
0.886
Age
39.420
18.816
Travel time (minutes)
46.143
27.330
Distance (kilometers)
13.720
14.300
Number of transfers
0.879
0.783
In vehicle travel time (minutes)
29.557
29.557
Access time (minutes)
5.507
4.591
Egress time (minutes)
5.059
4.357
Walking distance to access stop/station (kilometers)
0.865
0.521
Wait time (minutes)
0.100
0.151
Angle between origin, destination and access station
81.708
49.683
Categorical Variables
Percentage
Access stop/station type
TTC station
94.6
Regional station
5.40
Gender
Female (%)
56.5
Male (%)
43.5

Driving License
Yes
57.3
No
42.7
Employment Type
Full time
43.392
Work at home full-time
1.231
Work at home part-time
0.665
Not employed and others
39.703
Part time
15.009
Occupational Category
General Office / Clerical
12.545
Manufacturing /
Construction / Trades
3.932
Professional /
Management/ Technical
19.906
Retail Sales and Service
23.814
Not Employed and others
39.804
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FIGURE 1. Relative Angle between Origin, Destination and Access Station
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(a) Distribution of the origin location of the travelers (b)Distribution of the destination location of the travelers
(b) Distribution of the access stations
FIGURE 2: Distribution of the Origin, Destinations and Access Stations of the Travelers

ECONOMETRIC MODEL
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Multinomial logit (MNL) discrete choice model for access stop/station location choice is used for the
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empirical investigation (McFadden, 1973). In this modelling approach, each traveler is assumed to get
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a certain level of utility for each access station. The total utility ( of each access stop/station
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location is composed of systematic utility  of access station and random utility components (
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with zero mean and  scale. The systematic utility is a function of linear-in-parameters of the observed
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attributes (, where  is the parameter vector and  are the variables. The error term of the
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MNL model is assumed to be independently and identically distributed (IID) extreme values. This
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assumption provides proportional substitution pattern between all pairs of alternatives (Train, 2009).
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For each traveler, the random utility of access stop/station ( can be written as:
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
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The corresponding probability of choosing a stop/station location, :
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


 
17
18
This is a closed form formulation and can be estimated by using classical maximum likelihood
19
estimation technique. Here,  is a scale parameter. Once, estimated, the logarithm of the denominator
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given a measure of expected maximum utility of stop/station location, which is the measure of
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accessibility in our case (Ben-Akiva and Lerman, 1985). Therefore, from the estimated access
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stop/station location choice model, we can estimate the accessibility to transit, As as:
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


 
25
26
We estimated the model by considering maximum four feasible location as we observed in our study
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area, but the estimated accessibility measure can be applied for any number of feasible access
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stop/station location contexts. Since a single discrete choice model measures the accessibility, the scale
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parameter ( is normalized to unity.
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4. EMPIRICAL MODEL OF TRANSIT STOP/STATION LOCATION CHOICES
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Four different models are estimated and these are (Model 1) base model: the model excluding any
34
socio-economic variables and for all activity types (Model 2) model with socioeconomic attributes for
35
all activity types, (Model 3) model with socioeconomic attributes and for work activity (Model 4)
36
model with socioeconomic attributes and for personal and educational activities.
37
38
39
40

TABLE 3. Stop/station Location Choice Model Estimation Result
LOS only (no
socioeconomic
variables)
(model 1)
All trips (LOS and
socioeconomic
variables)
(model 2)
Work trips (LOS and
socioeconomic
variables)
(model 3)
Personal and educational
activity (LOS and
socioeconomic variables)
(model 4)
Number of Observation
77523
77523
16561
21953
The number of Parameters
9
16
16
16
Loglikelihood of the full model
-32331.665
-37112.586
-8053.399
-10268.538
Loglikelihood of the null model
-45280.642
-45280.642
-10432.453
-13424.764
Rho-Squared value against null model
0.286
0.180
0.228
0.235
Variable
Parameter
t-stat
Parameter
t-stat
Parameter
t-stat
Parameter
t-stat
Walk access time
-0.2985
-91.199
---
---
---
---
---
---
Number of transfer
-0.1965
-13.61
---
---
---
---
---
---
Transit in-vehicle travel time plus egress time
-0.0009
-0.918
---
---
---
---
---
---
Access distance multiplied by a dummy variable for if the angle between origin, destination and
the access stop/station is greater than 90 degree
---
---
-1.185
-30.381
-1.265
-16.29
-1.467
-19.27
Dummy variable if the access stop/station is a subway station (reference bus)
1.5781
75.004
1.020
50.721
1.907
38.166
1.125
26.325
Dummy variable if the access stop/station is a regional transit station (reference bus)
3.0664
72.744
1.814
47.408
1.209
13.843
0.976
9.720
Dummy variable if the access stop/station is a street car stop (reference bus)
-0.1051
-3.293
-0.148
-5.179
0.001
0.009
-0.118
-2.052
Walk access time for work activity
-0.0411
-9.097
---
---
---
---
---
---
Walk access time for educational activity
-0.1336
-21.21
---
---
---
---
---
---
Walk access time for personal activity
-0.0822
-14.324
---
---
---
---
---
---
Dummy for female interacted with a dummy for if the access distance is less than 0.5 Km
---
---
1.475
16.168
0.957
5.674
1.824
10.354
Dummy for female interacted with a dummy for if the access distance is between 0.5-1 Km
---
---
0.548
5.700
0.639
3.481
0.673
3.638
Dummy variable for age is less than 25 years old interacted with a dummy variable for if the
access distance is less than 0.5 Km
---
---
2.809
25.265
1.594
4.836
3.088
17.697
Dummy variable of age is greater than 55 years old interacted with a dummy variable for if the
access distance is less than 0.5 Km
---
---
1.327
11.448
0.478
2.205
1.886
8.744
Dummy variable of age is less than 25 years old interacted with a dummy variable for if the
access distance is between 0.5 to 1 Km
---
---
1.269
10.963
1.656
4.531
1.176
6.481
Dummy variable of age is greater than 55 years old interacted with a dummy variable for if the
access distance is between 0.5 to 1 Km
---
---
0.057
0.464
0.355
1.479
0.174
0.766
Dummy variable if the person is a full-time worker interacted with a dummy variable for if the
access distance is less than 0.5 Km
---
---
1.313
15.752
2.137
15.246
1.558
5.982
Dummy variable if the person is a part time worker interacted with a dummy variable for if the
access distance is less than 0.5 Km
---
8.845
1.312
8.845
1.984
6.207
1.047
3.936
Dummy variable if the person is a full-time worker interacted with a dummy variable for if the
access distance is between 0.5 to 1 Km
---
7.026
0.599
7.026
0.484
3.397
0.978
3.578
Dummy variable if the person is a part time worker interacted with a dummy variable for if the
access distance is between 0.5 to 1 Km
---
4.205
0.641
4.205
-0.130
-0.383
0.633
2.356
Dummy variable if the person's occupation is general office / clerical interacted with a dummy
variable for if the access distance is less than 0.5 Km
---
-1.590
-0.096
-1.590
0.284
2.743
-0.314
-1.805
Dummy variable if the person's occupation is retail sales and service interacted with a dummy
variable for if the access distance is less than 0.5 Km
---
7.134
0.395
7.134
0.590
6.105
0.419
3.075

Empirical models are presented in Table 3. Variables in the final models are selected based on
1
their statistical significance (95% confidence limit) and expected signs. Regardless, some
2
variables with lower statistical significance are retained in the model to compare the result with
3
other models. Goodness-of-fit against the null model is reported. It is found that accommodating
4
socioeconomic variables lowers the goodness-of-fit slightly as the model tends to capture diverse
5
levels of heterogeneity. However, it is worth accepting a slightly lower goodness-of-fit as the
6
models accommodate variables to capture diverse travel markets.
7
8
Walk access time is used as an indicator to station’s/stop’s proximity to the origin. The negative
9
sign indicates that travelers are less likely to choose an access stop/station with higher access
10
time. Travelers are less likely to choose a transit stop/station where the transit route contains a
11
high number of transfers. However, the model shows that travelers are more sensitive to walk
12
access time than the number of transfer. The transit in-vehicle travel time (IVTT) and egress time
13
variable show negative sign also, which means traveler tend to choose those transit routes, which
14
have shorter IVTT and egress time.
15
16
Stop/station type (regional transit, subway, streetcar, and bus) has high statistical significance in
17
the choice model of access location to transit. Travelers are more likely to choose a regional
18
transit than a subway station if both are within a reach as the regional transit faster than the local
19
transit. In addition, regional transit is very popular for cross regional commuters. The streetcar is
20
the least popular form of transit as it is typically slower in speed than the subway and so it has a
21
negative utility of choice. In terms of purpose of the trip, travelers are the most sensitive to the
22
walk access time to the transit station for an education activity related trip.
23
24
A dummy variable for whether the angle between origin, destination and the access stop/station
25
is greater than 90 degree is used as a variable in these models. This variable is interacted with
26
origin to access stop/station distance. Its negative sign indicates that if the distance is fixed for
27
two access stations, travelers will choose the stop/station with the lower angle between origin,
28
destination and the access station. This finding is similar to the results of some past studies
29
(Mahmoud et al 2014, Chen et al. 2015, Weiss and Habib 2017). For work activities people are
30
less likely to choose regional transit. A similar result is found for educational and personal
31
activity. For all three models (model 2,3 and 4) it is found that females are more likely to choose
32
a stop/station which is less than 0.5 km.
33
34
For all three models, people younger than 25 years are more inclined to walk to an access
35
stop/station than do the older people (age 55 or more). If the walk access distance in less than 0.5
36
km there is no significant differences in choosing an access stop/station for a full-time or part-
37
time worker. However, if the walk access distance is 0.5 km to 1 km, a part-time worker is less
38
likely to walk to an access stop/station if the trip purpose is work activity.
39
40
41

2
Hasnine et al 2017
6. COMPARISON OF ALTERNATIVE MEASURES OF ACCESSIBILITY TO
1
TRANSIT
2
3
To assess the impacts of changes to a transit system on regional accessibility, Arup
2
in
4
collaboration with Metrolinx (the Regional Planning Agency in the GTA) developed the
5
“Accessibility Toolkit” in 2015, which is programmed as an add-on to a transportation planning
6
software (TransCAD 7.0) considering count-based and gravity-based measure of accessibility
7
(Kramer et al 2017). In this study, the developed RUM-based measure of accessibility to transit
8
is added to this toolkit. Finally, it is used to compare the alternative measures of accessibility to
9
transit in the GTA. Three measures are compared and these are:
10
 A count-based measure of access to transit (stops within a 15-minute walk)
11
 A gravity-based measure of access to transit (access to transit score)
12
 A utility-based measure of access to transit (applying the estimated model of access
13
stop/station choice)
14
For consistency of comparison, the same origins, stations, and destinations are used in each
15
accessibility calculations, where relevant. Origins were defined as the points on the street
16
network nearest to dissemination area centroids, and destinations were defined as dissemination
17
area centroids themselves (with an added assumed walk time from the network to the centroid).
18
The set of possible access stations is defined as the points on the network at which transit
19
services stop. General Transit Feed Specification (GTFS) 2017 schedule data from all agencies
20
in the region are used for the calculation.
21
22
A simple measure of access to transit can be done with spatial analyses. In this example, transit
23
stops within a 15-minute walk along the street network from each origin point are counted. To
24
improve on the count-based measure of stops nearby, the access-to-transit score takes the
25
frequency (half of the headways) and access walk time into account. The logarithmic score of the
26
equivalent doorstop frequency (EDF) is used as a gravity-based measure (Kramer et al 2017).
27
The tool also selects only the nearest stop from each transit route to more closely represent the
28
reality of transit access choices.
29
30
 

   (4)
31
32
For utility-based accessibility measures we used the model with only level-of-service variables
33
(model 1) because this model has the highest goodness-of-fit and this model’s attributes are more
34
comparable with the attributes we used in a count-based and gravity-based method. Travel
35
attributes were prepared for modelling using methods consistent with the other accessibility
36
measures. The attributes are prepared for the model application as follows:
37
2
https://www.arup.com/en/offices/Canada/Toronto

3
Hasnine et al 2017
 Walk access time: Origin to stop/station walk time along network (4.8km/hr). Stations
more than 15 minutes away are excluded
 Number of transfers: Stop/station to destination transfers (generated using TransCAD
7.0 Pathfinder tool)
 Transit in-vehicle travel time plus egress time: Stop/station to destination total travel
time (generated using TransCAD 7.0 Pathfinder tool)
 Bus/Subway/Regional/Streetcar: Transit mode is looked up based on the mode of the
access stop in each origin-stop-destination chain
 Walk access time for personal activity: Selected
For each origin-station-destination trip chain, the model parameters are applied to calculate a
1
utility value. The route (access station) with the highest utility for each OD pair is chosen. These
2
maximum OD utilities are aggregated to an average at each origin point. For this example, the
3
trip purpose was chosen to be a personal activity, representing the ability to visit friends and
4
access high-density areas of the city.
5
6
To compare among these measures, all measures were converted to a 0-10 score on a logarithmic
7
scale, such that the median is consistent between measures. As the different measures of
8
accessibility quantify different things, the spatial patterns vary; however, we found that all
9
measures are revealing the common trend. For example, it is found that the downtown part of the
10
city of Toronto shows a higher score for all three measures. Figure 3 shows the detailed
11
comparison of these three measures.
12
13
Count-based measures (stops nearby) give spatial patterns of accessibility with relatively little
14
variation across the city region (Figure 3a). The measure of the number stops within a 15-minute
15
walk of each origin is higher in urban areas than in suburbs but does not consider the frequency
16
of the transit. The gravity-based measure of accessibility gives a more nuanced spatial pattern
17
with more contrast (Figure 3b). The access to transit score provides a more realistic pattern of
18
accessibility than a simple count of nearby stations since it includes the frequency of services
19
and walk time to stops in the calculation. The gravity-based accessibility shows much higher
20
scores in dense urban areas, major interchanges, and along major corridors than in other areas.
21
22
The average utility (over all destinations less than 60 minutes away) of the best access
23
stop/station choice was mapped for each origin (Figure 3c). The highest average density is found
24
within the city, areas along urban rail lines, especially the Bloor-Danforth subway line. The
25
spatial pattern of the utility-based accessibility is similar to the pattern of other accessibility
26
measures, but it gives more informative findings than simple count-based measures. It is found
27
that the utility-based measures provide slightly lower accessibility score (range 0 to 10) than
28
count-based and gravity-based method. Since count-based and gravity-based method does not
29
consider the transit availability at the stop/station depending on the destination choice, this
30
measure typically, add some non-feasible stations in the calculation.
31

4
Hasnine et al 2017
1
(a )Count-based accessibility (b) Gravity-based accessibility
2
3
(c) Utility-based accessibility (d) Difference: Count and Utility-based accessibility
4
5
(e) Difference: Gravity and Utility-based accessibility
6
FIGURE 3 Comparisons of Different Accessibility Measures
7

5
Hasnine et al 2017
The utility-based method is composed of a wide range of level-of-service attributes, which
1
provides more realistic but toned-down accessibility measures. Figure 3(d) shows the differences
2
between count-based and utility-based accessibility measures. It is found that in some suburban
3
areas where there are no subway lines have higher differences. A similar result is found when we
4
plotted the differences between gravity-based and utility-based accessibility (Figure 3e). The
5
transit connectivity is lower in the suburban areas and a count-based measure cannot capture that
6
accurately.
7
8
7. CONCLUSIONS AND RECOMMENDATIONS FOR FURTHER RESEARCH
9
10
The paper contributed to the existing literature on measuring access to transit in urban areas. This
11
paper is particularly focused on developing discrete choice model-based measure of accessibility
12
to explain the first-mile issue in urban transit. Transit access stop/station location choice models
13
were estimated using transportation level-of-service attributes different trip contexts and the
14
socioeconomic attributes of the trip makers. The best-fitted model is integrated into an
15
operational tool programmed in a GIS based traffic assignment software, TransCAD 7.0, the
16
accessibility toolkit. This allows comparing the proposed measures against conventional
17
measures: count of opportunities and gravity approach. Results of the comparisons reveal that the
18
conventional measures have the tendency to over-estimate access to transit. Moreover, the
19
conventional approaches overlook the trip-contexts and traveler perspectives and thereby lack in
20
representing travel behaviour.
21
22
For discrete choice model-based accessibility measure to transit, four separate models were
23
estimated. It is found that travelers are sensitive to walk access time to the stop/station and
24
number of transfers required in the respective transit lines while choosing an access station/stop.
25
Moreover, female travellers are more sensitivity to walk time than do the male travellers. People
26
are less likely to choose a stop/station if the angle between origin, destination and access
27
stop/station is more than 90 degrees. This study shows that preference to alternative transit
28
services (regional versus local) depend on the purposes of the trips. Overall, it is proven that the
29
discrete choice model-based measures provide a conservative measure of access to transit than
30
do the conventional measures (count-based and gravity-based measures).
31
32
The study can be extended in multiple ways. One subsequent investigation that currently
33
underway by the authors is developing a similar measure, but for the access to destination (ATD)
34
by transit. In addition, the discrete choice models used in this study overlook the spatial auto-
35
correlation between different access stops/stations. Accommodating spatial autocorrelation
36
within a discrete choice model poses a methodological challenge and so is considered as a
37
recommendation for further study.
38
39
40

6
Hasnine et al 2017
ACKNOWLEDGEMENT
1
The research was funded by an NSERC Engage Grant. Authors acknowledge the valuable
2
suggestions and comments of Yan (Tony) Zhuang and Islam Kamel during the study. However,
3
all comments and interpretations are of the authors only.
4
5
REFERENCES
6
Albacete, X., Olaru, D., Paül, V., & Biermann, S. (2017). Measuring the Accessibility of Public
7
Transport: A Critical Comparison Between Methods in Helsinki. Applied Spatial
8
Analysis and Policy, 10(2), 161-188.
9
Al Mamun, M., & Lownes, N. E. (2011). A composite index of public transit accessibility.
10
Journal of Public Transportation, 14(2), 4.
11
Ben-Akiva, M. E., & Lerman, S. R. (1985). Discrete choice analysis: theory and application to
12
travel demand (Vol. 9). MIT press.
13
Bhat, C., Govindarajan, A., & Pulugurta, V. (1998). Disaggregate attraction-end choice
14
modeling: formulation and empirical analysis. Transportation Research Record: Journal
15
of the Transportation Research Board, (1645), 60-68.
16
Caliper. 2017. TransCAD. http://www.caliper.com/tcovu.htm (Accessed in May 2017)
17
Chakour, V., & Eluru, N. (2014). Analyzing commuter train user behavior: a decision framework
18
for access mode and station choice. Transportation, 41(1), 211-228.
19
Chen, C., Xia, J. C., Smith, B., Olaru, D., Taplin, J., & Han, R. (2015). Influence of parking on
20
train station choice under uncertainty for park-and-ride users. Procedia Manufacturing, 3,
21
5126-5133.
22
Curtis, C., & Scheurer, J. (2010). Planning for sustainable accessibility: Developing tools to aid
23
discussion and decision-making. Progress in Planning, 74(2), 53-106.
24
Data Management Group. (2011). Transportation Tomorrow Survey. Joint Program in
25
Transportation, University of Toronto, 2011.
26
Debrezion, G., Pels, E., & Rietveld, P. (2009). Modelling the joint access mode and railway
27
station choice. Transportation Research Part E: logistics and transportation review, 45(1),
28
270-283.
29
Debrezion, G., Pels, E., & Rietveld, P. (2007). Choice of departure station by railway users.
30
El-Geneidy, A., Levinson, D., Diab, E., Boisjoly, G., Verbich, D., & Loong, C. (2016). The cost
31
of equity: Assessing transit accessibility and social disparity using total travel cost.
32
Transportation Research Part A: Policy and Practice, 91, 302-316.
33
Foda, M. A., & Osman, A. O. (2010). Using GIS for measuring transit stop accessibility
34
considering actual pedestrian road network. Journal of Public Transportation, 13(4), 2.
35

7
Hasnine et al 2017
Geurs, K. T., & Van Wee, B. (2004). Accessibility evaluation of land-use and transport
1
strategies: review and research directions. Journal of Transport geography, 12(2), 127-
2
140.
3
Givoni, M., & Rietveld, P. (2014). Do cities deserve more railway stations? The choice of a
4
departure railway station in a multiple-station region. Journal of Transport Geography,
5
36, 89-97.
6
Handy, S. L., & Niemeier, D. A. (1997). Measuring accessibility: an exploration of issues and
7
alternatives. Environment and planning A, 29(7), 1175-1194.
8
Hanson, S., & Schwab, M. (1987). Accessibility and intraurban travel. Environment and
9
Planning A, 19(6), 735-748.
10
Hansen, W. G. (1959). How accessibility shapes land use. Journal of the American Institute of
11
planners, 25(2), 73-76.
12
Hasnine, M. S., Kamel, I. R., & Habib, K. N. (2017). Using Google Map to Impute
13
Transportation Level-of-Service Attributes: Application in Tour-based Mode Choice
14
Modelling. To be Presented at the 11th International Conference on Transport Survey
15
Methods, September 24-29, 2017, Esterel, Quebec, Canada.
16
Kramer, A., Borjian, S., Camargo, F., Graovac, A., & Falconer, R.W.(2017) Accessibility
17
Planning for Social Equity: Analysis of Current and Future Transit Networks in the
18
Region of Toronto, Canada. Presented at the 96th Annual Meeting of Trans. Res. Board,
19
January 8–12, 2017.
20
Lythgoe, W. F., & Wardman, M. (2004). Modelling passenger demand for parkway rail stations.
21
Transportation, 31(2), 125-151.
22
Mahmoud, M., Habib, K., & Shalaby, A. (2014). Park-and-Ride access station choice model for
23
cross-regional commuting: case study of Greater Toronto and Hamilton Area, Canada.
24
Transportation Research Record: Journal of the Transportation Research Board, (2419),
25
92-100.
26
McFadden, D. (1973). Conditional logit analysis of qualitative choice behavior.
27
Niemeier, D. A. (1997). Accessibility: an evaluation using consumer welfare. Transportation,
28
24(4), 377-396.
29
Srour, I., Kockelman, K., & Dunn, T. (2002). Accessibility indices: Connection to residential
30
land prices and location choices. Transportation Research Record: Journal of the
31
Transportation Research Board, (1805), 25-34.
32
Statistics Canada.(2016). Census Program 2016. http://www12.statcan.gc.ca/census-
33
recensement/2016/dp-pd/index-eng.cfm
34
Train, K. E. (2009). Discrete choice methods with simulation. Cambridge university press.
35

8
Hasnine et al 2017
Vickerman, R. W. (1974). Accessibility, attraction, and potential: a review of some concepts and
1
their use in determining mobility. Environment and Planning A, 6(6), 675-691.
2
Weiss, A., Habib, K. N. (2017). Examining the difference between park and ride and kiss and
3
ride station choices using a spatially weighted error correlation (SWEC) discrete choice
4
model. Journal of Transport Geography, 59, 111-119.
5
6