Transit accessibility for commuters considering the demand elasticities of distance and transfer

Journal of Transport Geography 56 (2016) 138–156

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Journal of Transport Geography journal homepage: www.elsevier.com/locate/jtrangeo

Transit accessibility for commuters considering the demand elasticities of distance and transfer Wangtu (Ato) Xu a,⁎, Yongling Li b, Hui Wang a a b

Department of Urban Planning, School of Civil and Architecture Engineering, Xiamen University, Xiamen 361005, China Department of Human Geography and Planning, Faculty of Geosciences, Utrecht University, 3584 CS Utrecht, The Netherlands

a r t i c l e

i n f o

Article history: Received 4 June 2015 Received in revised form 1 September 2016 Accepted 6 September 2016 Available online xxxx Keywords: Transit accessibility Timetable Floating catchment method Demand elasticity Distance and transfer tolerance Xiamen City

a b s t r a c t In this paper, a “by transit accessibility (BTA)” measure to evaluate the impacts of travel distance and transfer tolerance on the convenience of commuting by transit on a regional scale is proposed. Considering the spatiotemporal factors for commuting efficiency evaluation, the timetable-dependent passenger carrying capacity of the transit station and the time-varying passenger demand at originating sites have been formulated into the BTA model. Moreover, the proposed BTA measure could reflect the commuting trip demand elasticity, which is caused by travel distance and transfer tolerance. In the meantime, this BTA measure can provide an important basis for transit timetable adjustment in the study area during different time periods. The proposed measure is tested on a small transit network to display its function, and finally, it is applied to an empirical case to draw practical findings. © 2016 Published by Elsevier Ltd.

1. Introduction Recently, it is necessary for many countries to introduce a series of policies to emphasize the dominant position of public transit. During the last two decades, transit accessibility measures have drawn major concerns of researchers who aimed to enhance the priority of the public transit system. Transit accessibility is also a key indicator which reflects the coordinated relationships between the transit system, land use, and other urban infrastructures (Mamun and Lownes, 2011). In this paper, the measure of “by transit accessibility (BTA)” for commuters is proposed. Aiming at creating a new BTA measure for evaluating the convenience of going work by transit for commuters, two parameters are added into the existing BTA index. These two parameters are used to reflect the demand elasticity of travel distance and transfer tolerance. Moreover, for examining the BTA in the spatiotemporal dimension, a time-dependent zonal BTA index for the evaluating the transit accessibility level of the traffic analysis zone (TAZ) is designed. With the proposed regional BTA measures, a model for realtime transit timetable adjustment over all the study area is presented correspondingly. The significant difference between the proposed methodology and the existing one is that, it considers the demand elasticity of travel distance and transfer in the BTA measure, and that, timedependent factors embedded in the proposed BTA measures could be used to evaluate the zonal BTA level for the TAZ, and to adjust the transit timetable at any time if necessary. Finally, the proposed timetable ⁎ Corresponding author. E-mail address: [email protected] (W.(A.) Xu).

http://dx.doi.org/10.1016/j.jtrangeo.2016.09.001 0966-6923/© 2016 Published by Elsevier Ltd.

adjustment method ensures the time-varying balance between the supply and the demand of transit services for commuters. The rest of this paper has been organized as follows. Relevant literatures are reviewed in Section 2. In Section 3, the proposed methodology is demonstrated. Section 4 offers an example to display the detailed implemental processes of the proposed models. An empirical study is given out in Section 5. The conclusions and future research issues are summarized in Section 6. 2. Literature review 2.1. Accessibility Numerous methods have been used for evaluating the accessibility of infrastructure and public services (Gulliford et al., 2001). Although there has not been a unified definition for “accessibility” in the existing literature, most researchers agree that accessibility refers to the relative ease to access a location (or an infrastructure), to obtain a required service, or to participate in an activity. Following Khan (1992), Luo and Qi (2009), Luo and Wang (2003), Wang and Luo (2005) and Wang and Tang (2013), the definitions of accessibility were categorized into four types versus dichotomous dimensions (the potential and revealed versus the spatial and aspatial), which are the potential spatial (geographic access), the potential aspatial (social access), the revealed spatial (geographic access) and the revealed aspatial (social access) accessibility. Revealed spatial accessibility focuses on the actual utilization of facilities or services, while potential spatial accessibility evaluates the possible aggregate utilization or possible availability of facilities or services in a

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subject region. On the other hand, the revealed aspatial accessibility cares about the non-spatial related welfare, profit or bonus which could be accessed or obtained by the specific group of people, e.g., the pension that the aged people could get. Conversely, the potential aspatial accessibility refers to the possible immaterial profits could be obtained in the given region or for the specific human group. Table 1 shows the representative measures of accessibility according to the categories explained above. It is not necessary to introduce all methods for accessibility measurement in detail. However, the gravity method, which is the most representative method in the potential spatial dimension, and the basis of general accessibility measurement, should be emphasized when reviewing the accessibility literature. The gravity method for accessibility measurement is commonly based on Hansen's (1959) potential equation: Ai ¼

X

  a j f cij

ð1Þ

j

where, Ai refers to the accessibility of zone i. aj denotes the attractiveness of zone j, and is reflected by the resource at zone j, such as employment positions. f(cij) is the decay function of the generalized cost cij (e.g. distance, travel time, monetary cost, etc.) between zone i and j, and commonly with a family of forms in the scientific literature (Mamun et al., 2013): Power: f(cij) =c−γ ij ; Exponential: f(cij) = exp(c−γ ij ), and −γ Combined: f(cij) = k ⋅ c−γ ij ⋅ exp(cij ).where, k and γ are user-defined parameters. The limitation of Eq. (1) is that it takes only the “supply side”, without accounting for the “demand side” for accessibility measures. Several researchers such as Khan (1992), Kwan (1998), Luo and Qi (2009), Luo and Wang (2003), Wang and Luo (2005) and Wang and Tang (2013) improved the gravity method by adding to the effect of the “demand”. Particularly worth mentioning is the primary models of the floating catchment area (FCA) method used by Peng (1997), Shen (1998) and Wang and Minor (2002). Most of the previous accessibility measures of the FCA were based on pre-defined and arbitrary administrative

Table 1 Summarization of representative publishes involved in accessibility measures. Spatial Revealed

Potential

● Statistical analysis: Páez et al. (2012); ● Space–time measures: Hägerstrand (1970), Kwan (1998), Tribby and Zandbergen (2012), Welch and Mishra (2013), Fransen et al. (2015), Tong et al. (2015); ● Mathematical formulation based approach: Tuzun Aksu and Ozdamar (2014), Wang et al. (2015), Yang et al. (2015). ● Gravity-based method: Hägerstrand (1970), Hansen (1959), Wang and Tang (2013); ● Trip destination based methods: Mavoa et al. (2012), Shi and Ying (2008); ● Trip origin based methods:Curl et al. (2015), Luo and Wang (2003); ● Origin–destination based measures Curl et al. (2015), Handy and Niemeier (1997).

Aspatial ● RP/SP survey based statistical analysis: Ben-Akiva and Lerman (1985), Cherchi and Ortúzar (2002), Geurs et al. (2010), Leitham et al. (2000), Marcucci and Gatta (2011) ● Sociological approach: Bocarejo and Oviedo (2012)

● Activity based analysis: Ben-Akiva and Lerman (1985), Cascetta et al. (2013), Dong et al. (2006); ● Social and economic analysis: Burchardt (1999), Witter (2010), Lucas et al. (2001).

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boundaries and had different values in neighbouring areas. The FCA method overcomes these drawbacks using a dynamic buffering technique to measure the accessibility of the buffered zones (Peng, 1997). The FCA method is undoubtedly representative and practical, however, the searching distance threshold setting causes an inherent drawback. That is, the actual supply-demand distance might exceed the threshold value. For this sake, Radke and Mu (2000) proposed a twostep floating catchment area method (2SFCA), in which the limitation of the FCA was effectively overcome. Later, the 2SFCA method has attracted widespread attention among researchers, such as Luo and Qi (2009), Luo and Wang (2003), Mamun et al. (2013) and Wang and Luo (2005). The 2SFCA method was advanced and transformed according to changes of the environmental inputs. Moreover, it has been widely used and embedded in many GIS software programs, such as ESRI ArcGIS and CALIPER TransCAD. Some scholars provided different approaches for measuring accessibility in the framework of a survey-statistics-analysis. The evaluated accessibility was more or less in the aspatial dimension. Occasionally, the utility theory, which displays the relationship between accessibility and social-economical characteristics (e.g., social class, job type, income level, sex, age, etc.), was applied in the literature related to accessibility measures (Cascetta et al., 2013; Cherchi and Ortúzar, 2002; Marrocu and Paci, 2013). A wider generalization of the measuring methods for the accessibility was presented by Wang and Tang (2013), Geurs et al. (2015) and Neutens (2015). 2.2. Transit accessibility measures 2.2.1. General research on transit accessibility Measures of transit accessibility have been widely proposed in transport literature and could be divided into “to transit accessibility (TTA)” and “by transit accessibility (BTA)” (Moniruzzaman and Páez, 2012). TTA measures were derived from Hansen's (1959) gravity model presented in Eq. (1), which is used to evaluate the ease of getting to a transit station (Lin et al., 2014). With those measures, the service levels of the transit facilities were evaluated based on physical factors, such as walking time (distance), on-board time (or distance), obstacles or built environmental factors. In contrast, BTA measures concern the convenience of finishing a specific activity (e.g., shopping, entertainment, commuting) by transit. Geurs and van Wee (2004) stated the difference between TTA and BTA. They defined TTA as “access” and BTA as “locational accessibility (LA)” in their work. There are mainly two differences between the TTA and the BTA measures: (a) their evaluated objects are different — TTA measures generally examine the physical feature of transit facilities (such as the location, size, coverage, etc.), but BTA measures are commonly used for evaluating the convenience of taking the transit vehicle to travel or finish an activity for a specific human group; (b) they adopt different types of evaluating indexes — TTA is calculated based on built environment factors (Moniruzzaman and Páez, 2012), such as the walking distance (or time) to the nearest transit station, the number of intersections which should be passed through to get to the transit station, etc.; on the other hand, the evaluating index of BTA always considers the time or cost spent on the round trip by transit to accomplish the specific activity, or to reach the designated place to obtain the necessary service (Graham et al., 2015). As a matter of fact, the terms TTA and BTA are often used interchangeably as “transit accessibility” or “the accessibility of a transit system” in various circumstances. However, they are not the same, but were not clearly distinguished in many empirical analyses, such as Delmelle and Casas (2012), Foth et al. (2013), etc. 2.2.2. TTA measures Measures of TTA are commonly combined with built environmental factors as well as social and socioeconomic factors of transit facility users. Murray et al. (1998) and Vandenbulcke et al. (2009) respectively studied the time to reach a transit station from a given location.

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Similarly, Lin et al. (2014) indicated that key variables, such as distance from the origin to a train station, land-use diversity, and connections to stations, all affected TTA for aged people. Some researchers suggested that TTA should be evaluated within certain temporal and spatial scopes of transit facilities (Melbye et al., 2015). They gave an essential indicator to evaluate TTA, i.e., the attachment area of a station, which was also called the buffer area to constrain the reachability of peripheral inhabitants. Hadas (2013) measured the connectivity of transit network based on GIS map data to enable assessing the TTA with spatial analysis by GIS software. To lengthen the radius of the catchment area, many researchers and engineers suggested adding a Park & Ride or Bike & Ride facility around station areas (Ji and Gao, 2010; Kim, 2011; Martens, 2007; Mingardo, 2013). In addition, other researchers found that improving the facility to accommodate transferring between multimodal trips was essential to TTA enhancement (Lau and Chiu, 2004; Mingardo, 2013).

necessarily impact the performance of the commuting efficiency, were rarely modelled in current BTA indexes. In sum, it has neither previously been intended to quantify the impacts of travel distance and transfer tolerance elasticity to evaluate the BTA incorporating transit timetable. In order to overcome the limitation of the existing work, two dimensionless parameters expressing impacts of the maximum tolerance of travel distance and transfer on commuting demand reduction are presented. What is important is that, the adjustment scheme for a transit timetable based on zonal (regional) BTA measures during different time periods is proposed. With the proposed method, it could not only evaluate the BTA level for the commuter in a given time period, but also, it could balance the supply of transit service and demand of commuting trips during different time periods in the study area.

2.2.3. BTA measures Generally speaking, it was very popular to evaluate BTA for different social activities based on socioeconomic factors of individuals and characteristics of transit systems (Hansen, 1959; Wang and Luo, 2005; Fan et al., 2014; Tilahun and Fan, 2014; Widener et al., 2015). BTA measures were often formulated as a function of the spatial relationship between different activities and the level of service of the transit system (Caschili and De Montis, 2013; Caschili et al., 2015; Geurs et al., 2015). Recently, Owen and Levinson (2015) calculated BTA via the possibility that a commuter would choose a transit mode rather than an automobile for a commuting trip based on characteristics of the surrounding area. They suggested that the cumulative opportunity approach for BTA measuring was promising to use in ridership and mode share modelling. In Lei and Church's (2010) opinion, BTA measures should be formulated using space-time constraints. They addressed that the travel time or spatial characteristics of the origin and destination areas of the trip by transit should be considered when evaluating BTA between two points in the city. Extending the work of O'Sullivan et al. (2000), Lei and Church (2010) and Mavoa et al. (2012) successively proposed a BTA measure that incorporated bus schedules as well as the spatial attributes of the origin and destination. Tribby and Zandbergen (2012) and Foth et al. (2013) also stated that BTA should be measured based on time-special factors. From the perspective of the passengers, there were also BTA measures that were qualified via the maximal utility, such as Chorus and de Jong (2011), Gulhan et al. (2013) and Rastogi and Krishna Rao (2003). In particular, as the most common activity in the daily lives of people, commuting was frequently connected with the BTA measurement (Pucher, 2002). Especially, for special groups that cannot accommodate themselves with cars, e.g., low income residents, the handicapped or the young workforce, which always commute by transit, BTA is a key indicator that directly determines their travel efficiency and travel cost. As a result, there have been a great number of works that measure commuting efficiency with BTA measures (Owen and Levinson, 2015). Most of the research on BTA for the commuting trips focuses on enhancing the profits of transit operators or utilities of passengers (Horner, 2004). Representatively, Reggiani et al. (2011) studied BTA for commuting trips based on urban economic theory (Reggiani et al., 2011). Kawabata and Shen (2007) explained the reason of spatial dispatch of commuting activity in the San Francisco Bay Area. They claimed that a transport policy would be more effective in improving job opportunities by transit than by only updating the level of service (LOS) of the transit system. The Brookings Institution (2011) measured how many jobs in US metro areas are reachable by transit in 90 min or less, and found that the typical metropolitan resident can reach approximately 30% of jobs in their metropolitan area by transit in 90 min. However, there is not much research that addresses the measure of BTA for commuters from the perspective of travel demand elasticity. Furthermore, the travel distance and transfer count on the transit network, which will

Before addressing the methodology, some key terms used in this paper should first be clarified. The site (or place) where the commuting trip originates from or is destined to is called the commuting demand generator (CDG), which includes two types: the community and the employment site. A community site refers to a particular area or place where many people live. An employment site refers to the workplace. A commuter travels between his/her community and employment site on every workday. In reality, the community and the employment site are always area places. For this consideration, once a buffer area of the transit station with a radius equals to 1500 m geographically intersects with the area of the community (or the employment site), it deems that the community (or employment site) is serviced by the transit station (TRB, 2013). Moreover, it assumes that each community (or employment) site is serviced by only one transit station. Consequently, the community and community site could be considered as point objects. Finally, the location of the community (or the employment site) is determined as the access (or the gate) which is closest to the serviced transit station. In the transportation planning field, a traffic analysis zone (TAZ) is the most commonly used statistical unit, which is constructed from census information. In addition, a TAZ always provides the socioeconomic data and resident travel information. Obviously, TAZ transit accessibility measures could provide a more powerful and practical description of transit quality for commuters in a given region. Hence, the BTA measure of the TAZ is provided in this paper. An index called zonal “by transit accessibility score (ZBTAS)” is used as the BTA measure of the TAZ. Fig. 1 details the infrastructure involved in the BTA measure of this paper. Assuming that each transit route has two directions, the one in which the commuter starts is the upward direction. In contrast, the reverse one is the downward direction. The commuting trip using the upward direction transit service is called the production trip. Similarly, the commuting trip using the downward direction is the attraction trip. Moreover, it assumes in this paper that the transit vehicle in service has a unique capacity. The framework of the proposed methodology is as follows. First, an index called the “supply to demand ratio (S2Dr)” is used to reflect the balance between the demand of the commuting trip and the passenger carrying capacity of the transit station. Secondly, the “by transit accessibility index (BTAI)” is calculated based on a modified two-step floating catchment (M2SFCA) method for each CDG, regardless of the community or employment location. Thirdly, the total ZBTAS is calculated by aggregating the BTAI values of all CDGs located within the TAZ. Finally, according to the obtained ZBTAS of the TAZ, the timetable of some transit routes could be adjusted to balance the supply and demand of the transit system during different time periods. Certainly, it should distinguish the two types of S2Dr of the transit station for the community and the employment site. For the commuting trip demand produced in the community, the S2Dr of the transit station would be called the “supply to production demand ratio (S2PDr)”. For the

3. The methodology

W.(A.) Xu et al. / Journal of Transport Geography 56 (2016) 138–156

141

CDG TAZ 2 Community

Transit station

Employment site

Transit route

Walk link

TAZ 1

Up-direction

Down-direction

Fig. 1. The main infrastructure involved in BTA measures of this paper.

employment site, where the commuting trip demand is attracted, the S2Dr is named the “the supply to attraction demand ratio (S2ADr)”. These two types of S2Dr are described as follows. From the point of view of the production trip from the community, the S2PDr of each transit station can be calculated as follows: S0 ðt Þ Xs

PRs ðt Þ ¼

F cs ðt Þ

ð2Þ

c∈fcjT cs ≤ T max ;ϕcs ≤ Φmax g

where:PRs(t) denotes the S2PDr of transit station s ∈ S during time period t.Sds (t) denotes the passenger carrying capacity of the dth direction of transit station s ∈ S during time period t (here, d = 0 represents the updirection). Apparently, Sds (t) is determined based on the transit timetable. Accordingly, it hasSds ðtÞ ¼ ∑ δsl U dl ðtÞV; d ¼ f0; 1g, where Udl (t) del

notes the service frequency of transit route l on the dth direction during time period t; δsl denotes the attribution relationship between the station and transit route: if transit route l passes station s, δsl = 1, otherwise δsl = 0; V denotes the uniform transit vehicle capacity, which includes the standing space. Fgs(t) , g ∈ {c, e} denotes the “realized commuting trip distribution (RCTD)” between CDG g and transit station s. For community c, the RCTD between it and its designated transit station s could be calculated ∑ δsl U 0l ðtÞV l

as F cs ðtÞ ¼ c∈fcjT cs ≤ T

∑ max

max

;ϕcs ≤ Φ

g

Oc ðtÞ  ð1−β t 

; ∀s∈S, T cs ϕcs max Þð1−β ϕ  max Þ T Φ

where, Oc(t) denotes the potential commuting trip demand origin at community c during time period t, that is, the production commuting trip demand at community c. Tcs denotes the shortest-path (SP) travel distance by transit between community c and station s, which includes the SP walking distances from the community to its nearest station, and the SP vehicle travel distance from the nearest station of community c to station s. ϕcs denotes the minimum transfer times on the shortest-path by transit between community c and station s. Tmax denotes the tolerable maximal SP travel distance by transit between any origin-destination (OD) pair. For convenience, it will be called the travel distance tolerance threshold.

Φmax denotes the tolerable maximal transfer times on the shortestpath by transit between any OD pair. For convenience, it will be called the transfer tolerance threshold. According to Modesti and Sciomachen (1998), more than two times of transfers in transit trip are generally intolerable for transit-users. Once the transfer count exceeds two, the penalty of the travel time would increase in the power order. Hence, the upper bound of transfer count is set as two in this paper. βt (βϕ) is the dimensionless parameter expressing the marginal reduction in commuting trip demand, resulting from a unit increase in the travel distance (transfer time) by transit. These two parameters imply the elasticity of the travel distance and transfer count by transit to the commuting trip demand. They also reflect the impacts of the maximal travel distance and transfer count tolerance on the reduction of the commuting trip demand. Based on Eq. (2), the BTAI of each community during each time period can be calculated: X

BTAIc ðt Þ ¼

PRs ðt Þ

s∈fsjT cs ≤ T max ;ϕcs ≤ Φmax g

0

B B X B ¼ B B s∈fsjT cs ≤ T max ;ϕcs ≤ Φmax g @

X l

X

c∈fcjT cs ≤ T max ;ϕcs ≤ Φmax g

1 δsl U 0l ðt ÞV 

T cs Oc ðt Þ  1−βt  max T

C C  C C; ∀c∈C ϕcs C 1−βϕ  max A Φ

ð3Þ Similarly, it is easy to calculate the BTAI of each employment site during each time period. On the attraction demand side, the S2ADr of each transit station can be calculated as follows: ARs ðt Þ ¼

X e∈fejT se ≤ T max ;ϕse ≤ Φmax g

X

¼

X e∈fejT se ≤ T max ;ϕse ≤ Φmax g

S1s ðt Þ    T se ϕse De ðt Þ  1−βt  max 1−βϕ  max T Φ δsl U 1l ðt ÞV

ð4Þ

l

  ; ∀s∈S T se ϕse 1−βϕ  max De ðt Þ  1−βt  max T Φ

where, ARs(t) denotes the S2ADr of transit station s∈ S during time period t. S1s (t) denotes the downward direction passenger carrying capacity of transit station s ∈ S during time period t. Here, d = 1 in Sds (t)

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represents the downward direction. De(t) denotes the potential commuting trip demand destined at employment e during time period t. Other notations are similar to those of Eqs. (2) and (3). Thus, the BTAI of each employment site during each time period could be determined as follows: X

BTAIe ðt Þ ¼

ARs ðt Þ

B B B ¼ B B max max s∈fsjT se ≤ T ;ϕse ≤ Φ g @

X

X

X

l

1 δsl U 1l ðt ÞV 

De ðt Þ  1−β t 

e∈fejT se ≤ T max ;ϕse ≤ Φmax g

T se T max



C C C C; ∀e∈E ϕse C 1−β ϕ  max A Φ

ð5Þ A detailed explanation of notations is presented in Appendix 0. Clearly, the process of calculating BTAI for each CDG is similar to the 2SFCA method of Luo and Wang (2003). The major modification is the consideration of different types of demand points as well as the demand reduction caused by the travel distance and transfer tolerances. The detailed procedure for calculating the BTAI of each CDG is presented as follows: Step 1: For each transit station s, select all reachable CDGs within the range of travel distance and transfer tolerance during each time period t. Step 2: Compute the supply-to-demand ratio, that is, the S2PDr of the community or the S2ADr of the employment site during each time period t. Step 3: For each CDG, search all transit stations within the range of travel distance and transfer tolerance during each time period t. Step 4: Sum up the supply-to-demand ratio of all these transit stations for each CDG during each time period t. Finally, the ZBTAS of a TAZ during the tth time period can be calculated as: ZBTASz ðt Þ ¼ γ1 

X c∈C

4. Computational example 4.1. Transit network and relevant parameter values of the example

s∈fsjT se ≤ T max ;ϕse ≤ Φmax g

0

threshold of the ZBTAS for TAZ z during time period tk. ZBTAStzk, min is the lower threshold of the ZBTAS for TAZ z during time period tk.

δcz BTAIc ðt Þ þ γ 2 

X

δez BTAIe ðt Þ; ∀z∈Z

ð6Þ

e∈E

where, γ1 and γ2 are the proportional parameters and γ1 + γ2 = 1. δcz and δez are 0–1 variables. If community c (employment site e) is located within TAZ z, δcz (δez) = 1, and 0 otherwise. In practical operation, the existing transit timetable should often be adjusted during each time period to balance the supply and demand (David, 2006). The traditional methods for transit timetable adjustment could be classified as time period oriented adjustment (TPOD) and zone oriented adjustment (ZOD) methods (Vuchic, 2005). TPOD refers to adjusting timetables of some transit routes, of which the transportation capacities are unbalanced with the demand during some time periods. ZOD refers to adjusting the timetables of those transit routes serving TAZs in which the transit service quality is intolerable. In this paper, both the TPOD and the ZOD methods are used together to adjust the timetables of some transit routes based on the timedependent transit accessibility characteristics obtained according to the previous steps. The transit routes, of which the timetables should be adjusted for servicing their TAZs, have a ZBTAS out of the range of the given LoS thresholds, such that: Lt1 ∪Lt 2 ∪…∪Ltk ∪… n o  ¼ ∩ lδzl ¼ 1; ZBTASz ðt k Þ≤ZBTAStz;k min ; or ZBTASz ðt k Þ≥ ZBTAStz;k max ; ∀z ∀t k

ð7Þ where, Ltk is the set of transit routes, of which the timetables should be adjusted during time period tk. δzl denotes the attribution relationship between the transit route and the TAZ. If transit route l services TAZ z, it is equal to 1, and otherwise it is equal to 0. ZBTAStzk, max is the upper

In this section, an example is presented to describe the proposed methodology in detail. The example transit network is shown in Fig. 2, in which there are three TAZs (denoted as zi, i = 1, 2 and 3), three transit routes (denoted as li, i = 1 (red), 2 (green) and 3 (blue)), six transit stations (denoted as si, i = 1, …,6), six communities (denoted as ci, i = 1, …, 6) and six employment sites (denoted as ei, i = 1, …, 6). The travel distance tolerance threshold Tmax is set as 4 units, and the transfer tolerance threshold is set equal to 2. Parameters βt and βϕ are set equal to 0.1 and 0.3, respectively. The uniform transit vehicle capacity V is set equal to 60 persons/vehicle. The proportional parameters for calculating ZBTAS of the TAZ, γ1 and γ2, are set equal to 0.5, respectively. For the convenience of computation, this example considers only two time periods that consist of the peak time (t1 = 1) and the offpeak time (t2 = 2). Each transit route is operated bi-directionally. That is, d = {0, 1}, where d = 0 represents the upward direction and 1 is the downward direction. Furthermore, the vehicle travel time on each transit link (i.e., the segment connecting two consecutive stations) is set equal to 1 unit. Each community is assumed to produce 1000 commuting trips during the peak time period and half (500) during the offpeak time period. Each employment is assumed to attract 500 commuting trips during the peak time and half (250) during the off-peak time. The characteristics of each TAZ, transit route, transit station, community and employment site are provided in Tables 2 and 3. Bypassing the last two rows, Columns 3–5 (δsl) of Table 2 provide the 0–1 index of the attributing relationship between the station and the transit route. For instance, δs1l1 =1 (i.e., the number of cell (1, 3)) demonstrates that the station s1 is on transit route l1. Columns 6–17 show the network characteristics of CDGs. After omitting the travel time on the walking link that connects the CDG to the nearest transit station, Columns 6–17 (with head via triplet: δcz, [Tcs,ϕcs]) show the attribution relationship between each community and TAZ δcz, the SP travel distance by transit between each community and transit station Tcs, and the transfer times on the SP by transit between the community and station ϕcs. For illustration, the triplet “0, [3,1]” in the cell crossing Row z1 to Row s1 and Column c5 indicates that community c5 is not located within TAZ z1 (δc5z1 = 0), the SP travel distance by transit between community c5 and station s1 is 3 units (Tc5s1 =3), and the transfer times on the SP by transit is 1 (ϕc5s1 = 1). Similarly, the triplet “δez, [Tse,ϕse]” details the attribution relationships between each TAZ, station and employment site. Finally, Table 3 illustrates the supply or demand characteristics for each transit route or CDG during the peak time period and off-peak time period. For example, the numbers “45” and “15” state that the service frequencies of transit route l1 is set to 45 vehicles during the peak time period and 15 vehicles during the off-peak time period, regardless of the direction, respectively. That is, Ul10(1) = Ul11(1) =45 vehicles, and Ul10(2) = Ul11(2) = 15 vehicles. Furthermore, the numbers “1000” and “500” of each community except c6 indicate that one of these communities potentially produces 1000 commuting (person) trips during the peak time and 500 during the off-peak time (i.e., Oc(1) = 1000 , Oc(2) = 500 , c = c1 , … c5). Specifically, it can be observed that the potential commuting trips produced at community c6 are only half of those of the other communities during both the peak and the offpeak time. This is because community c6 is connected to two stations; therefore, the commuting trip demands should be divided into two equal parts to avoid the repeated computation. In the same way, the potential commuting trip demands attracted to each employment site during peak and off-peak time periods, De(1) and De(2) , ∀ e, are also shown in Table 3.

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Lengend

Community Employment site Transit station Walk link (Access connector) Transit link

Fig. 2. The transit network and CDGs for a computation example.

The RCTD between community c1 and station s1 at the peak time period is.

Except for the parameters of transit accessibility measures, the thresholds for the transit timetable adjustment are set as follows: ZBTAS1z , min = 6.0, and ZBTAS1z , max = + ∞; ZBTAS2z , min = 0, and ZBTAS2z,max =4.5.

Tc

s

s

¼ 1000  ð1−0:1   04Þð1−0:3  02Þ ¼ 1000; F c1 s1 ð2Þ ¼ 500: Similarly, Fc2s1(1)= 1000.00, Fc2s1(2)= 500. Fc3s1(1)= 1000.00, Fc3s1(2)= 500. Fc4s1(1)= 950, Fc4s1(2)= 475. Fc5s1(1)= 765, Fc5s1(2)= 382.5. Fc6s1(1)= 382.50, Fc6s1(2)= 191.25.

4.2. Computational results Based on the relevant parameters presented above, the transit accessibility measures and transit timetable adjustment can be carried out as follows:

✧ 1.3. Calculate the S2PDr of each transit station: PRsj(tk) , j = 1, …6 ; tk =1 , 2.

● Step 1. Calculate BTAI for each community ci, i = 1, 2, …, 6. ✧ 1.1. For each station sj ,j = 1 , … , 6, select the available communities within the travel distance and transfer tolerance thresholds ci ∈ {ci |Tcisi ≤Tmax, ϕcisi ≤ Φmax}. ✧ 1.2. Calculate the RCTD between each available community and transit station during each time period:

The S2PDr of each station, PRsj(tk), can be calculated according to Eq. (2). Still, station s1 is taken as an illustration. During the peak time period (tk = 1), there is only one transit route (l1), which services s1 with a service frequency of Ul10(1) = 45 vehicles. Consequently, the passenger carrying capacity of transit station s1 in the upward direction during the peak time period is Ss10(1) = Ul10(1) × V = 45 × 60 = 2700 persons. Similarly, the passenger carrying capacity in the downward direction during the off-peak time period can be calculated as Ss10(2) = Ul10(2) × V =15× 60 = 600 persons. As shown in Fig. 2, within the tolerance thresholds of the travel distance (4 units) and the transfer (2 times), station s1 services all the six communities. As a result, the effective S2PDr during the two time periods of s1 could be calculated

ϕc s

Tc s

ϕc

1 1 1 1 Þð1−βϕ  Φmax Þ F c1 s1 ð1Þ ¼ Oc1 ð1Þ  ð1−β t  T max

i j i j F ci s j ðt k Þ ¼ Oci ðt k Þ  ð1−βt  T max Þð1−βϕ  Φmax Þ; ∀ci ∈fci jT ci si ≤T max ;

ϕci si ≤Φmax g; t k ¼ 1; 2. For instance, for transit station s1, the available communities are within 3 units of distance and 2 transfers, with a scope of c1, c2, c3, c4, c5 and c6.

Table 2 Basic parameters of the transit network for computational example. TAZ

z1 z2 z3

Station

s1 s2 s3 s4 s5 s6

δcz, [Tcs,ϕcs]

δsl

δez, [Tse,ϕse]

l1

l2

l3

c1

c2

c3

c4

c5

c6

e1

e2

e3

e4

e5

e6

1 1 1 0 0 0

0 0 1 1 1 0

0 0 0 0 1 1

1, [0,0] 1, [1,0] 0, [2,0] 0, [3,1] 0, [4,1] 0, [5,2]

1, [0,0] 1, [1,0] 0, [2,0] 0, [3,1] 0, [4,1] 0, [5,2]

1, [0,0] 1, [1,0] 0, [2,0] 0, [3,1] 0, [4,1] 0, [5,2]

0, [2,0] 0,[1,0] 1, [0,0] 0, [1,0] 0, [2,0] 0, [3,1]

0, [3,1] 0, [2,0] 0, [1,0] 1, [0,0] 1, [1,0] 1, [2,1]

0, [4,1] 0, [3,1] 0, [2,0] 1, [1,0] 1, [0,0] 1, [0,0]

1, [0,0] 1, [1,0] 0, [2,0] 0, [3,1] 0, [4,1] 0, [5,2]

1, [0,1] 1, [0,0] 0, [1,0] 0, [2,1] 0, [3,1] 0, [4,2]

0, [0,2] 0,[1,0] 1, [0,0] 0, [1,0] 0, [2,0] 0, [3,1]

0, [5,2] 0, [4,2] 0, [3,1] 1, [2,1] 1, [1,0] 1, [0,0]

0, [5,2] 0, [4,2] 0, [3,1] 1, [2,1] 1, [1,0] 1, [0,0]

0, [5,2] 0, [4,2] 0, [3,1] 1, [2,1] 1, [1,0] 1, [0,0]

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Transit lines

Peak time vehicle carrying capacity (vehicles)

Off-peak time vehicle carrying capacity (vehicles)

community–station pair (s6–c1) is equal to zero. This implies that all six transit stations except s6 services community c1 within the travel distance and transfer tolerance thresholds. Therefore, the BTAI of community c1 can be obtained according to Eq. (5):

l1 l2 l3

45 30 20

15 15 10

BTAIc1 ð1Þ ¼

Table 3 Supply or demand characteristics of transit lines and CDGs for computational example.

Community c1 c2 c3 c4 c5 c6

Peak time producing commuting trips (person trips) 1000 1000 1000 1000 1000 500

Off-peak time producing commuting trips (person trips) 500 500 500 500 500 250

Employment site e1 e2 e3 e4 e5 e6

Peak time attracting commuting trips (person trips) 500 500 500 500 500 500

Off-peak time attracting commuting trips (person trips) 250 250 250 250 250 250

X n

o

s∈ sjT c1 s j ≤ T

max

;ϕc

1s j



ci ∈ ci jT ci s1 ≤ T max ;ϕc s ≤ Φmax



F ci s1 ð1Þ

BTAIc1 ð2Þ ¼

X n

o

s∈ sjT c1 s j ≤ T max ;ϕc

2700 ¼ ¼ 0:53: 1000 þ 1000 þ 1000 þ 950 þ 765 þ 382:5 S0 ð2Þ X s1 

ci ∈ ci jT ci s1 ≤ T max ;ϕc s ≤ Φmax

PRs j ð2Þ ¼

5 X

PRs j ð2Þ ¼ 2:38:

j¼1

max sj ≤Φ

In this way, the BTAI of each community is calculated. ● Step 2. Calculate the BTAI of each employment site ei, i = 1, 2, …, 6. The calculation process is similar to that of the BTAI for the community (see above for more detail). The RCTD between each transit station and employment site and the effective S2ADr of each transit station are presented in Table 5.

According to the results obtained in the two previous steps, the ZBTAS of each TAZ during each time period could be computed according to Eq. (6). The results of BTAIs and ZBTASs have been presented in Table 6.

i 1

PRs1 ð2Þ ¼

PRs j ð1Þ ¼ 2:91;

j¼1

max

● Step 3. Calculate ZBTAS of each TAZ during each time period.

S0 ð1Þ X s1

PRs1 ð1Þ ¼

5 X

and

1

according to Eq. (2):

≤Φ

PRs j ð1Þ ¼



● Step 4. Transit timetable adjustment to balance the supply and demand.

F ci s1 ð2Þ

i 1

¼

900 ¼ 0:35: 500 þ 500 þ 500 þ 475 þ 382:50 þ 191:25

In the same way, the effective S2PDr of each station can be calculated. The relevant results are presented in Table 4. ✧ 1.4. Calculate the BTAI value of each community. Based on the obtained PRsj(tk) , j = 1 , … 6 ; tk = 1 , 2, i.e., the values shown in Table 4, the BTAI for each community could be computed according to Eq. (5). Here, the calculating process of BTAIc1(tk) , tk = 1 , 2 is used as an illustration. Referring to the Fcs(t) values presented in Table 4, it could clearly be found that only the RCTD value of the

As shown in Table 6, only TAZ z2 has a ZBTAS lower than the specific threshold ZBTAS1z,min = 6.0. Therefore, it is obtained that L1 =∅ according to Eq. (7). This implies that no transit route is required to adjust the timetable during the peak time period. Given the threshold of the ZBTAS2z,max = 4.5, Table 5 demonstrates that each TAZ has a ZBTAS larger than this threshold. As a result, this implies that L2 ={l1, l2,l3}. This phenomenon demonstrates that the service frequency of each transit route should be shortened to balance the supply and the demand during offpeak time period after reducing 5 vehicle runs of both directions for each transit route during the off-peak time period. That is, the new service frequencies of all transit routes during the off-peak time period are as follows: Ul10(2) = Ul11(2) = 10, Ul20(2) = Ul21(2) = 10 and Ul30(2) = Ul31(2) = 5. Then, the ZBTAS of each TAZ is determined according to

Table 4 The resultant S2PDr of each transit station on the example transit network during the peak and off-peak time periods. Time period

t1 = 1

t2 = 2

Station

s1 s2 s3 s4 s5 s6 s1 s2 s3 s4 s5 s6

S0s (t) (person trips)

Fcs(t) (person trips) c1

c2

c3

c4

c5

c6

1000.00 975.00 950.00 786.25 765.00 0.00 500.00 487.50 475.00 393.13 382.50 0.00

1000.00 975.00 950.00 786.25 765.00 0.00 500.00 487.50 475.00 393.13 382.50 0.00

1000.00 975.00 950.00 786.25 765.00 0.00 500.00 487.50 475.00 393.13 382.50 0.00

950.00 975.00 1000.00 975.00 950.00 786.25 475.00 487.50 500.00 487.50 475.00 393.13

765.00 950.00 975.00 1000.00 975.00 807.50 382.50 475.00 487.50 500.00 487.50 403.75

382.50 393.13 475.00 487.50 500.00 500.00 191.25 196.56 237.50 243.75 250.00 250.00

2700.00 2700.00 4500.00 1800.00 3000.00 1200.00 900.00 900.00 1800.00 900.00 1500.00 600.00

∑

c∈fcjT cs ≤ T max ;ϕcs ≤ Φmax g

5097.50 5243.13 5300.00 4821.25 4720.00 2093.75 2548.75 2621.56 2650.00 2410.63 2360.00 1046.88

F cs ðtÞ (person trips)

PRsj(t)

0.53 0.51 0.85 0.37 0.64 0.57 0.35 0.34 0.68 0.37 0.64 0.57

W.(A.) Xu et al. / Journal of Transport Geography 56 (2016) 138–156

145

Table 5 The resultant S2ADr of each transit station on the example transit network during the peak and off-peak time periods. Time period

t1 = 1

Station

s1 s2 s3 s4 s5 s6 s1 s2 s3 s4 s5 s6

t2 = 2

S1s (t) (person trips)

Fse(t) (person trips) e1

e2

e1

e1

e1

e1

500.00 487.50 475.00 393.13 382.50 0.00 250.00 243.75 237.50 196.56 191.25 0.00

425.00 500.00 487.50 403.75 393.13 315.00 212.50 250.00 243.75 201.88 196.56 157.50

350.00 487.50 500.00 487.50 475.00 393.13 175.00 243.75 250.00 243.75 237.50 196.56

0.00 315.00 393.13 403.75 487.50 500.00 0.00 157.50 196.56 201.88 243.75 250.00

0.00 315.00 393.13 403.75 487.50 500.00 0.00 157.50 196.56 201.88 243.75 250.00

0.00 315.00 393.13 403.75 487.50 500.00 0.00 157.50 196.56 201.88 243.75 250.00

the steps presented above. The results are ZBTASz1(2) = 4.07, ZBTASz2(2) = 2.08 and ZBTASz3(2) = 6.06. Compared to the lower threshold ZBTAS2z,max = 4.5, it is clear that ZBTASz3(2) ≤ ZBTAS2z,max. Again, it has L2 = {l3} and the service frequency of l3 should still be reduced. Finally, after setting Ul30(2) = Ul31(2) = 1 vehicles, the requirement of the lower threshold is satisfied. In this example, it demonstrates that the methodology presented in this paper could not only determine the TTA of the transit station (with the S2Dr) but also the BTA level of each CDG (with the BTAI value). Simultaneously, the regional BTA level could be evaluated based on the ZBTAS value of the TAZ. More importantly, the timetable of some transit routes could be adjusted according to the ZBTAS value of the TAZ. From example, it is apparent that there are a lot of user-defined parameters in the proposed model, such as limit thresholds and proportional parameters of the ZBTAS. In practical applications, how to set values for these parameters generally needs a careful discussion among decision-makers according to the practical requirement. It is recommended that the trial and error, or the expert consultation method could be adopted to determine values for these parameters. Commonly, for the study area, if most of the commuters in the study area use transit to go work, and the proportion of residential land areas were high, it is recommended that the larger ZBTAS threshold value and a relatively large γ1 value should be used. Conversely, if the dependence on commuter transit was relatively less, and the proportion of employment land areas was high, it is suggested that a smaller ZBTAS and relatively large γ2 values are adopted. At the same time, according to Eqs. (3) and (5), if parameters βt and βϕ were set equal to 0, these two BTAIs (regardless of which time period is) would be equivalent to the 2SFCA measure of Luo and Wang (2003). For this sake, the limit threshold of the ZBTAS value could be determined by varying proportional parameter values in Eq. (3), as βt and βϕ are set equal to 0.

∑

F se ðtÞ (person trips)

e∈fejT se ≤ T 0 ;ϕse ≤ Φ0 g

2700.00 2700.00 4500.00 1800.00 3000.00 1200.00 900.00 900.00 1800.00 900.00 1500.00 600.00

1275.00 2420.00 2641.88 2495.63 2713.13 2208.13 637.50 1210.00 1320.94 1247.81 1356.56 1104.06

ARsj(t)

2.12 1.12 1.70 0.72 1.11 0.54 1.41 0.74 1.36 0.72 1.11 0.54

5. Empirical case study 5.1. The study area, data sources and operation with GIS software In this section, the proposed methodology is applied to evaluate the BTA for the bus transit-dependent commuter of Xiamen City, China. Xiamen City (also called Amoy) is a city on the southeast coast of China on the Taiwan Strait. There are 335 TAZs, 508 communities and 19,402 employment sites distributed all over the city. The database of CDGs for the empirical study, including community and employment site data, was provided by the Xiamen Municipal Commission of Urban Planning. The database includes the geographical location data, as well as the residential/working population data. In Xiamen City, 283 bus routes with 1431 bus stations provide daily bus service from 6:00 a.m. to 11:00 p.m. for the commuters. Two time periods: the peak time period (t1 = 1: 7:00–8:30, a.m.) and the off-peak time period (t2 = 2: 10:30– 12:00) are considered for this empirical study. The map of Xiamen City as well as the study area is shown in Fig. 3. First, it must be emphasized here that each CDG, regardless of the community or the employment site, is connected to the nearest transit station at a walking distance (nearer than 1500 m) by a walking link (also called an access connector). Certainly, a CDG possibility connects many stations within walking distance. Under this circumstance, the demand of each CDG is divided into equal parts because such processing will prevent the repeat computation of the capacity supply of a transit station for carrying the commuter (this operation has been stated in the computational example in the above section). Currently, almost all of the geographical information system (GIS) software packages (such as ESRI ArcGIS, CALIPER TransCad, MapInfo, etc.) allow the user to perform the necessary operation to connect the point features to the line features. In this case, the Network Analysis Tool in ESRI Arcmap V.

Table 6 The resultant BTAI of each CDG and TBTAS of each TAZ on the example transit network during the peak and off-peak time periods. CDG

c1 c2 c3 c4 c5 c6 e1 e2 e3 e4 e5 e6

BTAI (t1 = 1)

2.91 2.91 2.91 3.48 3.48 3.48 6.76 7.31 7.31 5.19 5.19 5.19

BTAI (t2 = 2)

2.38 2.38 2.38 2.96 2.96 2.96 5.35 5.89 5.89 4.48 4.48 4.48

δcz(δez)

1 1 1 0 0 0 1 1 0 0 0 0

0 0 0 1 0 0 0 0 1 0 0 0

z1

0 0 0 0 1 1 0 0 0 1 1 1

z2

z3

ZBTAS (t1 = 1)

ZBTAS(t2 = 2)

ZBTAS(t1 = 1)

ZBTAS(t2 = 2)

ZBTAS(t1 = 1)

ZBTAS(t2 = 2)

7.75

6.25

5.39

4.42

11.27

9.67

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W.(A.) Xu et al. / Journal of Transport Geography 56 (2016) 138–156

Kinmen Xiamen Island Taiwan Strait

Bus station

Community

Bus route

Employment site

TAZ

Adminstrative district

Water area

Fig. 3. Map of Xiamen City as well as bus transit routes & stops and CDGs (including communities and employment sites) for empirical study.

10.0 is used to conduct the connecting operation, after which all CDGs are connected to bus stations on the bus transit network according the specific topology rules. On the demand side, the commuting trip demand depending on the bus transit service is calculated firstly, according to the statistics of the Resident Travel OD Survey of Xiamen City, 2009. The generating rates

of potential production and attraction commuting trips are summarized in Table 7. With the data shown in Table 7, the potential commuting trip demand of each CDG is determined. For instance, the potential production commuting trip demand of a community with a population of pop during the peak time period could be calculated as Oc(1)=pop×2.39×32.31% ×10.1%.

W.(A.) Xu et al. / Journal of Transport Geography 56 (2016) 138–156

147

Table 7 Basic parameters for calculating the potential commuting trips depending on the bus transit of Xiamen City, China. Production commuting trip rate (trip / day ∗ (person))

Attraction commuting trip rate (trip / d ∗ (position))

Modal share of bus transit

2.39

2.09

32.31%

Moreover, the existing timetable of the bus transit system on Xiamen City is taken as the data source of the supply side. The record of the data source is shown in Fig. 4, which shows the detailed information of each bus run that operates during a total day, including the vehicle run ID, the departure time, the station bus route sequence, etc. Based on this data source, the supply of each station during the two time periods: Sds (t), d=0,1 ; t =1,2; ∀s could be calculated correspondingly. 5.2. Analytical results and comparisons With the basic parameters stated above, the influences of travel distance and transfer count (to the commuting trip demand) with BTAI values are determined firstly. As far as the user-defined parameters, the travel distance tolerance threshold Tmax is set equal to 6000 m and the transfer tolerance threshold Φmax equal to 2 according to travel survey of Xiamen City (Xiamen Municipal Commission of Urban Planning, 2009). The proportional parameters for calculating ZBTAS of the TAZ, γ1 and γ2 are set equal to 0.5, respectively. The results are obtained by executing the procedure with the software ESRI ArcMap v.10.0. 5.2.1. Effects of the travel distance and transfer elasticity The BTAI of CDGs and the ZBTAS of TAZs are obtained by keeping one of the elasticity parameter values (βt and βϕ) fixed equal to a very small value and change the value of the other one from 0 to 1. Fig. 5 details the changes of the mean and standard variance of the resultant BTAI and ZBTAS values for various βϕ from 0 to 1 as βt is fixed equal to 0.01 in the two time periods. As demonstrated in Fig. 5, when βt is fixed equal to 0.01, the BTAI values of CDGs and ZBTAS values of TAZs increase as βϕ increases. Corresponding to Fig. 5, Fig. 6 shows evidence that both the BTAI and ZBTAS values increase as βt increases from 0.01 to 1 when βϕ is fixed equal to 0.01. These two figures demonstrate that the increases of βt and βϕ cause the overall decrease of BTAIs in Xiamen City. The increases of βt and βϕ (the elasticity of the travel distance as well as the transfer count to the commuting trip demand) means that commuters increasingly care more about the service level of the bus transit system. In cases where the provided transit services could not satisfy them, they would rather choose other transportation means to commute. Consequently, the supply capacity of the bus system might exceed the commuting demand. As a result, the BTAI and ZBTAS values increase correspondingly. According to these two figures, the increase of βϕ causes greater increases of BTAI and ZBTAS than those of βt. This implies that the commuter of Xiamen City would rather travel straight on a distant transit route than transferring several times to save travel distance. As it has been shown, the increase of the mean BTAI or ZBTAS versus the increase of βϕ (see Fig. 5) is approximately two times that of βt (see Fig. 6). The

Commuting trip percentage during 7:00–8:30 am

Commuting trip during 10:30–12:00 am

Production

Attraction

Production

Attraction

10.1%

9.82%

3.31%

3.01%

increases of the standard variances of BTAI and ZBTAS in Fig. 5 are approximately four times of those in Fig. 6. Based on these results, it could be addressed that increasing one transfer time between an OD pair is equal to an increase of 2000 m commuting distance of a straight trip by bus in Xiamen City. Moreover, the larger variances of BTAI and ZBTAS caused by the increases of βϕ further prove that the commuter cares more about the transfer times than the travel distance. For demonstrating effects of βt and βϕ more clearly, both the benchmark result (without considering βt and βϕ) and the comparative results (calculated with the proposed model) of ZBTAS values are presented in Fig. 7. As shown in Fig. 7, as βϕ and βt increase from 0.00 to 0.50 to 0.99, the colors emerging in the map of the ZBTAS changes from light to dark. Apparently, if βϕ and βt are set equal to 0, BTA measures calculated with Eqs. (3) and (5) would be equivalent to the 2SFCA measure of Luo and Wang (2003). That is, Plane a and d of Fig.7 present the benchmark of the spatiotemporal ZBTAS values calculated with the standard 2SFCA. Correspondingly, other panels present the spatiotemporal ZBTAS values calculated by the proposed models with various of βt and βϕ values. For clearly demonstrating the spatial difference of ZBTAS values calculated by the different methods, some dotted-line rectangles were added to highlight regions which own the relatively large ZBTAS values (see the red TAZs). As evidenced in panels a and d of Fig. 7, there is only some TAZs within Xiamen Island that have the red color. Accordingly, there is only one dotted-line rectangle in panel a or panel d of Fig. 7. On the other hand, in panels b, c, e and f of Fig.7, the ZBTAS values calculated with parameters βϕ and βt are smaller across Xiamen City. There are many dotted-line rectangles containing the red TAZs over all the study area. It could be asserted that based on the results in panels a and d, the spatial distribution of transit service provision (measured via the ZBTAS value) in Xiamen City has centered on the Island area, and owns a large spatial variance between the Island area and the mainland area. On the other hand, once parameters βϕ and βt are added into the BTA measure, the transit service provision of Xiamen City displays a multiple center form according to ZBTAS values in panels b, c, e and f of Fig.7. Based on these comparisons, it could be confirmed that adding the two parameters into the standard 2SFCA measure could make the BTA index more even in the spatial dimension and in line with the actual situation. In the standard 2SFCA measure, the effect of demand elasticity of the transfer as well as the travel distance is not considered. As a result, if there are transit services in a region, the standard 2SFCA measure would consider that all these transit services would be used by people in this region. Hence, the ZBTAS values would necessarily be lower in panels a and d of Fig.7. However, the standard 2SFCA measure does not make clear that if the transfer and travel distance of the transit

Fig. 4. Dataset of the bus transit timetable of Xiamen City for empirical study.

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W.(A.) Xu et al. / Journal of Transport Geography 56 (2016) 138–156 50.00

400.00

45.00

350.00

40.00 300.00

35.00 30.00

250.00

25.00

200.00

20.00

150.00

15.00 100.00 10.00 50.00

5.00

0.00

0.00 0.1 0.6 1.1 1.6 2.1 2.6 3.1 3.6 4.1 4.6 5.1 5.6 6.1 6.6 7.1 7.6 8.1 8.6 9.1 9.6

0.1 0.6 1.1 1.6 2.1 2.6 3.1 3.6 4.1 4.6 5.1 5.6 6.1 6.6 7.1 7.6 8.1 8.6 9.1 9.6

a) The changes of the mean and standard variance of the resultant BTAIs of communities 16.00

50.00

14.00

45.00 40.00

12.00

35.00

10.00

30.00

8.00

25.00

6.00

20.00 15.00

4.00

10.00

2.00

5.00

0.00 0.1 0.6 1.1 1.6 2.1 2.6 3.1 3.6 4.1 4.6 5.1 5.6 6.1 6.6 7.1 7.6 8.1 8.6 9.1 9.6

0.00 0.1 0.6 1.1 1.6 2.1 2.6 3.1 3.6 4.1 4.6 5.1 5.6 6.1 6.6 7.1 7.6 8.1 8.6 9.1 9.6

b) The changes of the mean and standard variance of the resultant BTAIs of employment sties 100.00 30.00 90.00 80.00

25.00

70.00 20.00

60.00 50.00

15.00

40.00 10.00

30.00 20.00

5.00

10.00 0.00 0.1 0.6 1.1 1.6 2.1 2.6 3.1 3.6 4.1 4.6 5.1 5.6 6.1 6.6 7.1 7.6 8.1 8.6 9.1 9.6

0.00 0.1 0.6 1.1 1.6 2.1 2.6 3.1 3.6 4.1 4.6 5.1 5.6 6.1 6.6 7.1 7.6 8.1 8.6 9.1 9.6

c) The changes of the mean and standard variance of the resultant ZBTAS of TAZs Fig. 5. The changes of the mean and standard variance of the resultant BTAIs and ZBTASs for various βϕ from 0.05 to 1 as βt is fixed equal to 0.01 in the two time periods.

trip were intolerable, the transit-user would not use the provided service at all. Thus the supply to demand ratio of the transit system in these regions would be large. This situation would undoubtedly cause the larger BTAI and ZBTAS. That is why there are more red TAZs in panels b, c, e and f of Fig.7. In other words, the regions located within the dotted-line rectangles in the mainland area of Xiamen City are those places which own transit services with an intolerable transfer or travel distance. Apparently, the standard 2SFCA measure is unable to detect these TAZs. For this sake, it could be confirmed that the measure proposed in this paper could help the decision-maker to make clear the “quality” of transit service provision in the spatiotemporal dimension. At the same time, it indicates in Fig.7 that the ZBTAS increases as β ϕ and βt increase, which is consistent with the results shown in Figs. 5 and 6. Moreover, the color changes in the ZBTAS map during the off-peak time period (the sub-figures in the lower row) are not

as intense as those during the peak time period (the sub-figures in the upper row). Based on this evidence, it is known that the commuters do not care as much about the BTA level during the off-peak time as they do during the peak-time. However, results of the standard 2SFCA presented in panels a and d of Fig. 7 could not reflect these differences. 5.2.2. Effects of the travel distance and tolerance thresholds The effects of the travel distance and transfer tolerance thresholds on the BTA level of Xiamen City are also examined. The resultant mean and variance of ZBTAS values of all TAZs versus various travel distances and transfer tolerance thresholds are presented in Figs. 8 and 9. As shown in Fig. 8, as the travel distance tolerance threshold increases, the mean of the ZBTAS decreases correspondingly, regardless of which combination of βϕ and βt is used (see panels a and b). This

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149

100 90

20

80 70

15

60 50

10

40 30 20

5

10 0

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demonstrates that if the travel distance tolerance threshold is small, the bus station is constrained to service within a region with a small diameter, which results in the situation where the commuting trip demand is relatively lower than that when the travel distance tolerance threshold is large. Apparently, if the passenger carrying capacity is utilized by a small number of commuters, the ZBTAS value is relatively high. On the contrary, the longer the travel distance tolerance threshold is, the same passenger carrying capacity needs to be assigned to a larger number of commuters distributed within the subject area. Correspondingly, the average ZBTAS of this region would be declined. Furthermore, the variance of ZBTASs in the peak time period is relatively larger than that in the off-peak time period (see panels c and d). These results

imply that commuters are more vulnerable to the effect of travel distance tolerance in the peak time period than in the off-peak time. If one of the tolerance thresholds (βϕ and βt) is changed, the variance of the ZBTAS would also change accordingly. However, the change rate in the peak period is relatively higher than that in the off-peak time. Fig. 9 shows the changes of ZBTAS values versus various transfer tolerance thresholds by transit, Φmax. As it is displayed, both the mean and variance of the ZBTAS decreases as Φmax decreases. The transfer tolerance threshold Φmax stands for commuters' tolerance limit towards the maximal transfer count on their journey. Apparently, a smaller Φmax implies that the commuter has a lower tolerance towards the transfer. That is, commuters would rather use other methods of

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TTAS Fig. 7. ZBTAS of the TAZ versus various βt and βϕ during different time periods. (For interpretation of the references to color found in the text regarding this figure, the reader is referred to the web version of this article.)

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transportation to commute rather than to transfer many times to their workplaces. The larger Φmax indicates that the commuter does not care much about the number of transfers of the journey. In this circumstance, the mean and variance of the ZBTASs of all TAZs would decrease because the bus transit system should service more people than when the transfer tolerance threshold is small. During that time, commuters might choose other transport means on account of losing patience with the transfer.

5.2.3. Bus timetable adjustment The bus timetable of Xiamen City is adjusted based on ZBTASs of all TAZs under the combination of parameters as follows: βt = 0.01, βϕ = 0.1, T max = 6000 m, γ 1 = γ2 = 0.5, ZBTAS 1z , min = 5.5, ZBTAS1z , max = 25, ZBTAS 2z , min = 0, and ZBTAS 2z , max = 3.2. According to Eq. (7), the service frequency of bus transit routes passing the TAZs during the peak and off-peak time periods is adjusted. This process requires increasing 120 runs of bus transit vehicles in

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the upward direction inside Xiamen Island during the peak time period. Simultaneously, it needs to reduce 55 runs of vehicles during the off-peak time period outside the Xiamen Island. For comparison, the contour maps of ZBTASs of TAZs during the peak time period before and after timetable adjustment are plotted and shown in Figs. 10 and 11 respectively. In Fig. 10, it could be observed that before the bus timetable adjustment, the contour lines of the ZBTAS are uneven during the peak time period, which indicates that the BTA measures of all TAZs are distributed unequally. It is encouraging that the contour lines of ZBTASs in Fig. 11 are denser and more even than those in Fig. 10. These results

demonstrate that the bus timetable adjustment has improved the transit accessibility level during the peak period for Xiamen City. But on the other hand, adjusting the timetable is a procedure that requires data with higher precision than the ones that come from models. Usually field data is used for this purpose. As a result, it is necessary that the passenger occupancy data of some transit vehicles are reported in real-time. Once it was found that the passenger occupancy of the transit vehicles exceeded the required level after the bus timetable adjustment, the timetable needs to re-adjusted based on the ZBTAS and passenger carrying data. That is, the transit timetable adjustment in this paper could be improved if some real-time survey data were provided.

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6. Conclusions and discussions In this paper, a modified two-step floating catchment area method to determine the “by transit accessibility” measures during different time periods is proposed. In the transit accessibility measuring model, impacts of the demand elasticity of travel distance and transfer are taken into account. Furthermore, a transit timetable adjustment scheme based on the time-dependent “by transit” accessibility measures of the TAZs is recommended. The proposed transit accessibility measures could not only reflect the time-dependent transit service level of a region, but also the supply to demand balance between the community, employment site and the transit station. For city planners, the proposed model could not only be used for transit timetable adjustment, but also for optimizing the structure of the urban transit network. Furthermore, the proposed BTA measure could be applied to examine the commuting efficiency by transit. Commuting efficiency is one of the key indicators which reflects the coordination feature of urban job-housing land-use configuration. Consequently, it hopes that the proposed BTA measures could be supplementary indicators for the evaluation of urban land use planning. Finally, from

the perspective of the transit-dependent commuter, if the ZBTAS information could be embedded onto the handy real-time transportation information platform, he/she could design the commuting trip and select the best commuting route in advance to cut down the unnecessary commuting costs or commuting time spent on transfer or detouring. Of course, a related limitation of this study is that the methodology does not consider passengers' personal socioeconomic and demographic features. Socioeconomic and demographic features have a strong effect on the choice of commuting transport means. This would necessarily impact the commuting trip demand depending on the transit services. Consequently, in future research, these issues of transit accessibility measures would be considered.

Acknowledgements This work was supported by the National Natural Science Foundation of China (NSFC) under Grant No. 51208445 and partly by Humanity and Social Science Youth foundation of the Ministry of Education of China (under Grant No. 12YJCZH237).

Appendix A ● Notations

C/c, ci E/e, ei g S/s, si Z/z, zi T/t, tk d PRs(t) Sds (t) Udl (t) δsl

Set of communities and the index Set of employment sites and the index Index of the CDG, g ∈ {c,e} Set of transit stations and the index Set of traffic analysis zones and the index Set of time periods and the index Set of the directions of a transit route and the index; commonly, d= {0, 1} represents a set of the “upward direction” and “downward direction”. The supply to production (commuting trip) demand ratio of transit station s ∈ S during time period t The passenger carrying capacity of the dth direction of transit station s ∈ S during time period t The service frequency of transit route l on the dth direction during time period t 1; transit route l pass station s The attribution relationship between the station and transit route, 0; otherwise V The uniform transit vehicle capacity The reduced production trip distribution between community c and transit station s Fcs(t) The reduced attraction trip distribution between employment site e and transit station s Fse(t) The potential commuting trip demand origin at community c during time period t Oc(t) The potential commuting trip demand destined at employment e during time period t De(t) Tcs The shortest-path (SP) travel distance by transit between community c and transit station s The minimum transfer number on the shortest-path by transit between community c and station s ϕcs The travel distance tolerance threshold, which denotes the tolerable maximal SP travel distance by transit between any OD pair Tmax The transfer tolerance threshold, which denotes the tolerable maximal transfer times on the shortest path between any OD pair Φmax Dimensionless parameters expressing the marginal increase in passenger demand reduction resulted from a unit increase in the travel distance by transit βt Dimensionless parameters expressing the marginal increase in passenger demand reduction resulting from a unit increase in the transfer times βϕ by transit “by transit accessibility” index (BTAI) of community c during time period t BTAIc(t) ARs(t) The supply to attraction (commuting trip) demand ratio of transit station s during time period t The shortest-path (SP) travel distance by transit between employment site e and transit station s Tse Denotes the minimum transfers number on the shortest-path by transit between employment site e and station s. ϕse “by transit accessibility” index (BTAI) of employment site e during time period t BTAIe(t) Zonal “by transit accessibility score” (ZBTAS) of traffic analysis zone z during time period t ZBTASz(t) The proportional parameters used to calculate ZBTAS and γ1 + γ2 = 1 γ1, γ2 δcz 1; community c locates within traffic analysis zone z 0; otherwise δez 1; employment place e locates within traffic analysis zone z 0; otherwise Ltsi Set of transit routes of which the timetables should be adjusted during time period ti δzl The attribution relationship between the transit route and the TAZ: 1; transit route l services TAZ z 0; otherwise k ZBTAStz,max The upper threshold of ZBTAS value for TAZ z during time period tk k ZBTAStz,min The lower threshold of ZBTAS value for TAZ z during time period tk μ(BTAIg) , g ∈ {c, e} Mean BTAI of CDG g σ(BTAIg) , g ∈ {c, e} Standard variance of the BTAI of CDG g The mean BTAI of the community during time period tk μ[BTAIc(tk)] σ[BTAIc(tk)] The standard variance of the BTAI of the community during time period tk μ[BTAIe(tk)] Mean of the BTAI of the employment site during time period tk σ[BTAIe(tk)] The standard variance of the BTAI of the employment site during time period tk μ[ZBTAS(tk)] Mean of ZBTAS of the TAZ during time period tk (continued on next page)

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APPENDIX A. (continued) σ[ZBTAS(tk)] μ(ZBTAS) σ(ZBTAS)

The standard variance of the ZBTAS of the TAZ during time period tk Mean of ZBTAS of the TAZ Standard variance of the ZBTAS of the TAZ

● Acronyms BTA TTA LoS SP OD CDG BTAI TAZ ZBTAS 2SFCA S2Dr S2PDr S2ADr RCTD

References Ben-Akiva, M., Lerman, S.R., 1985. Discrete Choice Analysis: Theory and Application to Travel Demand. MIT Press, Cambridge, MA. Bocarejo, S.,.J.P., Oviedo, H.,.D.R., 2012. Transport accessibility and social inequities: a tool for identification of mobility needs and evaluation of transport investments. J. Transp. Geogr. 24, 142–154. Brookings Institution, 2011. Missed Opportunity: Transit and Jobs in Metropolitan America, Metropolitan Infrastructure Initiative Series and Metropolitan Opportunity Series. Burchardt, T., 1999. (cited in F.C. Hodgson and J. Turner, 2003. Participation not consumption: the need for new participatory practices to address transport and social exclusion. Transp. Policy 10, 272. Cascetta, E., Cartenì, A., Montanino, M., 2013. A New Measure of Accessibility Based on Perceived Opportunities. Procedia — Social and Behavioral Sciences 87 pp. 117–132. Caschili, S., De Montis, A., 2013. Accessibility and complex network analysis of the U.S. commuting system. Cities 30, 4–17. Caschili, S., De Montis, A., Trogu, D., 2015. Accessibility and rurality indicators for regional development. Comput. Environ. Urban. Syst. 49, 98–114. Cherchi, E., Ortúzar, J., 2002. Mixed RP/SP models incorporating interaction effects. Transportation 29, 371–395. Chorus, C.G., de Jong, G.C., 2011. Modeling experienced accessibility for utilitymaximizers and regret-minimizers. J. Transp. Geogr. 19, 1155–1162. Curl, A., Nelson, J.D., Anable, J., 2015. Same question, different answer: a comparison of GIS-based journey time accessibility with self-reported measures from the National Travel Survey in England. Comput. Environ. Urban. Syst. David, B., 2006. Urban transit: operations, planning, and economics edited by Vukan R. Vuchic J. Reg. Sci. 46, 566–568. Delmelle, E.C., Casas, I., 2012. Evaluating the spatial equity of bus rapid transit-based accessibility patterns in a developing country: the case of Cali, Colombia. Transp. Policy 20, 36–46. Dong, X., Ben-Akiva, M.E., Bowman, J.L., Walker, J.L., 2006. Moving from trip-based to activity-based measures of accessibility. Transp. Res. A Policy Pract. 40, 163–180. Fan, Y., Allen, R., Sun, T., 2014. Spatial Mismatch in Beijing, China: Implications of Job Accessibility for Chinese Low-age Workers. Habitat International 44 pp. 202–210. Foth, N., Manaugh, K., El-Geneidy, A.M., 2013. Towards equitable transit: examining transit accessibility and social need in Toronto, Canada, 1996–2006. J. Transp. Geogr. 29, 1–10. Fransen, K., Neutens, T., Farber, S., De Maeyer, P., Deruyter, G., Witlox, F., 2015. Identifying public transport gaps using time-dependent accessibility levels. J. Transp. Geogr. 48, 176–187. Geurs, K.T., van Wee, B., 2004. Accessibility evaluation of land-use and transport strategies: review and research directions. J. Transp. Geogr. 12, 127–140. Geurs, K., Zondag, B., de Jong, G., de Bok, M., 2010. Accessibility appraisal of land-use/ transport policy strategies: more than just adding up travel-time savings. Transp. Res. Part D: Transp. Environ. 15, 382–393. Geurs, K.T., De Montis, A., Reggiani, A., 2015. Recent advances and applications in accessibility modelling. Comput. Environ. Urban. Syst. 49, 82–85. Graham, S., Lewis, B., Flanagan, B., Watson, M., Peipins, L., 2015. Travel by public transit to mammography facilities in 6 US urban areas. J. Transp. Health 2, 602–609. Gulhan, G., Ceylan, H., Özuysal, M., Ceylan, H., 2013. Impact of utility-based accessibility measures on urban public transportation planning: a case study of Denizli, Turkey. Cities 32, 102–112. Gulliford, M., Hughes, D., Figeroa-Munoz, J., Guy's, K.s., Health, S.T.S.o.M.P., Group, H.S.R., 2001. Access to health care: report of a scoping exercise for the National Coordinating Centre for NHS Service Delivery and Organisation R and D (NCCSDO) 26

“by transit” accessibility “to transit” accessibility Level of service The shortest-path Origin–destination Commuting demand generator, refers to the community and the employment site “by transit” accessibility index of CDG Traffic analysis zone Zonal transit accessibility sore of TAZ Two-steps floating catchment area method, see Luo and Wang (2003) Supply-to-demand ratio Supply-to-production demand ratio Supply-to attraction demand ratio Realized commuting trip distribution

February 2001 (with minor amendments August 2001). Guy's, King's and St Thomas' School of Medicine. Public Health and Health Services Research Group. Hadas, Y., 2013. Assessing public transport systems connectivity based on Google Transit data. J. Transp. Geogr. 33, 105–116. Hägerstrand, T., 1970. What about People in Regional Science. Regional Science Association 24 pp. 1–12. Handy, S.L., Niemeier, D.A., 1997. Measuring accessibility: an exploration of issures and alternatives. Environ. Plan. A 29, 1179–1194. Hansen, W.G., 1959. How accessibility shapes land use. J. Am. Inst. Plann. 25, 73–76. Horner, M.W., 2004. Spatial dimensions of urban commuting: a review of major issues and their implications for future geographic research. Prof. Geogr. 56, 160–173. Ji, J., Gao, X., 2010. Analysis of people's Satisfaction with Public Transportation in Beijing. Habitat International 34 pp. 464–470. Kawabata, M., Shen, Q., 2007. Commuting inequality between cars and public transit: the case of the San Francisco Bay Area, 1990–2000. Urban Stud. 44, 1759–1780. Khan, A., 1992. An integrated approach to measuring potential spatial access to healthcare services. Socio Econ. Plan. Sci. 26, 275–287. Kim, K.S., 2011. Exploring transportation planning issues during the preparations for EXPO 2012 Yeosu Korea. Habitat International 35, pp. 286–294. Kwan, M.-P., 1998. Space–time and integral measures of individual accessibility: a comparative analysis using a point-based framework. Geogr. Anal. 30, 191–216. Lau, J.C.Y., Chiu, C.C.H., 2004. Accessibility of Workers in a Compact City: The Case of Hong Kong. Habitat International 28 pp. 89–102. Lei, T.L., Church, R.L., 2010. Mapping transit-based access: integrating GIS, routes and schedules. Int. J. Geogr. Inf. Sci. 24, 283–304. Leitham, S., McQuaid, R.W., Nelson, D., J., 2000. The influence of transport on industrial location choice: a stated preference experiment. Transp. Res. A Policy Pract. 34, 515–535. Lin, T., Xia, J., Robinson, T.P., Goulias, K.G., Church, R.L., Olaru, D., Tapin, J., Han, R., 2014. Spatial analysis of access to and accessibility surrounding train stations: a case study of accessibility for the elderly in Perth, Western Australia. J. Transp. Geogr. 39, 111–120. Lucas, K., Grosvenor, T., Simpson, R., 2001. Transport, the Environment and Social Exclusion. Joseph Rowntree Foundation/York Publishing Ltd., York. Luo, W., Qi, Y., 2009. An enhanced two-step floating catchment area (E2SFCA) method for measuring spatial accessibility to primary care physicians. Health Place 15, 1100–1107. Luo, W., Wang, F., 2003. Measure of spatial accessibility to healthcare in a GIS environment: synthesis and a case study in the Chicago region. Environ. Plan. B 30, 865–884. Mamun, S.A., Lownes, N.E., 2011. Measuring service gaps: accessibility-based transit need index. Anglais, pp. 153–161. Mamun, S.A., Lownes, N.E., Osleeb, J.P., Bertolaccini, K., 2013. A method to define public transit opportunity space. J. Transp. Geogr. 28, 144–154. Marcucci, E., Gatta, V., 2011. Regional airport choice: consumer behaviour and policy implications. J. Transp. Geogr. 19, 70–84. Marrocu, E., Paci, R., 2013. Different tourists to different destinations. Evidence from spatial interaction models. Tour. Manag. 39, 71–83. Martens, K., 2007. Promoting bike-and-ride: the Dutch experience. Transp. Res. A Policy Pract. 41, 326–338. Mavoa, S., Witten, K., McCreanor, T., O'Sullivan, D., 2012. GIS based destination accessibility via public transit and walking in Auckland, New Zealand. J. Transp. Geogr. 20, 15–22. Melbye, D.C., Møller-Jensen, L., Andreasen, M.H., Kiduanga, J., Busck, A.G., 2015. Accessibility, Congestion and Travel Delays in Dar Es Salaam — A Time–Distance Perspective. Habitat International 46 pp. 178–186. Mingardo, G., 2013. Transport and environmental effects of rail-based park and ride: evidence from the Netherlands. J. Transp. Geogr. 30, 7–16.

156

W.(A.) Xu et al. / Journal of Transport Geography 56 (2016) 138–156

Modesti, P., Sciomachen, A., 1998. A utility measure for finding multiobjective shortest paths in urban multimodal transportation networks1. Eur. J. Oper. Res. 111 (3), 495–508. Moniruzzaman, M., Páez, A., 2012. Accessibility to transit, by transit, and mode share: application of a logistic model with spatial filters. J. Transp. Geogr. 24, 198–205. Murray, A.T., Davis, R., Stimson, R., Ferreira, L., 1998. Public transport access. Transp. Res. D 3, 319–328. Neutens, T., 2015. Accessibility, equity and health care: review and research directions for transport geographers. J. Transp. Geogr. 43, 14–27. O'Sullivan, D., Morrison, A., Shearer, J., 2000. Using desktop GIS for the investigation of accessibility by public transport: an isochrone approach. Int. J. Geogr. Inf. Sci. 14, 85–104. Owen, A., Levinson, D.M., 2015. Modeling the commute mode share of transit using continuous accessibility to jobs. Transp. Res. A Policy Pract. 74, 110–122. Páez, A., Scott, D.M., Morency, C., 2012. Measuring accessibility: positive and normative implementations of various accessibility indicators. J. Transp. Geogr. 25, 141–153. Peng, Z., 1997. The job-housing balance and urban commuting. Urban Stud. 34, 1215–1235. Pucher, J., 2002. Renaissance of public transport in the United States? Transp. Q. 56, 33–49. Radke, J., Mu, L., 2000. Spatial decomposition, modeling and mapping service regions to predict access to social programs. Geogr. Inf. Sci. 6, 105–112. Rastogi, R., Krishna Rao, K.V., 2003. Defining transit accessibility with environmental inputs. Transp. Res. Part D: Transp. Environ. 8, 383–396. Reggiani, A., Bucci, P., Russo, G., 2011. Accessibility and impedance forms: empirical applications to the German commuting network. Int. Reg. Sci. Rev. 34, 230–253. Shen, Q., 1998. Location characteristics of inner-city neighborhoods and employment accessibility of low-income workers. Environ. Plan. B Plan. Des. 25, 345–365. Shi, J., Ying, X., 2008. Accessibility of a destination-based transportation system: a large airport study. Tsinghua Sci. Technol. 13, 211–219. Tilahun, N., Fan, Y., 2014. Transit and job accessibility: an empirical study of access to competitive clusters and regional growth strategies for enhancing transit accessibility. Transp. Policy 33, 17–25. Tong, L., Zhou, X., Miller, H.J., 2015. Transportation network design for maximizing space– time accessibility. Transp. Res. B Methodol. 81, 555–576 Part 2.

TRB (Transportation Research Board), 2013. Transit capacity and quality of service manual. Transit Cooperative Highway Research Program (TCRP), Washington, D.C, USA, Third edition. Tribby, C.P., Zandbergen, P.A., 2012. High-resolution spatio-temporal modeling of public transit accessibility. Appl. Geogr. 34, 345–355. Tuzun Aksu, D., Ozdamar, L., 2014. A mathematical model for post-disaster road restoration: enabling accessibility and evacuation. Transp. Res. E 61, 56–67. Vandenbulcke, G., Steenberghen, T., Thomas, I., 2009. Mapping accessibility in Belgium: a tool for land-use and transport planning? J. Transp. Geogr. 17, 39–53. Vuchic, V.R., 2005. Urban Transit: Operations, Planning, and Economics. Wiley. Wang, F., Luo, W., 2005. Assessing spatial and nonspatial factors in healthcare access in Illinois: towards an integrated approach to defining health professional shortage areas. Health Place 11, 131–146. Wang, F., Minor, W.W., 2002. Where the jobs are: employment access and crime patterns in Cleveland. Ann. Assoc. Am. Geogr. 92, 435–450. Wang, F., Tang, Q., 2013. Planning toward equal accessibility to services: a quadratic programming approach. Environ. Plan. B Plan. Des. 40, 195–212. Wang, G., Zhong, Y., Teo, C.-P., Liu, Q., 2015. Flow-based accessibility measurement: the place rank approach. Transp. Res. C 56, 335–345. Welch, T.F., Mishra, S., 2013. A measure of equity for public transit connectivity. J. Transp. Geogr. 33, 29–41. Widener, M.J., Farber, S., Neutens, T., Horner, M., 2015. Spatiotemporal accessibility to supermarkets using public transit: an interaction potential approach in Cincinnati, Ohio. J. Transp. Geogr. 42, 72–83. Witter, R., 2010. Public urban transport, travel behaviour and social exclusion – the case of Santiago de Chile. XII World Conference on Transportation Research, Lisbon. Xiamen Municipal Commission of Urban Planning, 2009. Resident Travel OD Survey of Xiamen City. Government of Xiamen City, China. Yang, S., Liu, X., Wu, Y.-J., Woolschlager, J., Coffin, S.L., 2015. Can freeway traffic volume information facilitate urban accessibility assessment?: case study of the city of St. Louis. J. Transp. Geogr. 44, 65–75.