Time dependent accessibility

Kaza, Nikhil Article Time dependent accessibility Journal of Urban Management Provided in Cooperation with: Chinese Association of Urban Management (CAUM), Taipei Suggested Citation: Kaza, Nikhil (2015) : Time dependent accessibility, Journal of Urban Management, ISSN 2226-5856, Elsevier, Amsterdam, Vol. 4, Iss. 1, pp. 24-39, https://doi.org/10.1016/j.jum.2015.06.001 This Version is available at: https://hdl.handle.net/10419/194413 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc-nd/4.0/ HOSTED BY Available online at www.sciencedirect.com Journal of Urban Management 4 (2015) 24–39 Research Article Time dependent accessibility Nikhil Kaza Department of City and Regional Planning, University of North Carolina at Chapel Hill, Campus Box 3140, Chapel Hill, NC 27599-3140, United States Received 26 February 2015; received in revised form 1 June 2015; accepted 2 June 2015 Available online 3 July 2015 Abstract Many place based accessibility studies ignore the time component. Relying on theoretical frameworks that treat distance between two fixed points as constant, these methods ignore the diurnal and seasonal changes in accessibility. Network distances between two nodes are dependent on the network structure and weight distribution on the edges. These weights can change quite frequently and the network structure itself is subject to modification because of availability and unavailability of links and nodes. All these reasons point to considering the implications of volatility of accessibility of a place. Furthermore, opportunities have their own diurnal rhythms that may or may not coincide with the rhythms of the transportation networks, impacting accessibility. Using the case of transit, where all these features are readily apparent simultaneously, I demonstrate the volatility in accessibility for two counties in North Carolina. Significant diurnal changes are observed in quarter of the locations and in the rest the changes are minimal mostly because of low levels of transit accessibility. I argue not for minimizing the volatility, but for acknowledging its impacts on mode choices, location choices and therefore on spatial structure of cities. &2015 The Author. Production and Hosting by Elsevier B.V. on behalf of Zhejiang University and Chinese Association of Urban Management. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Keywords: Accessibility; Public transportation; Social justice 1. Introduction Many studies on transportation accessibility assume that the underlying spatial topology is invariant. Borne out of a Newtonian conceptualization of space, accessibility is measured as either as a cumulative measure of opportunities that are available from a location at a certain distance (or other appropriate metric such as travel time) or weighted measure usually based on gravity or a random utility (for discussion see El-Geneidy & Levinson, 2006;Handy & Niemeier, 1997). In each of these approaches, there are no diurnal or seasonal changes in the distance metric between any two given points in space. The underlying assumption is that distance metric ( e.g. Euclidean/Manhattan) in a Cartesian plane is time invariant. The differences in the accessibility of a location then usually stems from the changes of the attributes of the locations and attractors (e.g. employment, destination types, types of households etc.) and the interest is usually on relative accessibility of one location with respect to another (Dalvi & Martin, 1976). In this paper, I want to argue that accessibility also depends upon the variable distance metric and should be given adequate attention. www.elsevier.com/locate/jum http://dx.doi.org/10.1016/j.jum.2015.06.001 2226-5856/&2015 The Author. Production and Hosting by Elsevier B.V. on behalf of Zhejiang University and Chinese Association of Urban Management. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). E-mail address: [email protected] Peer review under responsibility of Zhejiang University and Chinese Association of Urban Management. A Leibnitzian conception of space, by contrast, is a conceptualization of space that dependent on locations of objects relative to one another (Galton, 2001). Despite this abstractness, I argue that such mode of thinking allows us to rethink the distance metric as a variable and lends itself particularly well to a imagining a topological structure that changes over time. However, the network distance between two nodes is invariant, only if the underlying network structure is invariant. Many accessibility analyses not only focus on relative accessibility of locations, but also on relative changes in accessibility once a set of infrastructure investments (changes to network structure) are made (e.g. Golub, Robinson, & Nee, 2013). Furthermore, when travel times are used as measure of impedance, the distance metric during peak and off-peak hours between any two given points are different even without any physical changes to the network; the edges shorten and lengthen depending on the time of the day. In other words, the weighted network changes with time (though the weights remain finite). Consider the scenario where particular nodes or edges are no longer available. This situation is quite common during hazardous events (Litman, 2006) when some links and nodes disappear from the networks (or the weights become infinite) and therefore depending on their centrality can dramatically change the network distances between any two given nodes. This is another case of variant topological network. Thus, space with variable topological structure is not uncommon. All the above examples presented make a compelling case for considering the variable distance metric. There is perhaps a no better use case than transit that encompasses all the above situations. Even within an hour, the impedance between any two nodes (stops) is varying because of intermittent schedules and wait times. However, until recently even transit accessibility is still measured using invariant topological networks (Mavoa, Witten, & McCreanor, 2012;Tomer, Kneebone, & Puentes, 2011). These invariant networks usually assume a transit network during the peak morning commute. Automobile remains a dominant mode compared to transit, because it not only widens the spatial aspects of accessibility but the temporal aspects as well (Clifton, 2004). This is particularly true for non-work activities that fall outside the traditional work day schedule. Infrastructure support for bread-winning is the norm because of gendered assumptions that undergird planning analyses (Clifton, 2004;Law, 1999), and the transit provision is biased towards peak hours and work days. Unlike automobiles because the underlying network structure is dependent on un/harmonized schedules between different lines in the transit system that facilitate transfers, changes in these levels of service on a single line has ripple effects through the entire system. Depending on the time of the day, a line in the transit system may not be running and thus removing a set of links and nodes from the network. Thus, the impedance metric is very elastic within a single day and between weekdays and weekends. All these features make the case for using understanding the temporal patterns of transit accessibility, as there are analogues in other situations described earlier. It is, therefore, useful to study how the periodicity and breaks in the patterns of transit accessibility. It provides a starting point for understanding changes in other accessibility metric (such as automobile) instead of relying on the maxmin approach that underlies the consideration of peak travel times, or worse using max approach that ignores congestion all together. Furthermore, accessibility that only accounts for invariant impedance is usually based upon the assumptions that travel to work, and more insidiously, travel to particular kind of work (regular shift) is singularly important. Using Current Population Survey data from 2004, McMenamin (2007) claims that almost 30% of the US workers are able or constrained to work in shifts other than regular shifts. Furthermore, accessibility to amenities other than work is also important (Handy & Clifton, 2001) and because these amenities such as restaurants, retail establishments, hospitals have different rhythms than a traditional 9-5 job, changes in accessibility during the day and by seasons have implications both for users of as well as those employed at these amenities (Weber & Kwan, 2002). In their wide ranging review, Geurs and van Wee (2004) suggests that accessibility should account for land-use component, transportation component, temporal component and personal component. They suggest that each of these components is indirectly related to one another. Mamun et al. (2013) use a different approach to account for temporal coverage by accounting for per capita service frequency and distance decay factor. In this paper, I want to argue that there are more direct relationships and should be accounted for our in our measures of accessibility. While the spatial distribution of opportunities is important, it is also related to the temporal dimensions of these distributed opportunities (activity hours, duration etc.) (Crang, 2004). The temporal component not only affects the time available for opportunities by a person, but also whether or not such opportunities can be accessed by a person by a particular mode and with a reasonable cost. N. Kaza / Journal of Urban Management 4 (2015) 24–39 25 Furthermore, standard equity analysis for transit either measures the level of service in traditionally underserved areas by either measuring the headways or the number of jobs accessible via transit without actually accounting for whether such accessibility is constrained by time of the day. Such constraints are important to consider for equity analysis because, more often than not, persons in low income areas and underserved groups are likely to have nontraditional work arrangements and have significantly larger number of household maintenance trips that occur via transit and which may or may not be during regular ‘peak’hours and therefore are more likely to suffer from low levels of transit service and large investments in auto-oriented development (Bullard, Johnson, & Torres, 2004). To support these arguments, I begin by conceptualizing different accessibility measures and putting the place based accessibility measures into a single framework. I modify this framework to demonstrate that time could be readily incorporated and show for the case of transit how the method can be readily applied for much of the United States. I demonstrate the results of a specific case for two county region in North Carolina and draw some implications. Finally, the limitations of this study are acknowledged providing directions for future research. 2. Conceptual overview and methods In their scathing critique, Kwan and Weber (2003) argue for the decline of the importance of distance 1 in our conceptual understanding and explanation of the urban spatial structure and transportation behavior and location choice. Giving examples of number of studies that showed mixed results about the relationship of distance to the central business district with level of employment, and housing values they argue that new models of accessibility are required that would account for the temporal constraints on different individuals as well the problems associated with place based accessibility measures. They advocate for a person based accessibility measures that follow from Hägerstrand's (1970) conception of opportunities based on personal scheduling constraints (Miller, 1999) and for explicitly accounting for the temporal changes in space (e.g. Neutens, Delafontaine, & Scott, 2012). However, accessibility analysis is replete with place-based models instead of person-based models. Some of the main reasons are (1) place is an important aggregative mechanism that summarizes the experiences of persons, (2) planners and decision makers have abilities to affect places through infrastructure improvements, in more direct ways than they could affect persons and (3) data to compute personal accessibility because of individual scheduling constraints are hard to come by. Therefore it is of no surprise that place based models are still a common theme in the literature. The method proposed here bridges place based accessibility and space-time based measures and require only readily available data. In general, accessibility of a place i, with Kas a set of destinations is defined as Ai¼X jAK gðOjÞfðdijÞ In a distance-based measure of accessibility, jrefers to specific destinations such as central business district or bus stops, gðOjÞ¼1 and fðdijÞ¼dij where dij is the distance between jand i. In cumulative opportunities and gravity based models, gðOjÞis the number of opportunities (usually jobs) at location jor some other metric such as economic activity. Cumulative opportunities and gravity based measure are the same except for the weighting function. In the former case, the weighting function f, is an indicator function χdij oD, where Dis the threshold distance and in the latter case, it usually is eβdij , where βis the decay parameter. For the purposes of this analysis, the functional forms of fand gare largely irrelevant as the analysis is focused on the variability with respect to time. Therefore, I choose to demonstrate the concepts using the cumulative opportunities measure, though apart from computational considerations, there are no barriers in applying them to other place based accessibility measures. Accessibility of a place that is conditioned on time tis recast as At i¼X jAK χtATðOT jÞχdt ij oDðdt ijÞ where OT jis the number of opportunities (jobs) at a location jwith duration Tand χð:Þis a indicator function. I use two modes (walking and bus) to compute dt ij, which could also be extended to use other compatible modes that 1 Because geographic distance and travel time are both distances in different metric spaces, I use distance to refer to them both in the rest of the paper. N. Kaza / Journal of Urban Management 4 (2015) 24–3926 would allow mode shifts such as bicycle. Since I am interested in place based accessibility and equity implications, I choose block group centroids as the origins and individual establishments as the set K. With appropriate modifications, the same analysis can be conducted for a purely zonal or purely point geographies conditioned on the availability of the data. This kind of formulation is not novel. Polzin, Pendyala, and Navari (2002) uses time-of-day based accessibility using a hypothetical two route transit network. However, their work is focused on capturing demand by incorporating headways and spans. Perhaps the most similar formulation is by Anderson, Owen, and Levinson (2013) and Owen (2013). They use the transit schedules in Twin Cities, Minnesota to capture time dependent transit access in 1 min throughout the day. While they account for the variation in the transit schedule they do not account for the temporal variation in the available opportunities. In a similar study to this one, Farber, Morang, and Widener (2014) studied the temporal accessibility of supermarkets and the disparities among different racial groups, by considering the differences in transit provision and schedules, but do not consider duration of opportunity. The current study focuses all time dependent employment and not just supermarkets. The algorithm follows roughly the same logic as Lei, Chen, and Goulias (2012) and heavily uses the python code from Morang and Pan (2013) (see Fig. 1). The transit network is built from the Transit agencies’Generalized Transit File Specification (GTFS) files that are freely available online. Because in general, there are many transit agencies in a region that have operations that are complementary, I use multiple relevant GTFS files for a region to create a database for stops, links and schedules. The transit network is merged with road network from OpenStreetMap (OSM) that includes both limited access highways and local roads. To reach a transit station and other destinations from transit stations, I use a walking speed of a constant 4.8 km/h on the road network (see Krizek, El-Geneidy, & Iacono, 2007). Then feasible origin destination pairs are calculated based on the schedule of the transit lines using Dijkstra’s algorithm that is built in the ArcGIS™Network Analyst. Block group centroids or Origins are attached GTFS Files OSM Streets Compute O-D travel time between stops Modified Block Group Centroids Travel to Nearest Stop (Walk) Travel to Destination Stops (Transit) Walk to nodes on road network for remaining time Compute service area polygons Start Time Update start time Compute cumulative opportunity for each start time Fig. 1. Schematic of the algorithm. N. Kaza / Journal of Urban Management 4 (2015) 24–39 27 to the nearest node on the merged network and service area buffers are computed for each origin for every 10 min in the day. These service area buffers consider the feasible destinations based on both walking and transit and automatically includes wait times and transfers to different lines. Because GTFS identifies schedules by different days, I compute these buffers both for a typical weekday, Saturday and Sunday. This could also be extended to include seasonal variations as long as the GTFS data has the information. To reduce the computational time, I limit the analysis only to block groups that are close (within 3.6 km) to transit stations. 2 Employment within the buffers is calculated for each buffer and is assigned to block groups as a measure of accessibility for that particular time. Thus, creation of these buffers can be replicated anywhere in the United States where OSM and GTFS files are readily available. While I do not use this dataset in this analysis, synthetic employment from Longitudinal Employer-Household Dynamics dataset can be used for destinations with information about their industry classification. Duration, T,as defined by facility opening hours are not comprehensive in standard data sources like Google or Yelp for all establishments in all industry types. 3 Therefore, broad activity hours are inferred for each of the industry classes: 8am–6 pm for most industries, 6 am–2 am for food service (NAICS 722), 4 10 am–11 pm for retail (NAICS 44-45) are used to categorize the establishments and employment. These times are inferred from queries using sample of names of the establishment to the Google places API. 5 This is not ideal unlike Ahas et al. (2010) study, which uses cellphone data to both spatially and temporally fix the activity patterns in the city. 3. An use case The usefulness of the above concepts is demonstrated for a two county region; Orange and Durham Counties in North Carolina. These are the two main counties in the Durham-Chapel Hill-Carrboro Metropolitan Planning Organization (DCHC-MPO), which is responsible for transportation planning for the western part of the Research Triangle area in North Carolina. 6 Orange County is home to the University of North Carolina at Chapel Hill and Duke University is located in Durham County, both of whom are major employers in the region. The Research Triangle Park (RTP) is located Southern edge of Durham County, which is the home to many large employers and is not only the economic engine of the region but also for the state. Collectively, 0.4 million people call these counties their home and 333,822 are employed in these two counties in 34,241 establishments (see Table 1). In total there are 228 block groups in the two counties region, and 18 of them are too far from transit stops so I ignore them from the analysis. In general, the transit provision seems to align with the density (see Fig. 2); i.e. most of the jobs and households are relatively close to transit. However, as we will see later, that this does not translate to accessibility. Like many regions, transit service in the triangle is splintered among multiple agencies (see Fig. 2). The main agencies that provide transit are Durham Area Transit Authority (DATA), Chapel Hill Transit (CHT) and Triangle Transit (TTA). Because these transit systems connect up with other transit agencies in the region, I also consider Capital Area Transit (CAT) and C-Tran system to build a master regional transit service stops and lines, even though they are not considered in the set of origins. All these organizations run fixed line bus services. 7 In total, there were 3967 bus stops and 135 routes during the regular weekday. While there is regional effort underway to jointly plan for infrastructure improvements and provide a convenient trip planning interface, because of different mandates and organizational structures the operations are not necessarily coordinated. Chapel Hill Transit is a fare free system that relies on the contribution from the University where as the rest have fare structures that are not harmonized. Transfer from one system to the other is possible only with a regional bus pass, which is only sold online or at select stations. In this analysis, I also ignore these limitations and 2 With a walking speed of 4.8 km/h, this threshold eliminates destinations that can only be reached by walking in 45 min. The temporal variability of accessibility in such situations is conditioned only by the duration of the opportunity. 3 Industries such as NAICS codes 722 (Food Services) and 44-45 (Retail) are oversampled in Google and Yelp databases that are available through their Application Programming Interfaces (API). 4 The North American Industry Classification System (NAICS) is the standard used by Federal statistical agencies in classifying business establishments and is developed by Office of Management and Budget (OMB). http://www.census.gov/eos/www/naics/. 5 https://developers.google.com/places/documentation/ (accessed November 23, 2013). 6 The MPO’s jurisdiction is not exactly same as the study area. The jurisdiction covers all of Durham and the urbanized portion of Orange County and small portion of Chatham County. Since Chatham County does not have fixed route transit, it is not considered in the analysis. 7 There are other organizations that provide vanpools and paratransit, whom I will ignore as they are not widely used. N. Kaza / Journal of Urban Management 4 (2015) 24–3928 consider only travel time as cost of travel instead of a generalized cost. I also limit the number of transfers to one and set the maximum travel time (D) to 45 min. The average commute time in the two county region is 23 min, so this upper limit is not unreasonable. Any arbitrary Dcan be chosen without loss of generality. The GTFS files are available from http://www.gtfs-data-exchange.com/. The GTFS format is widely documented as they are used to create number of transit applications. In general, each agency provides a set of files that include Fig. 2. Regional context and transit systems in the study area. Wake county is shown for completeness, though is not used in the study area. The mixing of population and households are represented using a dot density plot; Bus lines from different transit agencies are also shown. (Source American Community Survey 2006–2010. GoTriangle.). Table 1 Sectoral classification of employment and establishments in 2011 in the study region. NAICS code Sector Count of establishments Employment 11 Agriculture, Forestry, Fishing and Hunting 394 975 21 Mining, Quarrying, and Oil and Gas Extraction 10 305 22 Utilities 19 511 23 Construction 2554 11,447 31–33 Manufacturing 914 30,477 42 Wholesale Trade 1010 6728 44–45 Retail Trade 2794 23,321 48 Transportation & Warehousing 560 4803 51 Information 829 6072 52 Finance and Insurance 1220 7576 53 Real Estate and Rental and Leasing 1902 8002 54 Professional, Scientific, and Technical Services 5431 36,680 55 Management of Companies and Enterprises 157 374 56 Administrative and Support and Waste Management and Remediation Services 7147 19,866 61 Educational Services 691 34,114 62 Health Care and Social Assistance 3142 94,903 71 Arts, Entertainment, and Recreation 684 3845 721 Accommodation 186 4831 722 Food Services and Drinking Places 668 10,914 81 Other Services (except Public Administration) 3749 13,905 92 Public Administration 180 14,173 N. Kaza / Journal of Urban Management 4 (2015) 24–39 29 “stops”,“routes”,“trips”,“stop_times”and “calendar”that combined together provide information on the schedule of every route during the day and the week. I use the National Establishment Time Series (NETS) dataset to locate the employment and establishments. This proprietary dataset is from Walls & Associates, who convert Dun and Bradstreet (D&B) archival establishment data into a time series. For our analysis we ignore the longitudinal information in the dataset and focus on the establishments present in 2011 along with the number of employees and their industry category (NAICS 2007 definitions). Establishments near all transit stops (including outside the two counties) are extracted and are used in the analysis. As mentioned previously, LEHD data could be substituted for this dataset. 4. Results I will discuss the results for all jobs without considering the characteristic function g(.) first and then discuss the time dependent accessibility that constrains some sectors more than others. As can be expected in the use case, large percentage of block groups (162 or 77%) does not exhibit any variation even in a weekday where schedules vary dramatically and transit is oriented towards work travel. While, it might be tempting to think then that the above analysis is futile, it should be noted that the block group with the maximum value accessibility has a value 1,231 compared to a maximum value of 129,573. It should also be noted that the maximum value of the just over half the total number of jobs in the two counties; i.e. almost half of the jobs have no transit access at anytime of the day from any location. Other invariant block groups have substantially less accessibility with only 22 block groups (10%) greater than 100. This is reflective of low levels of transit accessibility for a large portion of the region, rather than conceptual issues with the analysis. In other words, even if the block groups were relatively close to the bus stops, the schedules were arranged in such a way that within 45 min of combined walk and bus travel, many jobs are accessible to large areas in the region. The block groups with relatively high accessibility are essentially downtown areas in Durham, Chapel Hill and Carrboro areas, though not all of central city locations have the same high accessibility. Fig. 3. Median weekday accessibility for different block groups. N. Kaza / Journal of Urban Management 4 (2015) 24–3930 Fig. 4. Hourly median accessibility in each block group of Durham and Orange Counties. The lines are colored based on the proportion of the minorties and the break points reflect the median proportion in Orange County (0.27) and Durham County (0.56). N. Kaza / Journal of Urban Management 4 (2015) 24–39 31 daycare centers, hospitals, libraries, movie theaters and restaurants might be more important than across the board establishments. 7. Conclusions On a bus back from the airport in the mid-afternoon, I overhead a fellow passenger lamenting that his work trip on a bus takes over two hours, including transfers. During peak hours, when alternative routes were available, the trip to work would not have taken such a long time. This snippet of conversation prompted me to rethink if the standard measures of accessibility captured the lived experiences. What I have demonstrated in this paper, is that real distances vary over time even within a day and therefore, it is not unreasonable to expect that perceived costs are also quite different for different modes. Because transit is schedule dependent, it captures various features that are usually ignored in accessibility studies: We can easily visualize, in the case of transit, the changes in network structure and the associated robustness of accessibility and these can be ported to other modes. We can also examine which routes are central to determining the accessibility of the region by examining the changes in the accessibility when the level of service on the route changes and therefore determine the importance of particular links. Because institutional structure of transit provision is usually fragmented, studies such as this highlight the importance of coordination of schedules and operations. Ultimately, any measure of accessibility is imperfect reflection of the lived experience of the people. However, ignoring a key aspect, volatility, and focusing only on the level, can lead us misfocus infrastructure investments and programs. 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