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Free-floating bike share as a last mile transit connection : using hazard models to understand bike share… Vissers, M. Jake 2020-08-14

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Free-floating bike share as a last mile transit connection: using hazard models to understand bike share patterns at UBC M. Jake VissersAugust, 2020School of Community and Regional Planning, UBCGraduate Capstone Project2TABLE OF FIGURESFigure 1 - Histogram of idle duration (hours) for individual bikes ....................................................................4Figure 2 - Cumulative distribution of idle duration (hours) ...............................................................................4Figure 3 - Mean idle duration (hours) per 200 meter zones ................................................................................4Figure 4 - Idle duration heatmaps for four temporal frames ...............................................................................5Figure 5 - Nelson-Aalen cumulative hazard estimator for ‘nearby_time’ ..........................................................7Figure 6 - Schoenfeld residuals for ‘avg_temp’ ......................................................................................................7Figure 7 - Upper quartile transit index ...................................................................................................................8Figure 8 - Variable correlation matrix ....................................................................................................................8Figure 9 - Wesbrook and busy_road dummy variables ........................................................................................9Figure 10 - Four quartiles of transit_index  .........................................................................................................10TABLE OF CONTENTSABSTRACT ................................................................................................................................................................3I. INTRODUCTION .................................................................................................................................................3II. DATA AND METHODS .....................................................................................................................................4 A. Data ..............................................................................................................................................................4 B. Descriptive Statistics ...................................................................................................................................4 C. Cox Proportional Hazard Model ..............................................................................................................5 D. Model Specification ....................................................................................................................................6III. RESULTS ..............................................................................................................................................................9IV. DISCUSSION .......................................................................................................................................................9V. LIMITATIONS ....................................................................................................................................................11VI. ACKNOWLEDGMENTS ................................................................................................................................11References .................................................................................................................................................................113I. INTRODUCTIONABSTRACTThe University of British Columbia (UBC) launched its first permanent free-floating bike share (FFBS) in 2019 with the arrival of HOPR. This new system is part of a global trend which has seen FFBS grow significantly in the last five years. As such, exploring how this emerg-ing technology is being used has become more critical in planning for existing and future systems. Existing literature shows that proximity to transit can increase demand for FFBS, suggesting that FFBS may be an ef-fective first/last mile connection. The purpose of this study is to determine whether proximity to frequent transit increases FFBS demand at UBC. To do this, I ex-amine how ambient factors, such as weather, land use and transit, among others, affect bicycle idle duration, which I use as an inverse proxy for demand. This is done by estimating a Cox proportional hazard model, which models how each covariate affects the probabili-ty of a bicycle being booked. This study offers a unique exploration of how FFBS is used on a major university campus, particularly whether the system serves as a last mile connection for transit. These findings may benefit future planning decisions at UBC, as well as other uni-versities interested in FFBS. Bike share systems have grown significantly in the past decade, becoming an increasingly important piece of urban transportation networks. This growth has been further fueled in the last five years by the development of a new bike share technology: free-floating bike share (FFBS). While traditional docked bike shares require stations for both locking and payment, FFBS integrates both critical features into the bicycle itself, allowing for more flexibility and lower operating costs. These advan-tages have helped spur considerable growth worldwide. This is perhaps most notable in China, where the two largest FFBS companies, OFO and Mobike, have already collectively deployed roughly 15 million bikes and serve over 300 million users [6].  Understanding use patterns for this new technol-ogy is critical for cities, universities and operators to best utilize them. Because demand is often asymmetric within a system, bikes in a FFBS are often rebalanced to increase utilization, particularly around major transit stations during peak demand [8]. Additionally, a better understanding of FFBS use patterns could aid cities and universities in planning for bicycle infrastructure, tran-sit and public realm management.  Existing studies have posed a breadth of questions on the subject, examining both docked and free-float-ing bike shares. A 2017 study examined the distribution of bikes in a FFBS throughout the day to optimize the redistribution of bikes to meet demand [10]. The ef-fects of weather, time of day, population density, land use and transportation infrastructure on use patterns have also been explored in Singapore [12] and Shanghai [6], among other cities [3][14]. Furthermore, evidence exists that bike sharing systems may enhance transit usage [7][16], and conversely, the existence of transit can benefit bike share. Specifically, recent studies have found that the presence of transit has a positive effect on trip attractions [14] and frequency of use. These results suggest that bike share may serve as a first/last mile con-nection with transit [5]. This paper investigates FFBS at the University of British Columbia (UBC) to determine whether proxim-ity to transit increases demand. The study examines how ambient factors, such as weather, land use and transit, among others, affect bicycle idle duration, which is used as an inverse proxy for demand. Four months of FFBS trip data from August-November 2019 are utilized to estimate a Cox proportional hazard model. This model estimates the effect each covariate has on the probabil-ity of a bicycle being booked. Assuming that a higher booking probability indicates more demand, the model helps unpack how transit affect FFBS demand, and pro-vides clues to whether bike share is being used as a last mile transit connection on campus. Each HOPR bicycle generates GPS trip data that is linked to a unique bicycle ID, providing detailed trips of each individual bicycle. This data was provided by Cam-pus and Community Planning, as laid out by the HOPR licensing agreement. Transit, land use and weather data was also publicly available to use in this study.4II. DATA AND METHODSA. DataB. Descriptive Statistics The analysis uses data from HOPR, a FFBS at UBC. The original dataset contained information on 29,957 trips between August and November 2019. This data was used to generate a bicycle idle duration dataset, which tracks the duration that each bicycle was not in use. The variable idle_duration serves as the dependent variable in this analysis, which assumes an inverse rela-tionship between idle duration and bike share demand. To clean the data, I decided to only include points in which a bicycle stays in one place, within the cam-pus service area during the entire time it remained idle. This removed any points where the bicycle was moved by the operator for maintenance or rebalancing, or was tampered with between trips. Once removed, the final dataset contained 23,363 points.  A full set of variables can be found in Table I. The variation in bicycle idle duration is illustrated in Figure 1 and Figure 2. Figure 1 demonstrates the distri-bution of idle durations, and shows that the majority of bikes idle for no more than 6 hours. Figure 2 shows the same distribution of idle durations with a cumulative distribution. The vertical red line marks 72 hours, high-lighting that nearly 100 percent of bikes are checked out within 3 days.  Figure 3 explores the geospatial distribution of bi-cycle idle durations by showing the mean idle duration per 200 meter zones across campus. There are clearly a few patterns shown in this map. The academic core of campus appears to have shorter idle durations. Addi-tionally, pockets around major transit hubs on the east side of campus show shorter idle durations, but the pat-tern is less clear. Finally, large pockets in southeast cam-pus around the Wesbrook Village and Hampton Place neighborhoods exhibit higher idle durations, indicating lower system demand. Figure 4 examines the geospatial distribution of idle durations across 4 temporal frames: all idle durations, those longer than 24 hours, those longer than 48 hours and those longer than 72 hours. While only 9.3% of bi-cycles idle longer than 24 hours, it’s evident from Figure 4 that the spatial patterns are different for bikes with long idle durations. For example, Figure 4.d. shows a Figure 1 - Histogram of idle duration (hours) for individual bikesFigure 2 - Cumulative distribution of idle duration (hours)Figure 3 - Mean idle duration (hours) per 200 meter zones<66-99-1414-24>24cluster of bikes in the southeast corner of campus, in-dicating that longer idle durations disproportionately occur there.5C. Cox Proportional Hazard Model A Cox proportional hazard model was used to ex-plore the effect of several spatial, temporal and weather variables on the idle duration of bicycles. The model es-timates the probability of an event occurring at a given time. For this model, the event will be a bicycle being booked, ending the idle duration of that bike. Therefore, the model can be said to give the probability of an indi-vidual bicycle being booked at a given time. The Cox proportional hazard model is built around the proportional hazard assumption, which says that all individuals have the same baseline hazard function, scaled with a unique factor. Violations of this assump-tion can be tested with Schoenfeld residuals, along with a combination of statistical and visual tests. The covariates (xi) are assumed to have a propor-tional effect on a population-level baseline hazard (h0(t)) to generate a time-dependent individual hazard function. Additionally, the likelihood of an individual bicycle being checked out at a time i can be written as follows:Figure 4 - Idle duration heatmaps for four temporal framesa. All idle durations (N = 23363) b. Idle durations > 24 hours (N = 2176) c. Idle durations > 48 hours (N = 884) d. Idle durations > 72 hours (N = 452)  The general form for a Cox proportional hazard model is as follows:6D. Model Specification An initial model was specified which included the following variables from Table I: nearby_time, peak_time, avg_temp, precipitation, transit_index and build-ing_index. However, the variables nearby_time, peak_time, avg_temp and precipitation failed a statistical test for the proportional hazard assumption, and would re-quire further investigation. To explore the nearby_time variable, I split the data into quartiles and fit each one to a Nelson-Aalen cumu-lative hazard curve (Figure 5). The Nelson-Aalen fitter uses the following function to estimate the cumulative hazard rate, where ‘di’ represents events occurred and ‘ri’ represents the total population at risk [1]. Further, the partial likelihood is found through the product of individual likelihood functions across all events. The log of the following function can be maxi-mized to estimate model parameters [2]. These four curves shows the variation in hazard across the four quartile of the nearby_time variable. From this plot it’s clear that bikes with the most time spent near other bikes (nearby_time>1.3) have the low-est cumulative hazard rate. Conversely, bikes with no time spent near other bikes (nearby_time = 0), have the highest cumulative hazard rate, confirming the negative relationship between nearby_time and hazard found in Table II. However, the uneven change in cumulative hazard between each quartile suggests a non-linear re-lationship may exist. As such, a nearby_time2 term was added to the final model.  The dummy variables peak_time and precipitation were changed to fixed variables to address the propor-tional hazard assumption. This would allow the covari-ates to be included in the model without estimating their effect. The variable avg_temp failed the proportional haz-ard test as well. However, the Schoenfeld residual plot (Figure 6) showed an even distribution of residuals, in-dicating that any assumption violations were likely mi-nor. It was determined that the covariate is acceptable to remain in the model as is [13].  Additionally, the covariate building_index was di-vided into four categories, residential, academic, park-Table I - Variable summaryDescription Variable Name Min1st QuartileMedian Mean3rd QuartileMaxIdle duration of a bicycle (hours) idle_duration 0.0 0.7 2.1 9.4 10.6 633.5Proportion of idle duration within 50 meters of another bikesnearby_time 0.0 0.0 0.4 0.9 1.3 12.4Mean temperate during idle duration (˚C) avg_temp -2.5 8.5 11.1 12.0 15.8 27.0Frequency of transit around each bike (stops per hour ÷ distance² (m²))transit_index 0.0 0.1 0.1 6.6 0.3 143666.4Total building density around each bike (building footprint (m²)÷ distance² (m²))building_index 0.3 1.7 2.2 2.6 2.7 1604.8Building index for residential buildings residential 0.1 0.2 0.3 0.8 0.7 1604.2Building index for academic buildings academic 0.2 0.2 0.5 0.8 1.1 77.0Building index for parkades parking 0.0 0.1 0.1 0.2 0.2 59.5Building index for other buildings other 0.0 0.2 0.2 0.4 0.4 318.2Precipitation dummy precipitationPeak time dummy (booking occurs M-F, 8am-6pm)peak_time22.4% of bookings47.7% of bookings7Figure 5 - Nelson-Aalen cumulative hazard estimator for nearby timeFigure 6 - Schoenfeld residuals for avg tempEquation 1 - Model 1ing, and other, to investigate the impact of various building types. The functional form for this model can be found with Equation 1. A second model was also estimated with the tran-sit_index variable broken up into four quartiles and included as dummy variables relative to the first quar-tile. Initially, the new transit specification returned un-expected results that were inconsistent with literature. However, it turned out that unaccounted variables were influencing the model. Mapping high transit_index across the study area (Figure 7) highlighted a few patterns that could poten-tially impact model results. First, it was clear that high transit_index often occurred along high traffic and vol-ume roadways, which may be more hostile to cyclists than other parts of campus which are pedestrianized or traffic calmed. Second, a high transit_index pocket was present at the core of Wesbrook Village, a univer-sity neighborhood  located at the south end of campus. Although the neighborhood has a high transit_index, it is a primarily residential and commercial development over a kilometer south of the campus’s academic core. Because of this, it is reasonable to suspect that use pat-terns could differ from main campus.  To account for both of these potential effects, dum-my variables were created for idle bicycles in Wesbrook Village and within 50 meters of a 50 km/h or higher road. These variables are included in Model 2 (Equation 2), and visualized in Figure 9.Figure 7 - Upper quartile transit index Wesbrook Village50 kmh roadsUpper quartile transit index8Table II- Model summaryCoef SE HR Coef SE HRnearby_time -0.45 *** 0.01 0.63 -0.46 *** 0.01 0.63nearby_time2 0.05 *** 0.00 1.05 0.05 *** 0.00 1.05avg_temp 0.02 *** 0.00 1.02 0.02 *** 0.00 1.02transit_index 0.00 0.00 1.00 - - -transit_2 - - - 0.15 *** 0.02 1.16transit_3 - - - 0.13 *** 0.02 1.14transit_4 - - - 0.20 *** 0.02 1.22residential 0.00 0.00 1.00 0.00 0.00 1.00academic 0.02 *** 0.00 1.02 0.01 *** 0.00 1.01parking -0.47 *** 0.04 0.62 -0.68 *** 0.05 0.51other 0.00 0.00 1.00 0.00 0.01 1.00busy_road - - - -0.45 *** 0.03 0.64wesbrook - - - -0.43 *** 0.03 0.65NConcordancePartial AICPartial Log-LikelihoodPseudo R²Significance Codes: p<0.1 *, p<0.05 **, p <0.01 ***361343-1806590.146361768-1808760.145Model 1233630.672233630.674Model 2 A Cox proportional hazard model was estimated for each of the specifications described in Equation 1 and Equation 2. The full results for these estimations can be found in Table II, and can be understood as the probability of a bicycle being booked at a given time. A McFadden pseudo r2 value of 0.146 was calculated for Model 2, relative to the null log likelihood. This value was higher than that returned in Model 1, suggesting a better fit for the data. Further, a correlation matrix (Fig-ure 8) showed no significant variable interaction for Model 2.  Time spent near other bicycles has a significant neg-ative effect on booking probability, although the positive coefficient for the quadratic term nearby_time2 dimin-ishes the effect as the term nearby_time increases. Av-erage temperature and proximity to academic buildings both have significant positive effects on booking proba-bility, while proximity to parkades has a significant neg-ative effect. However, proximity to residential buildings and other building types showed no significant effect. Relative to quartile 1, both quartile 2 and 3 of tran-sit_index returned a positive effect, but their respective coefficients were not significantly different from each other. Quartile 4, however, returned the highest signif-III. RESULTSFigure 8 - Variable correlation matrixicant positive effect on booking probability, indicating proximity to highest frequency transit most increases bike share demand. Additionally, proximity to busy roads and Wesbrook Village each had a significant neg-ative effect on booking probability.9Figure 9 - Wesbrook and busy road dummy variablesWesbrook VillageBusy road 50 meter bufferEquation 2 - Model 2 Residential buildings had no effect on booking probability, which was an unexpected result. While much literature links population and building density to increased bike share use [3][5], the context at UBC is quite different to a city. Many residential buildings, par-ticularly undergraduate residences, are close enough to the main academic core that walking may be preferable.IV. DISCUSSION Wesbrook Village, a mixed-use neighborhood south of campus, had a significant negative effect on booking probability. This could be for a few reasons. Although Wesbrook Village has transit, the neighborhood may be too small for first and last mile bicycle connections. Further, the neighborhood is over a kilometer south of the campus core, and can only be reached by traveling on high speed roads (see Figure 9). It is possible that facilitating more bike share trips in Wesbrook Village would require more robust bicycle infrastructure be-tween the neighborhood and main campus. Another interesting finding was the significant neg-ative effect of parkades on booking probability. This finding indicates that bike share is likely not being used as a last mile connector for automobile trips to campus. The central question of this research, however, was to determine the effect of transit on bicycle booking probability. Assuming higher booking probability in-dicated more bike share demand, it’s clear that closer proximity to high levels of transit has a positive effect on bike share demand and may be an effective last mile Figure 10 - Four quartiles of transit index 2nd Quartile 1st Quartile3rd Quartile4th Quartile10V. LIMITATIONSI would like to thank Campus & Community Planning and HOPR for providing access to data and answering questions throughout the study.VI. ACKNOWLEDGMENTSThe study has a few potential limitations that could have impacted the results. The bike share system has a transit exclusion zone around one bus loop, preventing bikes from parking there, and also has a parking hub system, which encourages users to park bicycles in designated hubs. Although these factors may bias where bicycles are parked, they should not impact the relationship be-tween ambient factors and idle duration. In addition to these system conditions, more de-tailed data could improve the predictive capability of the model. For example, adding a covariate for bicycle infrastructure could be more precise than a busy_road dummy variable, and further explain the negative effect of bicycles at Wesbrook Village. Additionally, rather than frequency, investigating ridership counts could be a better measure for the transit_index variable.connection at UBC. This result concurs with existing literature which shows a positive relationship between bike share and transit [3][5][7][14]. However, while the highest quartile of the tran-sit_index variable saw the highest effect, the second and third quartile saw positive effects that were not sig-nificantly different. Mapping all four quartiles (Figure 10) clarified that the second and third quartiles of tran-sit_index appeared at places close to high-frequency transit, but not immediately adjacent. This result likely indicates that bike share is most effective as a last mile transit connection when it is available directly beside transit stops. Additionally, the negative effect of high speed roads indicates frequent transit on traffic calmed roads may further improve bike share as a last mile con-nection. By assessing the effect of transit, along with other factors, on bike share demand, his study improves the understanding of the HOPR network and could further advise future planning decisions. Given the unique lo-cation and geography of UBC, this study could also help inform FFBS planning in greater Vancouver, as well as other universities.111. Aalen, O.O. (1978). Nonparametric inference for a family of counting processes, Annals of Statistics 6, 701–7262. 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Origin and destination forecasting on dockless shared bicycle in a hybrid deep-learning algo-rithms. Multimedia Tools and Applications, 79(7), 5269–5280. https://doi.org/10.1007/s11042-018-6374-x7. Martens, K. (2007). Promoting bike-and-ride: The Dutch ex-perience. Transportation Research Part A: Policy and Practice, 41(4), 326–338. https://doi.org/10.1016/j.tra.2006.09.0108. Médard de Chardon, C., Caruso, G., & Thomas, I. (2016). Bike-share rebalancing strategies, patterns, and purpose. Journal of Transport Geography, 55, 22–39. https://doi.org/10.1016/j.jtrangeo.2016.07.0039. NelsonAalenEstimator.pdf. (n.d.). Retrieved August 8, 2020, from http://www.medicine.mcgill.ca/epidemiology/hanley/c609/Material/NelsonAalenEstimator.pdf10. Pal, A., & Zhang, Y. (2017). Free-floating bike sharing: Solv-ing real-life large-scale static rebalancing problems. Transpor-tation Research Part C: Emerging Technologies, 80, 92–116. https://doi.org/10.1016/j.trc.2017.03.01611. 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Comparative Analysis of User Behavior of Dock-Based vs. Dockless Bikeshare and Scootershare in Washington, D.C. 23.References 16. Zhang, Y., & Zhang, Y. (2018). Associations between Pub-lic Transit Usage and Bikesharing Behaviors in The United States. Sustainability, 10(6), 1868. https://doi.org/10.3390/su10061868

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