Since bicycle itself is a low-pollution and lowenergy-consumption vehicle, to follow the trend of building an eco-friendly transportation system, the public bicycle sharing system has been followed for years around the world. YouBike, which is the corresponding system in Taipei city, has become more and more popular and pervasive recently. In practice, once some rental station is out of bicycles, it will automatically inform the management system to transport bicycles from the other stations as soon as possible to service commuters and increase the utilization. However, from the manager's point of view, how to save the transport cost is the critical issue. In this paper, we find such real case is very similar to the k-server problem, which is a fascinating subject with extensive applications and deep open problems in the field of online algorithm [1]. We borrow this problem as a theoretical model to further address many aspects of transport issues, such as the usage and capacity of the rental station, and the fuel consumption and capacity of the truck used to transport bicycles. Also, algorithms used to solve the k-server problem can achieve theoretical results as references to efficiently transport YouBike.

For energy conservation and reduction of carbon emissions, an eco-friendly public transportation system is in dispensable in a modern country. Since a bicycle itself is a low-population and low-energy-consumption vehicle, many cities, including Taipei, have built a convenient public bicycle sharing system as an extension of the metro system to follow the trend.YouBike, a corresponding system in Taipei, has become more and more popular and pervasive recently. In practice, a commuter can rent a bicycle in a rental station. Once some rental station is out-of bicycles, it will automatically inform the management system and the system has to transport bicycles from other station or depository to supply it. From the viewpoint of commuters, they would like to obtain a bicycle as soon as possible; however, from the perspective of a manager, not only the utilization of the system, but also the transportation cost, is critical to maintain the operation. Hence how to address the online optimization problem and balance the bi-criteria issue is a hot topic. In [6], Li and Liu borrowed the k-server problem [9] to deliver a theoretical model to address this problem. Nonetheless, their model has some drawbacks that are insufficient to approach the real case. In this paper, we add new elements to improve their model and formally define the YouBike transport problem. Moreover, we consider this problem in a uniform space to further explore its inner properties and solution hardship. Finally, some indications for future works are also presented.Keywords--online algorithm, the k-server problem, YouBike, public bicycle sharing system