# Decision System Based on Markov Chains for Sizing the Rebalancing Fleet of Bike Sharing Stations
## 2 Literature Review
This knowledge can inform the planning of infrastructure, such as the placement of new stations or the design of bike lanes, to enhance the accessibility and usability of the system. Overall, the application of MC models in BSSs provides a powerful tool for data-driven decision making and sustainable urban mobility planning. A model that can help forecasting bike usage by using weather data was explored by [43], temperature and precipitation being the key factors discovered. The conclusion was that high temperatures and low or no precipitation result in increased bike usage. [PERSON] et al. [44] proposed a dynamic cluster-based framework for predicting over-demand in BSSs. Compared to the work of [43], they considered common and opportunistic contextual factors and modeled the relationship among bike stations, using a weighted correlation network. They also introduced a geographically-constrained clustering method. Based on the results obtained from the collected data of NYC Citi Bike and DC Capital Bikeshare, their framework improved the accuracy of predicting over-demand occurrences by considering dynamic contexts and spatial relationships among stations. However, article [45] discussed the importance of understanding the dynamics among stations in a BSS. The user's satisfaction level is a global indicator of system performance, but it does not capture the variations among stations. The availability rate, on the other hand, reflects the status of available bicycles in each station, which can vary based on their geographical locations. Article [45] emphasized the need for a comprehensive analysis of the system, to determine its dynamic behaviors, which is crucial for system control or redesign. In contrast with articles [43; 44], the current work's clustering strategy advantageously uses the bike stations' loads, which are directly related to the rebalancing needs. Moreover, compared to the approach in [45], the current work aimed at capturing the memoryless behavior of the bike stations' loads, Markov Chains being specifically chosen in modeling them because they are well-suited for capturing the dynamic behavior and transitions between different states in the system. In the context of rebalancing, the research in [46] focused on reducing operation costs by considering depot location. The study utilized K-means and WK-means algorithms to determine the optimal number and location of depots. The spatio-temporal patterns of bicycle sharing systems were also taken into account, providing valuable insights for rebalancing management [47; 48]. Study [47] aimed to identify spatio-temporal patterns in bike sharing station usage, using a model based on Functional Data Analysis (FDA). They developed a novel bi-clustering algorithm for functional data, which grouped stations and days with similar behavior. The analysis revealed distinct usage patterns based on city area and day of the week, providing valuable insights for fleet managers to effectively manage the service. The model presented in [17] provides a unique mathematical formulation for bike station clusters, which utilizes user bike flows from operational data in BSSs to optimize rebalancing planning. Unlike traditional models that focus on factors like travel distance or operational costs, this model incorporates user trip information for clustering. To efficiently solve the long-distance rebalancing problem, the researchers proposed a modified fast unfolding algorithm based on network theory.