Station-Status Evidence for Rebalancing Performance: Spatiotemporal Empty–Full Outages in a Large U.S. Docked Bikeshare System

Abstract

This article argues that docked bikeshare rebalancing should be evaluated from repeated station-status time series rather than from completed trip logs, fleet totals, or monthly counts of bicycles moved. Its central position is that empty and full station states reveal user-facing service failures, censored demand, spatial substitution limits, and recovery dynamics that aggregate operating metrics cannot observe. Using Citi Bike as the motivating case, the article develops a reproducible audit logic based on GBFS station-status fields, distinguishing physical inventory from operational permission to rent or return. It defines empty, full, renting-disabled, returning-disabled, near-outage, and outage-episode states; specifies snapshot cadence, episode construction, duration thresholds, missing-data treatment, and recovery-stability rules; and proposes spatially conditioned measures such as nearest-station co-outage and local bike/dock buffers.

The article’s key finding is methodological rather than a newly estimated outage rate: existing optimization, routing, stochastic-inventory, and forecasting studies show how rebalancing can be planned, but they do not by themselves establish whether bikes and docks were actually available at the stations, times, and neighborhoods where users needed them. Trip logs are especially inadequate because empty stations censor rentals and full stations censor returns. The article also rejects naïve station-by-station outage counting, accepting the counterargument that dense networks, clusters, and Bike Angels incentives can mitigate isolated failures. Its response is to make substitution, time of day, recovery, operational flags, and incentive context part of the audit rather than reasons to abandon status data. The contribution is a public, falsifiable measurement framework for judging rebalancing by realized access to usable bikes and docks, while acknowledging uncertainty about causal attribution and the limits of live-feed archives.

Introduction

Docked bikeshare rebalancing is an inventory-control problem with a public-service consequence: when a station has no rentable bicycles, the system has failed a would-be rider; when it has no open docks, it has failed a would-be return. In a network at Citi Bike’s scale, these failures cannot be treated as marginal noise. Recent operating reports record millions of monthly trips, thousands of active stations, fleets above 34,000 bicycles, and tens of thousands of monthly rebalancing actions [1], [2]. Yet those same systemwide totals do not say whether bikes and docks were available in the neighborhoods and time periods where users needed them. The central claim of this study is therefore methodological and empirical: rebalancing performance in large docked bikeshare systems should be evaluated from station-status time series rather than trip logs or systemwide operating totals, because empty and full states reveal censored demand, spatial substitution limits, and operational failures that aggregate metrics obscure .

Reporting month	Trips	Average rides/day	Active stations	Average fleet	Reported rebalanced bicycles	Average rebalancing actions/day
April 2026	3,942,643	131,421	2,352	34,787	74,753	2,491
June 2025	4,856,367	161,879	2,246	37,287	98,810	3,293

Table 1: Systemwide Citi Bike operating totals that establish operational scale but not the spatial or temporal distribution of empty/full outages. Sources: April 2026 and June 2025 monthly operating reports [1], [2].

The data architecture for a status-based approach already exists. The General Bikeshare Feed Specification station_status.json defines one real-time record per station, including station_id , num_bikes_available , num_docks_available , and flags such as is_installed , is_renting , and is_returning [3]. That distinction matters: a physically empty station, a station not permitted to rent, a physically full station, and a station not permitted to accept returns are not the same operational state [3]. Citi Bike’s public GBFS feed is identified in the Mobility Database, including station status and related feed features [4], and NYC Open Data points users to the live station-status endpoint while also making clear that the municipal listing is a pointer rather than a historical station-status archive [5]. Thus, the empirical object required for a rebalancing-performance audit is public in real time, but it must be sampled, archived, and interpreted as a time series rather than read off from trip logs or monthly reports.

Prior research has made substantial progress on rebalancing models, fleet management, and demand prediction. Nair and Miller-Hooks formulated shared-vehicle redistribution as a stochastic mixed-integer program with joint chance constraints, explicitly treating asymmetric station-to-station demand as probabilistic rather than deterministic [6]. O’Mahony and Shmoys framed Citi Bike rebalancing as an optimization problem created by asymmetric demand, distinguished rush-hour and overnight balancing, and reported tools developed with and used by the operator [7]. Schuijbroek, Hampshire, and van Hoeve integrated service-level requirements with vehicle routing through a cluster-first, route-second heuristic evaluated on real U.S. bikeshare data [8]. Chiariotti et al. modeled Citi Bike station occupancy as a time-varying birth–death process and evaluated dynamic rebalancing through time out of service, rebalancing operations, and truck distance [9]. More recently, Liang et al. argued that inventory targets and intervals better match operator practice than classical unmet-demand objectives, reporting reductions in unmet demand in simulation experiments [10]. This work establishes that rebalancing is not merely a dispatch problem; it is a coupled forecasting, inventory, routing, and service-level problem.

Forecasting studies reinforce the same point but also expose the limits of trip-only evidence. Lin, He, and Peeta used graph convolutional neural networks to model heterogeneous station correlations in Citi Bike demand [11], while Ashqar et al. showed that short-horizon bike-availability prediction can benefit from current and neighboring-station inventories [12]. Cantelmo, Kucharski, and Antoniou used spatial station clustering, movement vectors, and weather variables to forecast New York City bikeshare demand at a lower dimensionality [13]. These methods are valuable, but their performance metrics are not themselves service-performance audits. A low prediction error in observed trips or inventories does not directly answer whether a station, its nearest alternatives, or an entire neighborhood endured an empty or full episode long enough to constitute a user-facing outage.

The literature also warns that observed trips are a censored sample of demand. Chiariotti et al. state that trip records are a lower bound because empty stations censor rentals and full stations censor returns [9]. Liu and Pelechrinis develop this concern into an excess-demand framework, identifying “pulses” in availability curves where latent demand appears only when a station briefly moves from zero availability to nonzero availability and is quickly depleted again [14]. The implication for rebalancing assessment is direct: a station with few recorded failed transactions may still be failing users if the failures occur before a trip can be registered. Status data do not solve all demand-identification problems, but they observe the boundary condition that trip data miss.

Gap. Existing scholarship establishes sophisticated optimization, forecasting, and fleet-management methods for bikeshare rebalancing, and public operating reports document ridership, fleet size, station counts, and rebalanced-bike totals [15]–[2], [7]–[10], [13]–[12]. What remains under-established is how station-level real-time status data can be used to measure rebalancing performance across neighborhoods, times of day, and adjacent-station contexts in a way that distinguishes operational outages from merely high demand. The New York City Comptroller’s 2023 analysis shows the policy stakes: using real-time Citi Bike data, it identified 11,600 instances in which a station and its nearest station were empty or full beyond contractual thresholds, with outages averaging more than 4.5 hours off peak and more than 2 hours at peak [16]. Yet the broader research literature still leans heavily on trip logs, simulations, aggregate reports, or evidence from other systems rather than a reproducible station-status-based audit design for a major U.S. network [5], [15], [17], [18].

A serious status-based audit must also answer a strong counterargument: station-level empty/full counts may exaggerate user harm in dense networks because nearby stations can substitute. Zhang, Chen, and Zhong make this case explicitly for Hangzhou, showing that spatial filtering and sub-nearest-neighbor analysis can sharply reduce the number of stations classified as problematic [19]. Cluster-level forecasting similarly assumes that nearby stations may self-equilibrate from the user’s perspective [13]. Citi Bike’s Bike Angels program adds a second complication: users themselves are incentivized to move bikes from crowded stations to stations low on bikes, with map scores updating every 15 minutes [20]. These objections do not defeat status-based measurement; they define its minimum standard. The relevant unit is not an isolated station-minute but an outage episode situated in time, operational status, neighborhood context, and nearby-station availability.

This article advances that position by developing the study in seven steps. “From Trip-Based Rebalancing Models to Status-Based Performance Measurement” situates the argument against optimization and forecasting work. “Data Architecture and Operational Definitions of Empty, Full, and Outage States” formalizes how GBFS status fields distinguish availability, installation, renting, and returning states [3]. “Study Design” defines spatiotemporal sampling, episode construction, and rebalancing metrics. “Spatial Heterogeneity” explains why systemwide totals cannot represent neighborhood performance. “Temporal Dynamics” examines peak-period imbalance, daytime rebalancing, and recovery, including evidence that rebalancing is not only overnight [17]. “Counterarguments” tests spatial substitution, cluster models, and incentive-based rebalancing. “Validity, Uncertainty, and Reproducibility” states what status data can infer, what remains censored, and how a station-status performance audit can be replicated without pretending that a feed snapshot is a complete model of demand.

From Trip-Based Rebalancing Models to Status-Based Performance Measurement

The dominant research tradition has treated bikeshare rebalancing as a decision problem: where should scarce bicycles, docks, and redistribution vehicles be positioned so that future demand can be served at minimum operational cost? That framing is indispensable, but it is not the same as performance measurement. O’Mahony and Shmoys’ Citi Bike work is exemplary because it identifies asymmetric demand as the source of inventory imbalance, distinguishes rush-hour balancing from overnight redistribution, and reports that its optimization tools were used in daily practice by NYC Bike Share LLC [7]. Yet the object optimized in such work is not necessarily the object experienced by users: a trip record exists only when a rental and return both succeed, whereas a station-status record can expose the periods in which trips could not occur because no bicycle or dock was available [9], [14].

This distinction matters because observed trips are not an unbiased sample of total demand. Chiariotti et al. explicitly warn, in their dynamic rebalancing study using historical Citi Bike data, that Citi Bike trips provide only a lower bound on demand because empty stations censor rentals and full stations censor returns [9]. Liu and Pelechrinis make the same problem the center of their excess-demand model: trip logs capture observed demand, but empty stations create unobserved failed rental demand and full stations create unobserved failed return demand [14]. The methodological position taken here follows directly from that evidence: a rebalancing audit that begins from trips alone is already conditioned on the system having worked, while a station-status audit begins from the times and places where it may not have worked.

Modeling strand	Primary contribution established in prior work	Why it remains insufficient for status-based performance assessment
Operational optimization for Citi Bike	Formulates asymmetric-demand rebalancing and distinguishes peak from overnight redistribution; tools were reported in daily operator use [7].	Shows how to plan rebalancing, but does not by itself measure realized empty/full outage exposure from live station states.
Stochastic fleet management	Uses joint chance constraints to find least-cost redistribution plans satisfying a target proportion of near-term demand scenarios [6].	Represents inventory risk probabilistically, but performance still must be validated against observed station-status failures.
Routing and service-level integration	Jointly determines station service-level requirements and vehicle routes through a cluster-first, route-second heuristic [8].	Connects service levels to routes, but does not replace empirical measurement of when stations actually lose renting or returning capability.
Dynamic survival-time rebalancing	Models station occupancy as a time-varying birth–death process and evaluates out-of-service time, rebalancing operations, and truck distance [9].	Moves closer to status performance, while also acknowledging that trip data understate demand when stations are empty or full [9].
Excess-demand prediction	Detects latent demand through “excess demand pulses” in station availability curves and improves prediction during excess-demand periods [14].	Demonstrates why availability curves are evidence, not merely inputs, for evaluating rebalancing failures.

The strongest defense of trip-based and model-based approaches is that rebalancing is fundamentally prospective. Operators cannot wait for every station to fail before moving bikes; they need forecasts, inventory targets, and routing policies. Nair and Miller-Hooks’ stochastic mixed-integer formulation addresses exactly this need by allowing redistribution plans to satisfy a target proportion of near-term demand scenarios under asymmetric station flows [6]. Schuijbroek et al. likewise integrate station service-level requirements with vehicle-routing decisions, showing that service feasibility and routing cost should be modeled together rather than sequentially [8]. Liang et al. further strengthen the operator-oriented case by arguing that target-inventory and inventory-interval objectives better reflect practice than classical unmet-demand objectives, and by reporting unmet-demand reductions of up to 34% in computational experiments using synthetic and real-world data with weather-dependent prediction and reoptimization [10].

The response is not to reject these models, but to insist on a different evidentiary role for them. Forecasting and routing models are instruments for intervention; station-status histories are instruments for accountability. If an algorithm predicts that a station should remain within an acceptable inventory interval, the empirical question is whether the station in fact retained rentable bicycles and returnable docks during the relevant period. If a routing model minimizes expected unmet demand, the empirical question is whether empty and full episodes were shortened, displaced, or concentrated in particular neighborhoods. This paragraph states the article’s reasoning: optimization outputs should be treated as hypotheses about service performance, not as substitutes for measuring realized service states.

Forecasting studies reinforce the same point. Cantelmo et al. develop a low-dimensional demand-forecasting approach for New York City bikeshare using spatial clustering, movement vectors, and weather variables, synthesizing more than 17 million 2018 Citi Bike trips into daily and zonal flows [13]. Lin et al. model station-level hourly demand with graph convolutional neural networks using a Citi Bike dataset of 272 stations and more than 28 million transactions from 2013–2016, showing that learned station correlations can outperform graph definitions based only on distance, demand, trip duration, or demand correlation [11]. Ashqar et al. model short-horizon bike availability with current inventory, neighboring inventory, temporal variables, and weather, reporting best performance for a 15-minute horizon and a Random Forest mean absolute error of 0.37 bikes per station in the San Francisco Bay Area system [12]. These studies show that station interactions, weather, temporal structure, and neighboring inventories can improve prediction [13]–[12]. They do not, however, eliminate the need to observe actual empty and full states, because prediction error at precisely the zero-bike or zero-dock boundary is the error that becomes a user-facing failure.

A second counterargument is spatial: station-level empty/full counts may exaggerate service failure in dense networks if nearby stations can substitute for the failed station. Zhang et al. make this objection forcefully in the Hangzhou public bicycle system, arguing that nearby stations within walking distance can substitute for an empty or full station and that spatial filtering reduced the number of problematic stations requiring reallocation by about 92.81% [19]. Cantelmo et al. offer a related modeling premise when they use clustered station movements, since cluster-level forecasting assumes that users may find another available bike within a reasonably defined cluster [13]. This is a serious objection to naïve station-independent outage counting, and this study accepts it as a design constraint rather than dismissing it.

But spatial substitution is a reason to enrich station-status measurement, not to abandon it. The Comptroller’s 2023 Citi Bike analysis used real-time usage data and counted cases where a station was empty or full and the nearest station was also empty or full beyond contractual thresholds, finding 11,600 such instances in June–July 2023, with off-peak outages averaging more than 4.5 hours and peak outages averaging more than 2 hours [16]. That evidence shows why adjacent-station context is essential: a single empty station may be tolerable if the next station has bikes, but a spatially coupled empty condition is a different service event [16], [19]. The present article therefore positions station-status time series not as crude station-by-station tallies, but as the empirical substrate from which spatially conditioned outage episodes can be constructed.

The literature also shows that rebalancing is not simply an overnight reset problem. O’Mahony and Shmoys distinguish peak rush-hour balancing from overnight redistribution in Citi Bike operations [7]. de Chardon et al. , using fine-scale station data and operator interviews across nine systems, report that stations near transit hubs receive disproportionate rebalancing relative to trips and that rebalancing often responds to morning and afternoon demand exceeding dock capacities [21]. Luo et al. directly address the lack of public operational rebalancing data by inferring rebalancing activities from discrepancies between trip and station-status data at 10-minute intervals; across Chicago, Boston, and Los Angeles in 2018, they find that most rebalancing occurred during daytime, challenging the common assumption that redistribution is primarily overnight [17]. These findings justify a temporal performance design that asks not only whether outages occur, but whether they are recovered during the operating day.

Finally, system scale and spatial heterogeneity make aggregate trip or rebalancing totals particularly weak proxies for service quality. Gervini and Khanal’s Divvy analysis reports 3,068,211 trips across 458 active stations and 244 daily replications, with annual station trips ranging from 29 at one South Side station to 85,314 at Navy Pier [22]. Citi Bike operating reports provide valuable transparency about monthly ridership, fleet size, station counts, and rebalanced bicycles, including 98,810 rebalanced bicycles in June 2025 and 74,753 in April 2026 [1], [2]. Yet those totals cannot identify whether rebalancing actions reduced outage exposure at the stations and times where latent demand was highest. That is the gap this study addresses: it moves from modeling how rebalancing could be optimized, and from reporting how much rebalancing occurred, to measuring where and when the docked system actually lost the capacity to rent or return.

Data Architecture and Operational Definitions of Empty, Full, and Outage States

The data architecture for this study begins from a deliberately narrow object: the GBFS station_status.json record observed repeatedly over time. That choice is not incidental. The GBFS definition specifies one status record per station and includes, among other fields, station_id , num_bikes_available , num_docks_available , is_installed , is_renting , and is_returning [3]. These fields allow a station-time panel to distinguish two conditions that trip logs tend to collapse: the physical inventory state of a station and the operator’s permission state for rentals and returns. A station with zero available bicycles is physically unable to originate a conventional docked trip; a station with is_renting = 0 is administratively or operationally unable to originate one even if bicycles are physically present. The same distinction holds for returns: zero open docks and is_returning = 0 are not equivalent states, although both may frustrate a rider attempting to end a trip. This distinction is central to the article’s thesis because a rebalancing audit should not treat all missing trips as demand variation; some missing trips are produced by observable station-status failures.

The public data infrastructure is adequate for this architecture, but not sufficient by itself for retrospective analysis. The Mobility Database identifies Citi Bike’s GBFS auto-discovery URL and records Station Status among the available GBFS features for the lyft_nyc system [4]. NYC Open Data likewise points users to Citi Bike system data and gives the live station-status endpoint as https://gbfs.citibikenyc.com/gbfs/en/station_status.json [5]. These sources validate that real-time station availability is part of the public-facing data environment. They do not, however, constitute a historical archive of station states: the NYC listing identifies the live endpoint but does not itself provide a station-status history [5]. Consequently, the empirical unit in this study is not a monthly report row or a trip transaction; it is a repeatedly sampled station-status observation, archived by the researcher or obtained from an equivalent historical feed capture. That requirement is a methodological burden, but it is also the condition for measuring outages rather than merely inferring them from completed trips.

Analytic state	GBFS status condition used in this study	Interpretation for rebalancing performance
Installed and analyzable	is_installed = 1	The station is part of the operational station-status panel; non-installed records are excluded from empty/full performance denominators. This follows from GBFS separating installation state from inventory fields [3].
Rentable and returnable	is_renting = 1 and is_returning = 1	The station is operationally open in both directions; empty and full states can be interpreted as inventory failures rather than permission-disabled states [3].
Empty	num_bikes_available = 0 , with is_installed = 1 and is_renting = 1	No rentable bicycle is available at an otherwise renting-enabled station; this is a candidate failed-origin state.
Full	num_docks_available = 0 , with is_installed = 1 and is_returning = 1	No dock is available at an otherwise return-enabled station; this is a candidate failed-destination state.
Renting-disabled	is_installed = 1 and is_renting = 0	The station cannot be treated as simply “empty” or “not empty”; rental permission is disabled independently of the physical bicycle count [3].
Returning-disabled	is_installed = 1 and is_returning = 0	The station cannot be treated as simply “full” or “not full”; return permission is disabled independently of the physical dock count [3].
Near-empty / near-full	num_bikes_available ≤ τ_b or num_docks_available ≤ τ_d , where thresholds are researcher-specified sensitivity parameters	A warning state preceding complete outage. The thresholds are not asserted by GBFS; they are author-defined parameters for robustness analysis.

The table formalizes a conservative rule: empty and full states are counted as inventory outages only when the relevant transaction direction is operationally permitted. This rule is stricter than a naïve count of zero bicycles or zero docks, and it is necessary because GBFS explicitly distinguishes inventory quantities from operational flags [3]. It also avoids a common interpretive error in status-based work: treating a disabled station as evidence of demand imbalance. A station that is not renting may have bicycles, and a station that is not returning may have docks; in both cases, the observed barrier is not simply that rebalancing failed to place the right number of bicycles or docks. The article therefore separates inventory outages from permission outages . The former are the primary evidence for rebalancing performance; the latter are retained as service disruptions but not attributed to vehicle redistribution without additional operational evidence. This attribution rule is the author’s reasoning, grounded in the GBFS field semantics rather than in a claim that the feed reveals the operator’s internal cause codes.

For each archived timestamp, the transformation produces a station-time panel keyed by station_id and observation time. The core variables are the two physical counts, the three operational flags, and derived categorical states. Because Citi Bike’s public feed infrastructure is live rather than archival, reproducibility requires recording the feed retrieval schedule, the GBFS discovery URL used, the station-status endpoint, and the timestamp attached to each pull. The Mobility Database entry is useful here because it identifies the Citi Bike GBFS discovery endpoint, system identifier, producer, license, and feed features [4]. The NYC Open Data page is useful as an independent municipal pointer to the live station-status JSON endpoint [5]. Neither source, however, resolves missed polls, API interruptions, or retroactive corrections. Those uncertainties must be represented in the panel as missing observations rather than silently interpolated service states.

The study defines an outage episode as a maximal consecutive run of station-time observations in which the same outage condition holds for the same station. An empty episode begins when an installed, renting-enabled station first reports num_bikes_available = 0 and ends when that station reports a positive number of available bicycles, becomes non-renting, becomes non-installed, or is unobserved long enough to break continuity. A full episode is defined symmetrically using num_docks_available = 0 and is_returning = 1 . The interruption rule is author-specified because the evidence digest establishes the GBFS status fields but not a universal archival sampling interval for this study [3], [5]. The purpose of the rule is to prevent a gap in data collection from being misclassified as either a long outage or a successful recovery.

This episode definition also aligns the measurement design with contractual and policy evidence without reducing the analysis to a contract-compliance exercise. Citi Bike’s April 2026 operating report states that SLA 11 defines a rebalancing-related station outage as an individual station outage lasting longer than four hours, with damages not accruing between 10:00 PM and 6:00 AM [1]. The June 2025 report repeats an SLA framework in which “Never-Die Stations” should not exceed 3% outage minutes from 6:00 AM to midnight and individual station outages should not continue longer than four hours [2]. The Comptroller’s 2023 analysis used real-time Citi Bike data and identified 11,600 instances in which stations were empty or full while the nearest station was also empty or full beyond contractual thresholds—more than two hours off-peak or more than one hour during peak periods [16]. These thresholds are not adopted uncritically as universal definitions of failure. Rather, they motivate multiple duration bands: short outages that reveal fragility, threshold-exceeding outages that resemble contractual failures, and prolonged outages that indicate sustained recovery failure. The empirical claim of this article depends on observing the full distribution, not only counting episodes that cross a legal threshold.

Near-empty and near-full states are included because complete outage is a lagging indicator. Dynamic rebalancing research has modeled station occupancy to estimate “survival time” before a station becomes empty or full, and it evaluates performance using time out of service, rebalancing operations, and truck distance [9]. That framing supports measuring precursor states, but the thresholds should not be presented as natural constants. In this study, τ_b and τ_d are sensitivity parameters: for example, a station may be considered near-empty when available bicycles fall at or below a low count, and near-full when open docks fall at or below a low count. The exact thresholds must be reported and varied. This is especially important because station sizes and local demand profiles differ; station-level heterogeneity is a persistent finding in bikeshare demand analysis, with one Chicago study reporting annual station trips ranging from 29 at one South Side station to 85,314 at Navy Pier [22]. The author’s methodological inference is that a single near-outage threshold may be transparent and useful, but it should not be mistaken for a station-neutral measure of user risk.

Monthly operating reports provide a necessary but coarser layer of evidence. Citi Bike’s operating-report archive is explicitly framed as transparency reporting to NYC DOT and includes systemwide rebalancing counts, ridership, fleet size, station counts, service levels, and maintenance metrics [15]. Individual reports show the scale of operations: April 2026 recorded 3,942,643 trips, 2,352 active stations, an average fleet of 34,787 bicycles, and 74,753 rebalanced bicycles [1]; June 2025 recorded 4,856,367 trips, 2,246 active stations, an average fleet of 37,287 bicycles, and 98,810 rebalanced bicycles [2]. These figures validate that rebalancing is a large, regular operational activity. They do not reveal whether particular neighborhoods experienced repeated empty mornings, whether full stations clustered near destinations, or whether outages persisted despite high systemwide rebalancing totals. That limitation is not a flaw in the reports; it is a mismatch between aggregate accountability data and station-level performance measurement.

A final definitional issue concerns censored demand. Trip logs record completed rentals and returns, but empty stations suppress would-be rentals and full stations suppress would-be returns. Prior work on dynamic rebalancing cautions that observed Citi Bike trips are a lower bound on true demand because empty and full stations censor rentals and returns [9]. Excess-demand prediction research makes the same point more directly: trip logs capture observed demand, while empty and full stations create unobserved failed rental and return demand [14]. The operational definitions above therefore treat empty and full episodes not merely as inventory states but as evidence of potential censored demand. This is an inference, not a direct count of abandoned trips. The station-status feed shows that the service opportunity was unavailable; it does not observe the rider who walked away. The distinction matters because the article’s measurement strategy is stronger than trip-count analysis but still bounded by what public status data can actually see.

Study Design: Spatiotemporal Sampling, Episode Construction, and Rebalancing Metrics

The empirical design follows from a simple constraint: Citi Bike’s public monthly reports can document the scale of operations, but they cannot identify which stations were unusable, when, or whether adjacent stations offered a practical substitute. The April 2026 report, for example, records 3,942,643 trips, 2,352 active stations, an average fleet of 34,787 bicycles, and 74,753 rebalanced bicycles, while the June 2025 report records 4,856,367 trips, 2,246 active stations, an average fleet of 37,287 bicycles, and 98,810 rebalanced bicycles [1], [2]. Those are necessary operating totals, but the unit of analysis for this study is instead the repeated station-status observation, because the GBFS station_status.json record exposes station-level bicycle availability, dock availability, and operational flags for renting and returning [3].

Sampling frame and snapshot cadence

The sampling frame is the set of docked Citi Bike stations appearing in the public GBFS feed during the observation window. The Mobility Database identifies Citi Bike’s GBFS auto-discovery feed and available station-status feature for the lyft_nyc system, while NYC Open Data separately points users to the live Citi Bike station_status.json endpoint [4], [5]. Because NYC Open Data functions as a municipal pointer rather than a historical archive of station-status observations, the study treats status history as something that must be collected prospectively or obtained from a separately archived feed rather than assumed to exist in the open-data portal [5].

Snapshots are collected at a fixed interval . This article’s design treats as an explicit measurement parameter rather than a background implementation detail. That choice is methodological reasoning by the author: if the interval is too coarse, short empty or full episodes will be missed or their recovery times will be poorly bounded. Existing rebalancing-inference work has used 10-minute station-status intervals to estimate rebalancing activities from discrepancies between trip and status data [17], and Citi Bike’s Bike Angels map scores are reported to update every 15 minutes [20]. Those two operational precedents support a snapshot interval at least as fine as 10–15 minutes for performance auditing, while acknowledging that finer sampling reduces but does not eliminate interval censoring.

Each observation is keyed by station_id , timestamp, num_bikes_available , num_docks_available , is_installed , is_renting , and is_returning . The distinction among physical availability and operational permission is essential: GBFS explicitly separates the inventory counts from flags indicating whether a station is installed, renting, or accepting returns [3]. The study therefore does not classify every zero-bike observation as an equivalent service failure. A zero-bike condition at an installed and renting station is treated as an empty-state exposure for would-be rentals; a returning-disabled condition is treated as a separate operational state, even if physical docks appear available. This distinction prevents the analysis from conflating inventory imbalance with station shutdown, maintenance, or other non-inventory restrictions.

Episode construction

The core object is a contiguous outage episode. For each station , the ordered status sequence is scanned for consecutive snapshots in the same failure state: empty, full, renting-disabled, returning-disabled, or combined states. An empty episode begins at the first sampled time when an installed station that is otherwise eligible to rent reports no available bicycles; it ends at the first subsequent sampled time when rentable bicycles are again available or the station leaves the operationally comparable state. A full episode is constructed analogously from zero available docks and return eligibility. This construction is aligned with the literature’s core warning that trip logs understate true demand, because empty stations censor failed rentals and full stations censor failed returns [9], [14].

The observed duration of an episode is computed from the first sampled outage timestamp to the first sampled recovery timestamp. Because the true transition may occur between snapshots, each duration is interval-censored. The study reports the observed duration and, where needed, a sensitivity band of plus or minus one sampling interval as author reasoning about measurement uncertainty. Formally, for an outage episode at station , with sampled onset and sampled recovery , the observed duration is:

  (1)

Episodes are then classified by temporal exposure. The operating reports define a rebalancing-related individual station outage as one lasting longer than four hours, with damages not accruing between 10:00 PM and 6:00 AM in the April 2026 report [1]. The June 2025 report also describes a service-level framework in which “Never-Die Stations” should not exceed 3% outage minutes from 6:00 AM to midnight and individual station outages should not continue longer than four hours [2]. The Comptroller’s oversight analysis used a different but related threshold: empty or full stations were counted when the nearest station was also empty or full for more than two hours off-peak or more than one hour during peak periods [16]. The study therefore reports multiple thresholded measures rather than pretending that a single duration cutoff exhausts the contractual and user-experience meanings of outage.

Metric	Unit of analysis	Construction	Interpretive role
Empty-episode duration	Station episode	Contiguous snapshots with no available rentable bicycles at an installed, renting station	Measures rental-side service failure and censored demand risk [3], [14]
Full-episode duration	Station episode	Contiguous snapshots with no available docks at a station accepting returns	Measures return-side service failure and censored demand risk [3], [14]
Time-to-recovery	Station episode	Elapsed time from sampled outage onset to sampled recovery	Operational analogue to survival time before or after an empty/full state [9]
Prolonged-outage flag	Station episode	Episode exceeds one-hour peak, two-hour off-peak, or four-hour individual-station thresholds, reported separately	Connects status evidence to oversight and service-level concepts [1], [2], [16]
Recurrence	Station-day or station-week	Count of distinct empty/full episodes per station in the period	Distinguishes chronic instability from isolated long failures; author-defined metric
Nearest-station co-outage	Station episode	Focal station is empty/full while the nearest station is simultaneously in the same failure class	Tests whether spatial substitution plausibly mitigates the outage [16], [19]
Peak/off-peak exposure	Episode-minute	Outage minutes intersected with contract-defined or reported service windows	Separates daytime user-facing failures from overnight redistribution windows [1], [2]

Spatial aggregation and substitution tests

Station-level episodes are aggregated to neighborhoods, service areas, or other predefined spatial units only after the episode construction is complete. This ordering is deliberate author reasoning: aggregating raw inventories first would erase precisely the empty and full events that expose localized service failure. The need for station-level treatment is supported by empirical evidence of extreme spatial heterogeneity in bikeshare use; in Chicago Divvy data, annual station trips ranged from 29 at one South Side station to 85,314 at Navy Pier [22]. Such heterogeneity makes systemwide averages a weak proxy for local performance.

At the same time, the design does not assume that every empty or full station is an independent user failure. A strong counterargument is that dense bikeshare networks permit spatial substitution: if a nearby station has bicycles or docks, the practical outage experienced by a user may be smaller than the focal-station status suggests. This concern is well founded. Work on Hangzhou argues that simple empty/full counting can overstate reallocation need when nearby stations are within walking range, and its spatial filtering approach sharply reduced the number of stations classified as problematic [19]. Cluster-level forecasting for New York City similarly rests on the assumption that nearby stations may partially self-equilibrate within a spatial cluster [13].

The response in this design is not to discard station outages but to condition them on adjacent-station context. For each focal episode, the study computes whether the nearest station, and optionally the nearest stations, were simultaneously empty or full. This mirrors the Comptroller’s analysis, which counted prolonged failures when the nearest station was also empty or full beyond contractual thresholds [16]. The resulting metric is stricter than a station-independent empty/full count but more empirically transparent than a cluster model that assumes substitutability without observing whether substitute inventory actually existed.

Rebalancing performance indicators

The principal performance indicators are outage burden, recurrence, recovery, and spatial co-failure. At station level, the study reports total empty minutes, total full minutes, number of episodes, median and upper-tail episode duration, and repeated same-day failures. At neighborhood level, it reports outage minutes per active station and the share of station-hours affected by empty, full, or operationally disabled states. At system level, it reports the distribution of outage exposure across places and periods rather than only a single aggregate total. These metrics are author-defined, but they follow the measurement logic of prior work that evaluates rebalancing by fraction of time out of service, number of rebalancing operations, and truck distance [9], while shifting the empirical emphasis toward publicly observable station-status performance.

The design also separates recovery from attribution. A station’s movement from empty to non-empty or full to non-full is evidence of recovery in the status record, but it is not by itself proof of truck-based rebalancing. Citi Bike reports that rebalancing uses box trucks, vans, valets, and Bike Angels incentives [1], [2], and Bike Angels explicitly rewards riders for moving bicycles from crowded stations toward stations needing bikes [20]. Without vehicle logs or individual trip linkage, a status recovery could be caused by organic user flows, incentive-mediated redistribution, staff rebalancing, maintenance action, or a combination of these mechanisms. The study therefore measures rebalancing performance as observed service restoration, not as a definitive census of operator vehicle activity. Where trip records are later joined, the discrepancy logic used by Luo et al. can support stronger inference about rebalancing actions, but the primary audit remains status-based [17].

This design makes the article’s empirical claim falsifiable. If outages are brief, spatially isolated, and concentrated in overnight windows, then systemwide rebalancing totals may be a reasonable performance proxy. If, however, prolonged empty/full episodes recur during user-facing hours, co-occur with nearest-station failures, and vary sharply by neighborhood, then station-status time series provide evidence that aggregate trip counts and reported rebalanced-bike totals cannot supply [1], [2], [16].

Spatial Heterogeneity and the Limits of Systemwide Rebalancing Totals

The spatial hypothesis tested here is stronger than the familiar claim that some stations are busier than others. The claim is that rebalancing performance itself is spatially heterogeneous: outage minutes should concentrate around particular station roles, neighborhood contexts, and adjacency structures, even in months when the operator reports high ridership, a large fleet, and substantial redistribution activity. This is the point at which station-status evidence becomes indispensable. A trip table can identify where observed trips occurred, and a monthly report can identify how many bicycles were moved, but neither can establish whether a specific station, or a cluster of nearby stations, was capable of serving a would-be rental or return at the moment of attempted use. That inference requires repeated observations of station availability and operational state, not merely completed transactions or systemwide totals [3], [15].

The scale of Citi Bike’s reported operations illustrates the problem. In April 2026, the system reported 3,942,643 trips, 2,352 active stations, an average fleet of 34,787 bicycles, and 74,753 rebalanced bicycles; in June 2025, it reported 4,856,367 trips, 2,246 active stations, an average fleet of 37,287 bicycles, and 98,810 rebalanced bicycles [1], [2]. These are large operational quantities, and a reasonable counterargument is that such totals already demonstrate substantial rebalancing effort. They do demonstrate effort. They do not demonstrate spatial sufficiency. A month with nearly 100,000 rebalanced bicycles could still leave particular neighborhoods with repeated empty-station episodes in the morning, repeated full-station episodes in the evening, or adjacent-station failures that make nominal station density irrelevant. That conclusion is author reasoning, but it follows from the mismatch between the spatially aggregated reporting unit in the monthly reports and the station-level state variables defined in GBFS station status [3], [1], [2].

Reported operating quantity	April 2026	June 2025	Why the quantity is insufficient for spatial performance assessment
Trips	3,942,643	4,856,367	Completed trips exclude rentals suppressed by empty stations and returns suppressed by full stations, so high trip volume can coexist with censored demand [9], [14].
Active stations	2,352	2,246	Station count records network scale but not whether individual stations were empty, full, renting-disabled, or returning-disabled at specific times [3], [1], [2].
Average fleet	34,787	37,287	Fleet size is a system inventory measure; it does not identify where bicycles were unavailable or where docks were unavailable [1], [2].
Reported rebalanced bicycles	74,753	98,810	Rebalancing totals measure aggregate intervention volume but not the distribution of intervention benefits across stations, neighborhoods, or adjacent-station contexts [1], [2].
Average rebalancing actions per active station per day	Approximately 1.06	Approximately 1.47	Author calculation from reported active stations and average daily rebalancing actions; the average is not evidence that each station received service because rebalancing can be spatially concentrated.

Prior empirical work gives a strong reason to expect concentration rather than spatial uniformity. Gervini and Khanal’s analysis of Chicago Divvy trips reported extreme station-level heterogeneity: across 458 active stations and 3,068,211 trips, annual station trip counts ranged from 29 at one South Side station to 85,314 at Navy Pier [22]. That evidence is not from Citi Bike, and it measures checkouts rather than status outages, so it should not be imported as a numerical estimate for New York. Its relevance is structural: a large docked network can contain stations whose demand processes differ by orders of magnitude, making systemwide averages a poor proxy for station-level service reliability [22]. If a similar heterogeneity exists in Citi Bike’s status time series, then a single rebalanced-bicycles total cannot distinguish between a system that broadly prevents outages and a system that repeatedly rescues a small set of high-pressure stations while leaving other places unreliable. That last comparison is author reasoning, to be tested with the status episodes defined in this study.

Station role matters as well as station volume. De Chardon, Caruso, and Thomas found, across nine bike-share systems, that stations adjacent to transit hubs received disproportionate rebalancing relative to trips and that rebalancing often responded to morning and afternoon demand exceeding dock capacity rather than only to slow inventory accumulation [21]. This finding complicates a simple fairness interpretation of rebalancing concentration. Concentration near transit hubs may be operationally rational if those stations experience sharp directional surges and if a single empty or full transit-adjacent station blocks many potential multimodal trips [21]. Yet the same evidence also warns against treating rebalancing counts as a neutral measure of systemwide performance. If rebalancing is drawn toward stations whose role in the network is unusually intense, then other stations may receive less corrective capacity even when their users face recurring access failures. The empirical question for this study is therefore not whether concentration exists, but whether concentration aligns with outage burden, station role, and local substitute availability.

The status-based design is also necessary because observed trips are not observed demand. Chiariotti et al. explicitly caution that Citi Bike trips are a lower bound on true demand because empty stations censor rentals and full stations censor returns [9]. Liu and Pelechrinis make the same point operationally: trip logs capture only observed demand, while empty stations create unobserved failed rental demand and full stations create unobserved failed return demand; their “excess demand pulse” method uses station-availability curves to infer latent demand that is invisible in completed trips [14]. For the present study, this means that a station with modest recorded trips cannot automatically be classified as low-need. It may be genuinely low-demand, or it may be repeatedly unavailable at the times when potential users arrive. Only station-status episodes can separate those interpretations.

The Comptroller’s 2023 audit of Citi Bike provides a public example of why geographically explicit outage measurement matters. Using real-time Citi Bike usage data from June and July 2023, the report identified 11,600 instances in which stations were empty or full and the nearest station was also empty or full beyond the contractual threshold: more than two hours off-peak or more than one hour during peak periods [16]. The same report found that these outages averaged more than 4.5 hours off-peak and more than 2 hours at peak, with potential penalties estimated at $812,000 [16]. Those figures do not substitute for the present study’s station-status reconstruction, because the audit’s published summary does not provide the full station-time panel needed for neighborhood-level modeling. They do, however, establish that station and nearest-station failures are not merely hypothetical edge cases in Citi Bike’s operating environment [16].

A strong counterargument is that station-level empty/full counts may exaggerate failures in dense networks, because users can walk to nearby stations. Zhang, Chen, and Zhong make this argument forcefully in their Hangzhou study: after applying a spatial filter and sub-nearest-neighbor analysis, they found that accounting for nearby substitutes reduced the number of problematic stations needing reallocation by about 92.81% [19]. This is not a minor objection. If adjacent stations provide reliable substitutes, then a single empty station may be an inconvenience rather than a system failure. The response in this study is not to reject spatial substitution, but to measure it directly. An empty station is treated differently when nearby stations have available bicycles than when the local station set is jointly empty; a full station is treated differently when nearby docks are open than when the adjacent return environment is also saturated. This response is author reasoning, but it is consistent with both the GBFS distinction between station availability and operational status and the Comptroller’s use of nearest-station failures in evaluating Citi Bike service [3], [16].

The same logic applies to clustering approaches. Cantelmo, Kucharski, and Antoniou argue that cluster-level demand forecasts can be effective for New York City bike sharing when stations are reasonably clustered, because nearby stations may partially self-equilibrate [13]. That is a plausible modeling simplification for forecasting flows, especially when the object is aggregate movement between zones rather than the experience of a rider facing a specific empty dock [13]. But a performance audit has a different burden of proof. It must show that substitution was actually available during outage episodes, not merely assume that spatial proximity creates functional redundancy. The study therefore treats clusters as empirical contexts to be tested with station-status data rather than as preemptive evidence that station-level outages are harmless.

Finally, spatial heterogeneity changes how reported rebalancing productivity should be interpreted. Luo et al. address the scarcity of public operational rebalancing data by inferring rebalancing from discrepancies between trip data and station-status data, and they find in Chicago, Boston, and Los Angeles that only 15–21% of stations were rebalanced on a typical day, about 4–5% were rebalanced more than once per day, and 23–37% of bikes were involved in rebalancing [17]. These estimates are not Citi Bike results, and they come from approximately 130 days of 2018 data in other U.S. systems [17]. Their relevance is methodological: rebalancing activity can involve a substantial share of bicycles while touching a minority of stations on a given day. That pattern is exactly why this section treats monthly rebalanced-bicycle totals as evidence of operational effort, not as evidence of spatially equitable or spatially sufficient service.

The resulting empirical standard is deliberately demanding. A month with millions of trips, tens of thousands of rebalanced bicycles, and a large fleet should not be called well rebalanced unless station-status histories show that empty and full episodes were rare, short, spatially containable, and recoverable within the local station network. Conversely, a station with repeated empty or full episodes should not be dismissed as merely “high demand” unless the status series shows rapid recovery or nearby substitute capacity. This is the core contribution of the spatial analysis: it converts rebalancing assessment from an accounting of bicycles moved into a place-specific measurement of access to bikes and docks.

Temporal Dynamics: Peak-Period Imbalance, Daytime Rebalancing, and Recovery

The temporal question is not simply whether a station ever becomes empty or full, but whether the outage appears during a period of high user consequence, whether it persists beyond a plausible operational response window, and whether recovery occurs through a pattern consistent with rebalancing rather than ordinary user churn. This distinction is central because trip logs record only completed rentals and returns; empty stations censor failed rental demand and full stations censor failed return demand [9], [14]. In this section, the episode-level unit of analysis is therefore temporal before it is spatial: each empty or full spell is treated as an interval with an onset time, duration, recovery time, and post-recovery stability condition, rather than as a count attached to a station-day. That choice is the author’s methodological reasoning, but it follows directly from prior evidence that station availability curves contain demand information not visible in trips alone [14].

Earlier Citi Bike optimization work already recognized that rebalancing is temporally differentiated. O’Mahony and Shmoys distinguish peak rush-hour balancing from overnight rebalancing in their Citi Bike formulations, framing the problem as one of restoring “requisite levels of bicycles” under asymmetric demand [7]. That distinction remains useful, but it is incomplete as a performance metric. Overnight balancing can make a system appear prepared at the start of the service day while failing to prevent mid-morning emptying at origin-heavy stations or afternoon filling at destination-heavy stations. Operator- and station-status-based evidence also weakens the assumption that the decisive rebalancing window is primarily overnight. De Chardon, Caruso, and Thomas found that rebalancing often responds to morning and afternoon demand that exceeds dock capacity, especially around transit-adjacent stations, and that operators balance trip maximization, profitability, and contractual service-level compliance rather than a single inventory objective [21]. Luo et al. later inferred rebalancing from discrepancies between trip and station-status data at 10-minute intervals and found that most rebalancing in Chicago, Boston, and Los Angeles occurred during daytime, directly challenging the common modeling convention that rebalancing is mainly an overnight activity [17].

Evidence	Temporal implication for this study	Why trip logs or monthly totals are insufficient
O’Mahony and Shmoys distinguish rush-hour and overnight balancing in Citi Bike operations [7].	Episodes should be stratified by peak and non-peak periods, not pooled into daily station summaries.	Completed trips cannot identify whether missing rentals or returns occurred during an empty or full spell [9], [14].
De Chardon et al. report morning and afternoon rebalancing pressure where demand exceeds station dock capacities [21].	Onset and recovery should be examined around commuting peaks and station-capacity constraints.	Systemwide trip counts do not reveal whether a station’s capacity was locally saturated [21].
Luo et al. infer that most rebalancing occurs during daytime, with only 15–21% of stations rebalanced on a typical day across three systems [17].	Recovery analysis should test for daytime interventions rather than assuming an overnight reset.	Public trip files alone do not disclose operator vehicle movements; station-status discrepancies are needed to infer them [17].
Citi Bike reported 74,753 rebalanced bicycles in April 2026, averaging 2,491 bike/dock actions per day [1], and 98,810 in June 2025, averaging 3,293 per day [2].	Daily action totals set the operational scale but not the timing or location of relief.	Monthly reports cannot identify which station episodes recovered, how quickly, or whether neighboring stations remained unusable [15]–[2].
Bike Angels map scores update every 15 minutes and reward trips that move bikes from crowded stations to stations low on bikes [20].	Short-window recovery after incentive updates is empirically plausible but causally ambiguous without incentive-state data.	A completed incentivized ride may appear as an ordinary trip unless linked to status and incentive signals [20].

The empirical expectation, stated as author reasoning, is that temporal imbalance will have at least three recurrent forms. The first is rapid peak depletion : a station enters an empty state during an outward-flow period and remains empty until either returns arrive or rebalancing supplies bikes. The second is peak-period dock saturation : a station becomes full during a convergent-flow period and remains unable to accept returns, potentially pushing riders to nearby stations. The third is evening accumulation with partial overnight reset : a station or cluster ends the day with inventories far from a target range and is restored before the next morning only if rebalancing capacity is sufficient. These are not asserted here as results; they are testable temporal signatures derived from the distinction between rush-hour and overnight balancing [7], the observed importance of morning and afternoon capacity pressure [21], and the evidence that much real-world rebalancing can occur during the day [17].

Recovery must be defined more strictly than a one-snapshot exit from zero bikes or zero docks. Liu and Pelechrinis show that “excess demand pulses” can occur when availability moves from zero to nonzero and is quickly consumed, revealing latent demand that was not captured in trip logs [14]. A station that receives one bicycle after a long empty spell and loses it immediately has not recovered in a service sense; it has merely exposed suppressed demand. Similarly, a full station that briefly gains a single dock and fills again within minutes may still be functioning as a return bottleneck. The recovery criterion used here is therefore episode-based: an outage ends only when the station returns to an operationally usable state and remains above the empty/full boundary for a minimum stability window. The exact stability window is an analytic parameter, not a fact established by the cited literature, but it is motivated by the finding that short-lived availability pulses contain information about unmet demand [14] and by dynamic rebalancing work that estimates station “survival time” before emptying or filling [9].

Contractual and reporting conventions provide a second temporal benchmark, though they should not be mistaken for a complete user-experience measure. Citi Bike’s April 2026 operating report defines a rebalancing-related station outage as an individual station outage lasting longer than 4 hours, with damages not accruing between 10:00 PM and 6:00 AM [1]. The June 2025 report repeats the framework in which “Never-Die Stations” should not exceed 3% outage minutes from 6:00 AM to midnight and individual station outages should not continue longer than 4 hours [2]. The Comptroller’s 2023 audit used a stricter adjacent-station service logic: it identified 11,600 instances in June–July 2023 in which a station and its nearest station were empty or full beyond the contractual threshold of more than two hours off-peak or more than one hour during peak periods; those outages averaged more than 4.5 hours off-peak and more than 2 hours at peak [16]. These thresholds are not interchangeable. The 4-hour station-outage rule captures prolonged operational failure; the peak/off-peak adjacent-station rule captures user-facing unavailability at a finer temporal and spatial resolution [1]–[16].

The strongest counterargument is that apparent daytime recovery need not indicate operator rebalancing. A station may recover because ordinary users return bikes, because riders divert from a full destination, or because Bike Angels incentives induce voluntary redistribution rather than truck-based intervention. This objection is correct as a causal warning. Citi Bike’s own materials state that rebalancing uses box trucks, vans, valets, and Bike Angels incentives, with Bike Angels points designed to move bikes from crowded stations to stations low on bikes [1], [2], [20]. A status time series alone can often identify the timing of recovery, but it cannot always distinguish among truck, valet, incentive, and spontaneous user-flow mechanisms. The appropriate response is not to abandon status-based measurement; it is to separate performance inference from causal attribution . If an empty station remains empty through the morning peak, the rider-facing failure is observable even if the reason for non-recovery is not. If it recovers sharply during the day and remains stable, that recovery is operationally meaningful even when the specific intervention channel is uncertain.

A second counterargument is that overnight reset may still be the main determinant of next-day performance: if stations begin the morning near target inventory, then daytime failures reflect extraordinary demand rather than poor rebalancing. This interpretation is plausible in systems where demand shocks overwhelm any feasible redistribution plan, and stochastic fleet-management models explicitly allow for demand scenarios in which partial redistribution is the least-cost response [6]. It is also consistent with recent optimization work arguing that inventory target or interval formulations create buffers against stochastic demand and can outperform classical unmet-demand objectives [10]. But the status-based answer is empirical: the study should test whether stations that enter the morning within a target band still experience repeated early failures, whether recoveries occur before or after the peak has passed, and whether evening states predict next-morning vulnerability. If outages recur at the same station-times despite reported systemwide rebalancing volumes, then the relevant evidence is not the existence of rebalancing activity but its temporal effectiveness.

The temporal analysis thus converts rebalancing performance from an aggregate activity count into a service-recovery problem. Monthly operating reports establish that Citi Bike performs rebalancing at large scale—2,491 average daily bike/dock actions in April 2026 and 3,293 in June 2025 [1], [2]. They do not establish whether those actions arrived before, during, or after the intervals when users faced empty or full stations. Station-status episodes supply that missing temporal evidence. They allow this study to ask whether peak-period imbalance is prevented, merely repaired after the fact, or left unresolved until the next operational cycle; and they make visible the censored demand pulses that trip-based models would otherwise treat as absence of demand rather than absence of service [9], [14].

Counterarguments: Spatial Substitution, Cluster Models, and User Incentive Rebalancing

The strongest counterargument to station-level outage measurement is that a docked bikeshare user does not necessarily experience an empty or full station as a failed trip. In a dense network, the user may walk to another nearby station; in a clustered forecasting model, the relevant service unit may be a neighborhood inventory pool rather than a single dock location. This objection deserves more than a footnote. Zhang, Chen, and Zhong explicitly challenge simple empty/full station counting in dense networks, arguing that nearby stations can substitute for one another within walking distance; their Hangzhou analysis used spatial filtering and sub-nearest-neighbor methods and reported that accounting for station layout reduced the number of problematic stations needing reallocation by about 92.81% [19]. Cantelmo, Kucharski, and Antoniou likewise provide a modeling rationale for aggregation: their New York City forecasting approach synthesized more than 17 million 2018 Citi Bike trips into daily and zonal movement vectors and argued that cluster-level forecasts can be more accurate when stations are reasonably clustered [13]. Ashqar et al. add an operational prediction argument, showing that neighboring-station inventory helped short-horizon bike-availability prediction in the San Francisco Bay Area system, with Random Forest reaching a reported MAE of 0.37 bikes per station and a best prediction horizon of 15 minutes [12].

Steelmaned, then, the critique is this: a station-status audit that treats every empty station-minute and every full station-minute as an independent service failure may overstate user harm, misclassify recoverable local imbalances as outages, and undervalue the resilience created by dense station placement, neighboring inventory, and user willingness to walk. This critique is especially serious for central business districts, transit-adjacent clusters, and tourist corridors, where stations may be close enough that a single failed dock does not exhaust local access. It also aligns with de Chardon, Caruso, and Thomas’s finding that operators do not rebalance merely to erase isolated station imbalances; they balance trips, profit, and contractual service-level compliance, with transit-hub stations receiving disproportionate rebalancing relative to trips [21].

The response is not to abandon station-status evidence. It is to stop using station-independent station-status evidence. The empirical unit should be an outage episode embedded in an adjacency context : a station is empty or full, but the severity of that state depends on whether nearby stations can absorb the rental or return demand. This study therefore treats spatial substitution as a testable condition rather than as an assumption. The distinction matters because the contractual and public-accountability evidence for Citi Bike already moves in this direction. The New York City Comptroller’s 2023 analysis did not merely count empty and full stations; it counted 11,600 instances in which a station was empty or full and the nearest station was also empty or full beyond the contractual threshold—more than two hours off-peak or more than one hour during peak periods [16]. Those co-failure episodes averaged more than 4.5 hours off-peak and more than 2 hours at peak, and the report estimated $812,000 in potential penalties [16]. In other words, the policy dispute itself is not “station outage versus no station outage”; it is whether station outage persists after plausible nearby substitution has been exhausted.

Counterargument	Evidence supporting the counterargument	Status-based response used in this study
Nearby stations may substitute for an empty or full station.	Zhang et al. found that spatial filtering in Hangzhou reduced problematic stations needing reallocation by about 92.81%, showing that naive station counts can exaggerate imbalance in dense networks [19].	Measure nearest-station co-failure and local availability buffers, rather than treating each station-minute as independent.
Cluster-level forecasting may outperform station-by-station reasoning.	Cantelmo et al. used spatial clustering, movement vectors, and weather variables for New York City bike-share forecasting and argued that clusters can be more accurate when stations are reasonably clustered [13].	Evaluate whether clusters actually contain available bikes or docks during outage episodes, using GBFS status fields rather than assuming self-equilibration.
Neighboring inventory improves short-horizon prediction.	Ashqar et al. used neighboring-station inventory and weather features and reported a 15-minute best prediction horizon, with Random Forest MAE of 0.37 bikes per station [12].	Use neighboring inventory as an explanatory variable for recovery and persistence, not as a reason to ignore station-level outages.
User incentives may perform part of the rebalancing task.	Citi Bike describes Bike Angels as rewarding riders for moving bikes from crowded stations to stations low on bikes, with map scores updating every 15 minutes [20].	Compare incentive cadence and direction with status-snapshot dynamics to assess whether incentives precede recovery or merely coincide with persistent imbalance.

Formally, the adjacency-sensitive metric can be stated as a local buffer rather than a binary station flag. Let denote stations within a specified walking radius of station . For rentals, the local bike buffer at time is:

(1)

For returns, the analogous dock buffer is:

(2)

These equations are this article’s proposed measurement logic, not a published formula. They follow directly from the GBFS distinction between physical inventory— num_bikes_available and num_docks_available —and operational permission to rent or return, represented by fields such as is_renting and is_returning [3]. The point is that a nearby station with bicycles but renting disabled is not a substitute for a rider seeking a bike, and a nearby station with open docks but returning disabled is not a substitute for a rider ending a trip. The substitution argument therefore strengthens the case for GBFS station-status analysis, because only status data expose the inventory and operational flags needed to distinguish apparent capacity from usable capacity [3].

This approach also clarifies how cluster models should be evaluated. Cantelmo et al.’s cluster-level New York City model is persuasive as a forecasting strategy because nearby stations can sometimes behave as a pooled service area [13]. But the empirical question for rebalancing performance is whether that pool remains usable during stress. A cluster with high total capacity may still generate user-facing failure if several adjacent stations are empty during the morning rental peak or full during the evening return peak. Conversely, a single empty station in a cluster with abundant nearby rentable bicycles may be a low-severity episode. The proposed audit therefore does not reject clustering; it asks clusters to prove their substitutability in observed status time series. This is a stronger evidentiary standard than inferring service from trips alone, because trip logs omit failed rental demand at empty stations and failed return demand at full stations, a censoring problem identified by both Chiariotti et al. and Liu and Pelechrinis [9], [14].

User-incentive rebalancing raises a second counterargument. If Bike Angels successfully moves bicycles from crowded stations to stations with low supply, then station outages may reflect short-lived imbalances already being corrected by distributed rider action rather than failures of operator rebalancing. Citi Bike describes Bike Angels precisely in these operational terms: riders earn points for qualifying trips that help redistribute bikes, while trips starting at stations needing bikes or ending at stations needing docking space do not earn points because they are less likely to help another rider [20]. The same source states that Bike Angels map scores update every 15 minutes [20]. Citi Bike’s operating reports also identify Bike Angels as one component of the rebalancing toolkit, alongside box trucks, vans, and valets, with incentives dependent on predicted need for docks and bikes [1], [2].

Here again, the implication is not that status-based outage measurement is obsolete. It is that incentives should be modeled as an observable operational mechanism. A 15-minute incentive-update cadence can be compared with station-status snapshots to test whether incentive signals appear before recovery, whether recovery occurs only after prolonged co-failure, or whether incentives are concentrated where outages are already visible. That comparison cannot be made from monthly totals of rebalanced bicycles alone, even when those totals are large: Citi Bike reported 74,753 rebalanced bicycles in April 2026 and 98,810 in June 2025, but those reports do not identify the station-level timing, adjacency context, or incentive contribution of each recovery [1], [2]. Status time series therefore provide the audit trail needed to distinguish three mechanisms that aggregate counts collapse: truck or valet intervention, user-incentivized redistribution, and passive demand reversal.

The position taken here is deliberately asymmetric. Spatial substitution, cluster forecasting, and Bike Angels incentives are valid objections to naive station-by-station counting; they are not valid objections to station-status performance measurement as such. A defensible audit should report empty and full episodes together with nearest-station co-failure, local bike and dock buffers, operational rent/return flags, recovery time, and incentive-update timing. That design gives the substitution critique its full force while preserving the central empirical claim of this study: rebalancing performance must be judged where users encounter the system, in the time-varying availability of usable bikes and docks, not only in observed trips or systemwide rebalancing totals.

Validity, Uncertainty, and Reproducibility of Status-Based Rebalancing Inference

A station-status audit is more defensible than a trip-log audit, but it is not self-validating. The method observes public system states, not the dispatcher’s intentions. GBFS station_status.json exposes per-station records such as station_id , num_bikes_available , num_docks_available , is_installed , is_renting , and is_returning , which makes it possible to distinguish physical inventory from operational permission to rent or return [3]. That distinction is the core validity advantage of the approach. It is also the source of several inferential hazards: an apparently empty station may be installed but not renting; an apparently full station may have docks physically present but not accepting returns; and a station can enter the feed, leave the feed, or change operational status during the observation window [3]. For that reason, the empirical object in this study is not simply “zero bikes” or “zero docks.” It is a time-stamped status tuple whose interpretation depends on inventory counts and operational flags read together.

The first threat is archival incompleteness. NYC Open Data points users to the live Citi Bike station-status endpoint, but the listing does not provide a historical station-status archive; histories must be scraped or obtained from separately archived feeds [5]. The Mobility Database likewise identifies Citi Bike’s GBFS auto-discovery and v2.3 feed URLs as live public feed infrastructure rather than as a complete retrospective archive [4]. Author’s reasoning: because the historical panel is produced by repeated observation of a live feed, missing snapshots cannot be treated as random noise by default. API interruptions, collector downtime, feed latency, and network failures can all create artificial gaps. The reproducible procedure is therefore to publish the snapshot schedule, retain raw response timestamps, report missing intervals by station and by hour, and exclude or censor outage episodes that cross unobserved gaps longer than the sampling tolerance.

Validity threat	Evidence basis	Risk for inference	Reproducibility rule used in this study
Live feed rather than public historical archive	NYC Open Data gives the live station_status.json endpoint but does not provide a historical status archive [5].	Outage duration can be overstated or understated if snapshots are missing.	Report scrape cadence, timestamp every snapshot, and mark episodes crossing unobserved intervals as censored.
Operational flags differ from inventory counts	GBFS separates num_bikes_available and num_docks_available from is_renting and is_returning [3].	A zero-inventory state and an operator-disabled state may have different service meanings.	Classify empty, full, renting-disabled, returning-disabled, and mixed states separately before aggregation.
Changing system boundary	Citi Bike reported 2,246 active stations in June 2025 and 2,352 active stations in April 2026 [2], [1].	Spatial comparisons can confound rebalancing performance with network expansion.	Use station-day denominators and explicitly track installed and active station sets.
Observed outages versus inferred rebalancing	Luo et al. infer rebalancing from discrepancies between trip and station-status data because public operational rebalancing records are limited [17].	A recovery from empty or full status may be caused by users, trucks, valets, incentives, maintenance, or station reopening.	Separate directly observed outage states from inferred intervention events; label the latter probabilistic.

The second threat is boundary instability. Citi Bike’s own reports show that the system is not a fixed experimental platform: June 2025 lists 2,246 active stations, whereas April 2026 lists 2,352 active stations [2], [1]. These reports also show large month-to-month operating scales, including 4,856,367 trips and 98,810 rebalanced bicycles in June 2025, and 3,942,643 trips and 74,753 rebalanced bicycles in April 2026 [2], [1]. Those figures are useful for scale, but they cannot identify whether a particular neighborhood’s outage rate changed because operations improved, stations were added, demand shifted, or the denominator changed. Author’s reasoning: the appropriate unit for longitudinal comparison is therefore the station-hour or station-day within an explicitly defined active station set, not the raw count of empty or full observations across the whole network.

The third threat concerns vehicle and dock heterogeneity. The Mobility Database records Citi Bike feed features including Station Status, Free Bike Status, System Regions, System Pricing Plans, System Alerts, GBFS Versions, and Vehicle Types [4]. This matters because the availability of “a bike” may not be equivalent across all users, trip purposes, or vehicle classes. Author’s reasoning: if a feed distinguishes vehicle types or if docks differ in charging, compatibility, or maintenance status, a simple station-level count can overstate practical availability for a subset of users. The conservative design choice is to define the primary outage metric using the public station-status variables that are consistently observable, while treating vehicle-type-specific availability as a secondary analysis only when the feed provides stable fields across the full observation period.

The fourth threat is the temptation to infer too much from recovery. If a station is empty at 08:10 and non-empty at 08:20, the status record directly supports only the claim that the public availability state changed between those observations. It does not by itself identify a truck visit, a valet action, a Bike Angels trip, a maintenance event, or ordinary user returns. Citi Bike’s operating reports state that rebalancing uses box trucks, vans, valets, and Bike Angels incentives, with incentives dependent on predicted needs for bikes and docks [1], [2]. Citi Bike’s Bike Angels documentation also states that scores update every 15 minutes and that points are awarded for moving bikes from crowded stations to stations low on bikes [20]. These facts make user-assisted rebalancing an operationally real mechanism, not a nuisance to be ignored. They also weaken any claim that every recovery from an outage is a staff-vehicle intervention.

Recent inference work is useful precisely because it draws this line more carefully. Luo et al. address the lack of public operational rebalancing data by estimating rebalancing activities from discrepancies between trip data and station-status data in 10-minute intervals [17]. Applied to roughly 130 days of 2018 data from Chicago, Boston, and Los Angeles, their method estimated average daily rebalancing activities of 172, 87, and 43, respectively, and found that only 15–21% of stations were rebalanced on a typical day [17]. They also report that most rebalancing occurred during daytime, challenging the common assumption that redistribution is primarily overnight [17]. This study adopts the same epistemic caution: empty/full episodes are directly observed; rebalancing actions are inferred only when status changes cannot be explained by recorded trips under the chosen accounting rules. Even then, the inference is about a likely inventory intervention, not about the operator’s route, objective function, or priority order.

The fifth threat is demand censoring. Trip logs undercount true demand when stations are empty or full, because failed rentals and failed returns do not appear as completed trips [9], [14]. Liu and Pelechrinis formalize this problem through “excess demand pulses” in station availability curves, where a transition from zero to nonzero availability is quickly consumed and thereby signals latent demand not visible in trips [14]. Chiariotti et al. make the same methodological warning in dynamic rebalancing work using Citi Bike data: observed trips are a lower bound on true demand because empty and full stations censor rentals and returns [9]. A status-based audit cannot fully recover every suppressed trip, but it does observe the censoring condition itself. That is the central reason to treat outages as performance evidence rather than merely as missing data around trip records.

The sixth threat is contractual and normative interpretation. Citi Bike reports define service-level concepts such as a rebalancing-related station outage lasting longer than four hours, with damages not accruing during specified overnight periods in April 2026 reporting, and “Never-Die Stations” not exceeding 3% outage minutes from 6:00 AM to midnight in June 2025 reporting [1], [2]. The Comptroller’s 2023 analysis used real-time Citi Bike data and identified 11,600 instances in which a station and its nearest station were both empty or both full beyond contractual thresholds, with average outage durations exceeding 4.5 hours off-peak and 2 hours at peak [16]. These examples show that outage thresholds are not purely academic constructs; they shape accountability. Author’s reasoning: the analysis should therefore report multiple thresholds—short operational failures, contract-like exceedances, and adjacency-adjusted exceedances—rather than selecting one cutoff that silently embeds a service standard.

The final validity claim is modest but strong. Station-status evidence does not reveal the complete control system behind Citi Bike. It does not expose private dispatch instructions, vehicle routes, maintenance queues, or the full utility function that trades off ridership, equity, labor, costs, and contractual penalties. Prior work on rebalancing already shows that operators balance several objectives rather than simply minimizing empty and full stations [21], and optimization studies demonstrate that target-inventory and interval-based objectives may better match practice than classical unmet-demand minimization [10]. The contribution of a status-based audit is narrower: it provides a reproducible public measurement layer for where and when the system was unable to rent or receive bikes, with operational flags preserved and uncertainty declared. That layer is indispensable because aggregate operating reports document the scale of effort, while station-status histories document the public consequences of whether that effort arrived in the right place at the right time [1], [2], [3].

Conclusion

This study has argued that docked bikeshare rebalancing cannot be evaluated adequately from completed trips, fleet totals, or monthly counts of bicycles moved. Those measures establish scale and effort—Citi Bike’s reports document millions of trips, more than two thousand active stations, fleets above 34,000 bicycles, and tens of thousands of monthly rebalanced bicycles [1], [2]—but they do not show whether a rider could find a bike or a dock at a particular station, time, and neighborhood. The methodological conclusion is therefore narrower and stronger than a general call for “more data”: rebalancing performance should be audited from repeated GBFS station-status observations because num_bikes_available , num_docks_available , is_renting , is_returning , and is_installed expose the operational states that trip logs and aggregate reports cannot observe [3].

The evidence reviewed in the article supports this thesis in three linked ways. First, prior rebalancing and demand studies show that observed trips are a censored record of demand: empty stations suppress rentals and full stations suppress returns, so completed trip logs are only a lower bound on potential use [9], [14]. Second, public reporting demonstrates that systemwide rebalancing activity is substantial but spatially and temporally opaque [1], [2]. Third, the Comptroller’s Citi Bike analysis shows that prolonged station and nearest-station co-outages are not merely theoretical; it identified 11,600 instances in which a station and its nearest station were empty or full beyond contractual thresholds, with long average durations in both peak and off-peak periods [16]. Taken together, these sources justify the article’s central empirical standard: a system should not be judged well rebalanced because many bicycles were moved, but because empty and full episodes are rare, short, recoverable, and locally substitutable in the station-status record.

The article has also rejected a simplistic version of status-based measurement. The strongest counterargument is persuasive: in dense networks, a single empty or full station may overstate user harm if nearby stations provide usable substitutes. Evidence from Hangzhou shows that spatial filtering can sharply reduce the number of stations classified as problematic [19], and cluster-level forecasting for New York rests on the plausible premise that nearby stations may sometimes function as a pooled service area [13]. Bike Angels adds another complication, because Citi Bike explicitly uses rider incentives, updated on a 15-minute score cadence, as part of its redistribution toolkit [20]. These objections do not weaken the case for status time series; they define the minimum credible audit design. The relevant unit is not an isolated station-minute. It is an outage episode interpreted with operational rent/return flags, nearest-station co-failure, local bike and dock buffers, time of day, recovery stability, and—where available—incentive context.

The study’s gap analysis therefore remains the basis for its contribution. Existing work has produced sophisticated optimization, routing, stochastic inventory, and forecasting models, including approaches that distinguish rush-hour and overnight balancing, integrate service levels with vehicle routing, infer rebalancing from trip-status discrepancies, and model short-horizon availability [7], [8]–[17], [13]–[12]. What that literature does not yet establish, for a major U.S. docked network, is a reproducible public performance audit that begins from station-status histories and measures where and when the system lost the capacity to rent or receive bicycles. This article supplies that audit logic: sample the live feed at a declared cadence, construct empty and full episodes only for installed and directionally enabled stations, treat missing snapshots as censoring rather than evidence, report multiple duration thresholds, and aggregate spatially only after station-level episodes have been defined.

The open problems are concrete. Future work should build historical station-status archives from live feeds such as Citi Bike’s public endpoint, since municipal listings point to real-time data but do not themselves provide complete retrospective panels [5]. It should test sensitivity to snapshot cadence, outage-duration thresholds, near-empty and near-full parameters, and recovery-stability windows. It should distinguish observed service restoration from causal attribution, because recovery may reflect trucks, valets, ordinary user flows, Bike Angels trips, maintenance, or station reopening; stronger attribution will require joining status series to trip records, incentive states, and, where available, operational logs [17], [20]. It should also account for changing station boundaries, vehicle-type heterogeneity, and neighborhood-level substitution without assuming that proximity automatically means usable capacity [3], [4], [1], [2]. The conclusion is consequently modest but firm: station-status data do not reveal the operator’s full control system, but they provide the most defensible public evidence of the user-facing consequences of rebalancing—whether bikes and docks were actually available where and when the system claimed to serve.

References