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A holistic approach for modeling and predicting bike demand
Abstract
Bike-sharing systems have enjoyed tremendous success in many major cities around the world today as a new means of urban public transportation offering a green and facile solution for daily commuters and tourists. One common problem featured in these systems is that the distribution of bikes among stations can be quite uneven, due to various factors including topography, location of dockings, hours of service, safety and security, weather, rush hours or even during the occurrence of major events around the city. Such imbalances often result in shortage of bikes or bike parking racks. An unbalanced bike system indicates an unreliable form of transportation and disappointed users. Current studies in the literature are limited as they are not designed to handle fluctuating, high or unpredictable demand during large city events that typically affect multiple stations and require real-time rebalancing, during the event, to ensure seamless operation. In this work we solve the bike rebalancing problem while considering fluctuating demand that leads to an imbalance between supply and demand. We present “SmartBIKER”, a holistic and cost-effective framework for bike sharing systems addressing both normal operation and operation during major city events. SmartBIKER models bike demand during both normal operation and major events, identifies bike stations with low or high demand using two different forecasting models and determines a relocation strategy that maximizes the utility of the stations while minimizing the relocation cost. Our experimental evaluation shows that our approach is practical, efficient and outperforms state-of-the-art relocation and prediction schemes.
... In the spatial dimension, bike-sharing demand between adjacent stations mutually influences each other, displaying similar user travel patterns. Similarly, stations within the same functional zone may also exhibit comparable user travel patterns [2]. In the temporal dimension, bike-sharing demand exhibits continuous features. ...
Accurate bike-sharing demand prediction is crucial for bike allocation rebalancing and station planning. In bike-sharing systems, the bike borrowing and returning behavior exhibit strong spatio-temporal characteristics. Meanwhile, the bike-sharing demand is affected by the arbitrariness of user behavior, which makes the distribution of bikes unbalanced. These bring great challenges to bike-sharing demand prediction. In this study, a usage pattern similarity-based dual-network for bike-sharing demand prediction, called FF-STGCN, is proposed. Inter-station flow features and similar usage pattern features are fully considered. The model includes three modules: multi-scale spatio-temporal feature fusion module, bike usage pattern similarity learning module, and bike-sharing demand prediction module. In particular, we design a multi-scale spatio-temporal feature fusion module to address limitations in multi-scale spatio-temporal accuracy. Then, a bike usage pattern similarity learning module is constructed to capture the underlying correlated features among stations. Finally, we employ a dual network structure to integrate inter-station flow features and similar usage pattern features in the bike-sharing demand prediction module to realize the final prediction. Experiments on the Citi Bike dataset have demonstrated the effectiveness of our proposed model. The ablation experiments further confirm the indispensability of each module in the proposed model.
... Nevertheless, their focus was to provide a visual tool for both system operators and users, rather than test the accuracy of the models. Tomaras et al. [37] have proposed a combination of a Gradient Boosted Regression Tree, and a Holtz's model to create a tool called SmartBIKER that assist system operators with rebalancing. The authors tested their proposal using New York data. ...
Public Bicycle Sharing Systems (BSS) have spread in many cities for the last decade. The need of analysis tools to predict the behavior or estimate balancing needs has fostered a wide set of approaches that consider many variables. Often, these approaches use a single scenario to evaluate their algorithms, and little is known about the applicability of such algorithms in BSS of different sizes. In this paper, we evaluate the performance of widely known prediction algorithms for three sized scenarios: a small system, with around 20 docking stations, a medium-sized one, with 400+ docking stations, and a large one, with more than 1500 stations. The results show that Prophet and Random Forest are the prediction algorithms with more consistent results, and that small systems often have not enough data for the algorithms to perform a solid work.
Bike-sharing services are flourishing in Smart Cities worldwide. They provide a low-cost and environment-friendly transportation alternative and help reduce traffic congestion. However, these new services are still under development, and several challenges need to be solved. A major problem is the management of rebalancing trucks in order to ensure that bikes and stalls in the docking stations are always available when needed, despite the fluctuations in the service demand. In this work, we propose a dynamic rebalancing strategy that exploits historical data to predict the network conditions and promptly act in case of necessity. We use Birth-Death Processes to model the stations’ occupancy and decide when to redistribute bikes, and graph theory to select the rebalancing path and the stations involved. We validate the proposed framework on the data provided by New York City’s bike-sharing system. The numerical simulations show that a dynamic strategy able to adapt to the fluctuating nature of the network outperforms rebalancing schemes based on a static schedule.
This paper models the availability of bikes at San Francisco Bay Area Bike Share stations using machine learning algorithms. Random Forest (RF) and Least-Squares Boosting (LSBoost) were used as univariate regression algorithms, and Partial Least-Squares Regression (PLSR) was applied as a multivariate regression algorithm. The univariate models were used to model the number of available bikes at each station. PLSR was applied to reduce the number of required prediction models and reflect the spatial correlation between stations in the network. Results clearly show that univariate models have lower error predictions than the multivariate model. However, the multivariate model results are reasonable for networks with a relatively large number of spatially correlated stations. Results also show that station neighbors and the prediction horizon time are significant predictors. The most effective prediction horizon time that produced the least prediction error was 15 minutes.
Bike Sharing Systems (BSSs) experience a significant loss in customer demand due to starvation (empty base stations precluding bike pickup) or congestion (full base stations precluding bike return). Therefore, BSSs operators reposition bikes between stations with the help of carrier vehicles. Due to unpredictable and dynamically changing nature of the demand, myopic reasoning typically provides a below par performance. We propose an online and robust repositioning approach to min-imise the loss in customer demand while considering the possible uncertainty in future demand. Specifically, we develop a scenario generation approach based on an iterative two player game to compute a strategy of repositioning by assuming that the environment can generate a worse demand scenario (out of the feasible demand scenarios) against the current repositioning solution. Extensive computational results from a simulation built on real world data set of bike sharing company demonstrate that our approach can significantly reduce the expected lost demand over the existing benchmark approaches.
In this article, the authors highlight the role data plays in smart cities from the perspective of the data life cycle - data collection, analysis, and data-driven smart services. They examine the progress of the Chinese Smart City project and identify three unique challenges that the project faces in smart city development.
A new procedure for the static repositioning problem of a bike-sharing system has been proposed First, the withdrawal and return demands of each station at each time period are estimated using the system data Then, the target number of bicycles at each station is determined to minimize the cost of the estimated unsatisfied demand. Finally, the repositioning routes are constructed for each vehicle, minimizing the total distance and keeping a balance among vehicles The procedure can also be used to explore alternative configurations of the repositioning system. Public bike-sharing programs have been deployed in hundreds of cities worldwide, improving mobility in a socially equitable and environmentally sustainable way. However, the quality of the service is drastically affected by imbalances in the distribution of bicycles among stations. We address this problem in two stages. First, we estimate the unsatisfied demand (lack of free lockers or lack of bicycles) at each station for a given time period in the future and for each possible number of bicycles at the beginning of the period. In a second stage, we use these estimates to guide our redistribution algorithms. Computational results using real data from the bike-sharing system in Palma de Mallorca (Spain) are reported.
Detecting traffic events using the sensor network infrastructure is an important service in urban environments that enables the authorities to handle traffic incidents. However, irregular measurements in such settings can derive either from faulty sensors or from unpredictable events. In this paper, we propose an efficient solution to resolve in real-time the source of such irregular readings by examining the correlation and the consistency among neighbor sensors and exploiting the wisdom of the crowd. Our experimental evaluation illustrates the efficiency and practicality of our approach.
With the growth in social media, internet of things, and planetary-scale sensing there is an unprecedented need to assimilate spatio-temporally distributed multimedia streams into actionable information. Consequently the concepts like objects, scenes, and events, need to be extended to recognize situations (e.g. epidemics, traffic jams, seasons, flash mobs). This paper motivates and computationally grounds the problem of situation recognition. It describes a systematic approach for combining multimodal real-time big data into actionable situations. Specifically it presents a generic approach for modeling and recognizing situations. A set of generic building blocks and guidelines help the domain experts model their situations of interest. The created models can be tested, refined, and deployed into practice using a developed system (EventShop). Results of applying this approach to create multiple situation-aware applications by combining heterogeneous streams (e.g. Twitter, Google Insights, Satellite imagery, Census) are presented.
During the last years, several speed-up techniques for Dijkstra’s algorithm have been published that maintain the correctness of the algorithm but reduce its running time for typical instances. They
are usually based on a preprocessing that annotates the graph with additional information which can be used to prune or guide
the search. Timetable information in public transport is a traditional application domain for such techniques. In this paper,
we provide a condensed overview of new developments and extensions of classic results. Furthermore, we discuss how combinations
of speed-up techniques can be realized to take advantage from different strategies.
Due to increased traffic congestion and carbon emissions, Bike Sharing Systems (BSSs) are adopted in various cities for short distance travels, specifically for last mile transportation. The success of a bike sharing system depends on its ability to have bikes available at the "right" base stations at the "right" times. Typically, carrier vehicles are used to perform repositioning of bikes between stations so as to satisfy customer requests. Owing to the uncertainty in customer demand and day-long repositioning, the problem of having bikes available at the right base stations at the right times is a challenging one. In this paper, we propose a multi-stage stochastic formulation, to consider expected future demand over a set of scenarios to find an efficient repositioning strategy for bike sharing systems. Furthermore, we provide a Lagrangian decomposition approach (that decouples the global problem into routing and repositioning slaves and employs a novel DP approach to efficiently solve routing slave) and a greedy online anticipatory heuristic to solve large scale problems effectively and efficiently. Finally, in our experimental results, we demonstrate significant reduction in lost demand provided by our techniques on real world datasets from two bike sharing companies in comparison to existing benchmark approaches.
Due to increased traffic congestion and carbon emissions,
Bike Sharing Systems (BSSs) are adopted in various cities for
short distance travels, specifically for last mile transportation.
The success of a bike sharing system depends on its ability to
have bikes available at the "right" base stations at the "right"
times. Typically, carrier vehicles are used to perform repositioning of bikes between stations so as to satisfy customer requests. Owing to the uncertainty in customer demand and day-long repositioning, the problem of having bikes available at the right base stations at the right times is a challenging one. In this paper, we propose a multi-stage stochastic formulation, to consider expected future demand over a
set of scenarios to find an efficient repositioning strategy for bike sharing systems. Furthermore, we provide a Lagrangian decomposition approach (that decouples the global problem into routing and repositioning slaves and employs a novel DP
approach to efficiently solve routing slave) and a greedy online anticipatory heuristic to solve large scale problems effectively and efficiently. Finally, in our experimental results, we demonstrate significant reduction in lost demand provided by our techniques on real world datasets from two bike sharing companies in comparison to existing benchmark approaches.
Bike sharing systems, which provide a convenient commute choice for short trips, have emerged rapidly in many cities. While bike sharing has greatly facilitated people's commutes, those systems are facing a costly maintenance issue -- rebalancing bikes among stations. We observe that existing systems frequently suffer situations such as no-bike-to-borrow (empty) or no-dock-to-return (full) due to existing ad hoc rebalancing practice. To address this issue, we provide systematic analysis on user trip data, station status data, rebalancing data, and meteorology data, and propose BRAVO - the first practical data-driven bike rebalancing app for operators to improve bike sharing service while reducing the maintenance cost. Specifically, leveraging experiences from two-round round-the-clock field studies and comprehensive information from four data sets, a data-driven model is proposed to capture and predict the safe rebalancing range for each station. Based on this safe rebalancing range, BRAVO computes the optimal rebalancing amounts for the full and empty stations to minimize the rebalancing cost. BRAVO is evaluated with 24-month data from Capital, Hangzhou and NiceRide bikeshare systems. The experiment results show that given the same user demand, BRAVO reduces 28% of the station visits and 37% of the rebalancing amounts.
The proliferation of smart technologies has produced significant changes in the way people interact in a city. Smart traffic monitoring systems allow citizens and city operators to acquire a real-time view of the city traffic state. Furthermore, alternative means of transport, such as bike sharing systems, have enjoyed tremendous success in many major cities around the world today and provide real-time information regarding the mobility of the users. Such sources of urban data may act as human mobility sensors. Detecting the location and extent of large events in urban environments is a challenging problem. Previous work focuses mainly on identifying traffic flows and extract possible event sources. However, these solutions lack the ability to capture large areas of events, as they rely only on single-source data to identify user mobility or focus on identifying single locations rather than areas. In this paper we model the behavior of two different real-time data sources and we illustrate how they may be combined to acquire the area affected from a social event. We propose "fEEL" (Efficient Event Location identification), a novel algorithm to identify affected areas from social events using multiple heterogeneous sources of urban data. Our experimental evaluations show that fEEL is efficient and practical.
Bike-sharing systems have been deployed in many major cities around the world today. Bike sharing systems provide great advantages as a mean of urban public transportation facilitating a green solution for daily commuters and tourists. Users tend to use more often this type of transportation for their daily needs. The key to success for such systems is the efficient distribution of bikes among the bike stations in order to satisfy high user demands. Existing schemes in the literature focus either on predicting the bike station demand and modeling user mobility mainly focusing on making cycling more accessible to people, or on minimizing the costly and time-consuming movement of bikes among the stations while the system is in use. In this work our objective is to gain insights into the usage of bike sharing systems and in particular the pick-up and drop-off operations. Our goal is to get a better understanding of the bike mobility patterns and identify the key factors that lead to imbalances in the distribution of the bikes at the stations, towards creating effective and sustainable bike sharing systems.
Bike-sharing systems are widely deployed in many major cities, providing a convenient transportation mode for citizens' commutes. As the rents/returns of bikes at different stations in different periods are unbalanced, the bikes in a system need to be rebalanced frequently. Real-time monitoring cannot tackle this problem well as it takes too much time to reallocate the bikes after an imbalance has occurred. In this paper, we propose a hierarchical prediction model to predict the number of bikes that will be rent from/returned to each station cluster in a future period so that reallocation can be executed in advance. We first propose a bipartite clustering algorithm to cluster bike stations into groups, formulating a two-level hierarchy of stations. The total number of bikes that will be rent in a city is predicted by a Gradient Boosting Regression Tree (GBRT). Then a multi-similarity-based inference model is proposed to predict the rent proportion across clusters and the inter-cluster transition, based on which the number of bikes rent from/ returned to each cluster can be easily inferred. We evaluate our model on two bike-sharing systems in New York City (NYC) and Washington D.C. (D.C.) respectively, confirming our model's advantage beyond baseline approaches (0.03 reduction of error rate), especially for anomalous periods (0.18/0.23 reduction of error rate).
Bike sharing is booming globally as a green transportation mode, but the occurrence of over-demand stations that have no bikes or docks available greatly affects user experiences. Directly predicting individual over-demand stations to carry out preventive measures is difficult, since the bike usage pattern of a station is highly dynamic and context dependent. In addition, the fact that bike usage pattern is affected not only by common contextual factors (e.g., time and weather) but also by opportunistic contextual factors (e.g., social and traffic events) poses a great challenge. To address these issues, we propose a dynamic cluster-based framework for over-demand prediction. Depending on the context, we construct a weighted correlation network to model the relationship among bike stations, and dynamically group neighboring stations with similar bike usage patterns into clusters. We then adopt Monte Carlo simulation to predict the over-demand probability of each cluster. Evaluation results using real-world data from New York City and Washington, D.C. show that our framework accurately predicts over-demand clusters and outperforms the baseline methods significantly.
Bike sharing systems, aiming at providing the missing links in public transportation systems, are becoming popular in urban cities. A key to success for a bike sharing systems is the effectiveness of rebalancing operations, that is, the efforts of restoring the number of bikes in each station to its target value by routing vehicles through pick-up and drop-off operations. There are two major issues for this bike rebalancing problem: the determination of station inventory target level and the large scale multiple capacitated vehicle routing optimization with outlier stations. The key challenges include demand prediction accuracy for inventory target level determination, and an effective optimizer for vehicle routing with hundreds of stations. To this end, in this paper, we develop a Meteorology Similarity Weighted K-Nearest-Neighbor (MSWK) regressor to predict the station pick-up demand based on large-scale historic trip records. Based on further analysis on the station network constructed by station-station connections and the trip duration, we propose an inter station bike transition (ISBT) model to predict the station drop-off demand. Then, we provide a mixed integer nonlinear programming (MINLP) formulation of multiple capacitated bike routing problem with the objective of minimizing total travel distance. To solve it, we propose an Adaptive Capacity Constrained K-centers Clustering (AdaCCKC) algorithm to separate outlier stations (the demands of these stations are very large and make the optimization infeasible) and group the rest stations into clusters within which one vehicle is scheduled to redistribute bikes between stations. In this way, the large scale multiple vehicle routing problem is reduced to inner cluster one vehicle routing problem with guaranteed feasible solutions. Finally, the extensive experimental results on the NYC Citi Bike system show the advantages of our approach for bike demand prediction and large-scale bike rebalancing optimization.
As an innovative mobility strategy, public bike-sharing has grown dramatically worldwide. Though providing convenient, low-cost and environmental-friendly transportation, the unique features of bike-sharing systems give rise to problems to both users and operators. The primary issue among these problems is the uneven distribution of bicycles caused by the ever-changing usage and (available) supply. This bicycle imbalance issue necessitates efficient bike re-balancing strategies, which depends highly on bicycle mobility modeling and prediction. In this paper, for the first time, we propose a spatio-temporal bicycle mobility model based on historical bike-sharing data, and devise a traffic prediction mechanism on a per-station basis with sub-hour granularity. We extensively evaluated the performance of our design through a one-year dataset from the world's largest public bike-sharing system (BSS) with more than 2800 stations and over 103 million check in/out records. Evaluation results show an 85 percentile relative error of 0.6 for both check in and check out prediction. We believe this new mobility modeling and prediction approach can advance the bike re-balancing algorithm design and pave the way for the rapid deployment and adoption of bike-sharing systems across the globe.
In recent years crowdsourcing systems have shown to provide important benefits to Smartcities, where ubiquitous citizens, acting as mobile human sensors, assist in responding to signals and providing real-time information about city events, to improve the quality of life for businesses and citizens. In this paper we present REquEST, our approach to selecting a small subset of human sensors to perform tasks that involve ratings, which will allow us to reliably identify crowdsourced events. One important challenge we address is how to achieve reliable event detection, as the information collected from the human crowd is typically noisy and users may have biases in the answers they provide. Our experimental evaluation illustrates that our approach works effectively by taking into consideration the bias of individual users, approximates well the output result, and has minimal error.
Bicycle-sharing systems, which can provide shared bike usage services for the public, have been launched in many big cities. In bicycle-sharing systems, people can borrow and return bikes at any stations in the service region very conveniently. Therefore, bicycle-sharing systems are normally used as a short-distance trip supplement for private vehicles as well as regular public transportation. Meanwhile, for stations located at different places in the service region, the bike usages can be quite skewed and imbalanced. Some stations have too many incoming bikes and get jammed without enough docks for upcoming bikes, while some other stations get empty quickly and lack enough bikes for people to check out. Therefore, inferring the potential destinations and arriving time of each individual trip beforehand can effectively help the service providers schedule manual bike re-dispatch in advance. In this paper, we will study the individual trip prediction problem for bicycle-sharing systems. To address the problem, we study a real-world bicycle-sharing system and analyze individuals' bike usage behaviors first. Based on the analysis results, a new trip destination prediction and trip duration inference model will be introduced. Experiments conducted on a real-world bicycle-sharing system demonstrate the effectiveness of the proposed model.
A key challenge for rapidly growing cities of today is to provide effective public transport services to satisfy the increasing demands for urban mobility. Towards this goal, the Internet of Things has great potential to overcome existing deficiencies of public transport systems given its ability to embed smart technology into real-life urban contexts. In this paper, we show how this paradigm can be applied to the public transport domain and present the Urban Bus Navigator, an Internet-of-Things enabled navigation system for urban bus riders. UBN provides two novel information services for bus users: 1) micro-navigation and 2) crowd-aware route recommendation. Micro-navigation refers to fine-grained contextual guidance of passengers along a bus journey by recognizing boarded bus vehicles and tracking the passenger's journey progress. Crowd-aware route recommendation collects and predicts crowd levels on bus journeys to suggest better and less crowded routes to bus riders. We present the technical system behind the Urban Bus Navigator and report on results from an in-the-wild study in Madrid that indicates removed barriers for public transport usage and a positive impact on how people feel about bus journeys.
HLA-based simulation systems are prone to load imbalances due to lack management of shared resources in distributed environments. Such imbalances lead these simulations to exhibit performance loss in terms of execution time. As a result, many dynamic load balancing systems have been introduced to manage distributed load. These systems use specific methods, depending on load or application characteristics, to perform the required balancing. Load prediction is a technique that has been used extensively to enhance load redistribution heuristics towards preventing load imbalances. In this paper, several efficient Time Series model variants are presented and used to enhance prediction precision for large-scale distributed simulation-based systems. These variants are proposed to extend and correct the issues originating from the implementation of Holt's model for time series in the predictive module of a dynamic load balancing system for HLA-based distributed simulations. A set of migration decision-making techniques is also proposed to enable a prediction-based load balancing system to be independent of any prediction model, promoting a more modular construction.
In this paper, we present a personal journey advisor application for helping people to navigate the city using the available bike-sharing system. For a given origin and destination, the application suggests the best pair of stations to be used to take and return a city-bike, in order to minimize the overall walking and biking travel time as well as maximizing the probability to find available bikes at the first station and returning slots at the second one. To solve the journey advisor optimization problem, we modeled real mobile bikers' behavior in terms of travel time, and used the predicted availability at every bike station to choose the pair of stations which maximizes a measure of optimality. To develop the application, we built a spatio-temporal prediction system able to estimate the number of available bikes for each station in short and long term, outperforming already developed solutions. The prediction system is based on an underlying spatial interaction network among the bike stations, and takes into account the temporal patterns included in the data. The City ride application was tested with real data from the Dublin bike-sharing system.
This paper deals with a new problem that is a generalization of the many to many pickup and delivery problem and which is motivated by operating self-service bike sharing systems. There is only one commodity, initially distributed among the vertices of a graph, and a capacitated single vehicle aims to redistribute the commodity in order to reach a target distribution. Each vertex can be visited several times and also can be used as a buffer in which the commodity is stored for a later visit. This problem is NP-hard, since it contains several NP-hard problems as special cases (the TSP being maybe the most obvious one). Even finding a tractable exact formulation remains problematic.This paper presents efficient algorithms for solving instances of reasonable size, and contains several theoretical results related to these algorithms. A branch-and-cut algorithm is proposed for solving a relaxation of the problem. An upper bound of the optimal solution of the problem is obtained by a tabu search, which is based on some theoretical properties of the solution, once fixed the sequence of the visited vertices. The possibility of using the information provided by the relaxation receives a special attention, both from a theoretical and a practical point of view. It is proven that to build a feasible solution of the problem by using the one obtained by the relaxation is an NP-hard problem. Nevertheless, a tabu search initialized with the optimal solution of the relaxation often shows that it is the optimal one.The algorithms have been tested on a set of instances coming from the literature, proving their effectiveness.
A growing number of cities are implementing bike-sharing programs to increase bicycle use. One of the key factors for the success of such programs is the location of bike stations in relation to potential demand (population, activities and public transport stations). This study proposes a GIS-based method to calculate the spatial distribution of the potential demand for trips, locate stations using location–allocation models, determine station capacity and define the characteristics of the demand for stations. The results obtained are compared with the most commonly used location–allocation modeling approaches: minimizing impedance and maximizing coverage. For the objective of this study, the latter approach is more useful. Diminishing returns are observed in both cases: as the number of stations increases, there is less improvement in the fraction of the population covered and accessibility to stations. Because the spatial structure of the proposed network also plays an important role in bike-station use, an additional accessibility analysis was carried out to calculate the volume of activity to which a station has access. With this analysis, stations that are relatively isolated, and therefore of little use to potential users, can be eliminated.
We consider a graph with n vertices, all pairs of which are connected by an edge; each edge is of given positive length. The following two basic problems are solved. Problem 1: construct the tree of minimal total length between the n vertices. (A tree is a graph with one and only one path between any two vertices.) Problem 2: find the path of minimal total length between two given vertices.
It is shown by an analysis similar to that for the spinodal decomposition of a supersaturated solution that an array of dislocations, modelled by parallel screw dislocations, of uniform density, is unstable; the dislocations move to form a structure having a modulated dislocation density. It is suggested that the instability grows ultimately into a dislocation cell structure and that the cell size is given by the dominant wavelength of the density modulation. This wavelength λ m is found to be proportional to ρ-1/2 and furthermore the wavelength is given by λ m ≈ K c ·ρ-1/2=r c , where K c is a constant, ρ is the dislocation density and r c is defined as a dislocation‐dislocation interaction distance. Data in the literature relating to cell size are shown to support this result. Restrictions on the applicability of the analysis are discussed.
In this paper, we address the problem of determining the optimal fleet size for a vehicle rental company and derive analytical results for its relationship to vehicle availability at each rental station in the company’s network of locations. This work is motivated by the recent surge in interest for bicycle and electric car sharing systems, one example being the French program Vélib (2010). We first formulate a closed queueing network model of the system, obtained by viewing the system from the vehicle’s perspective. Using this framework, we are able to derive the asymptotic behavior of vehicle availability at an arbitrary rental station with respect to fleet size. These results allow us to analyze imbalances in the system and propose some basic principles for the design of system balancing methods. We then develop a profit-maximizing optimization problem for determining optimal fleet size. The large-scale nature of real-world systems results in computational difficulties in obtaining this exact solution, and so we provide an approximate formulation that is easier to solve and which becomes exact as the fleet size becomes large. To illustrate our findings and validate our solution methods, we provide numerical results on some sample networks.
Computation of the k-nearest neighbors generally requires a large number of expensive distance computations. The method of branch and bound is implemented in the present algorithm to facilitate rapid calculation of the k-nearest neighbors, by eliminating the necesssity of calculating many distances. Experimental results demonstrate the efficiency of the algorithm. Typically, an average of only 61 distance computations were made to find the nearest neighbor of a test sample among 1000 design samples.