# Decision System Based on Markov Chains for Sizing the Rebalancing Fleet of Bike Sharing Stations
## 2 Literature Review  
Understanding actual system behavior is essential for achieving a satisfactory control strategy. Knowing a system's functioning and response to inputs and conditions allows a comprehensive understanding to be gained. This knowledge enables the identification of critical parameters, analysis of system dynamics, and prediction of system responses. Key features for describing systems, like land use intensity [8], bike counts [9], trip data [10], and multiple categories [11], are used in the literature. Common algorithms used in the literature for feature evaluation are deep neural networks [8], dynamic linear models [9], gradient-boosting decision trees [10], and ensemble learning model-based methods [11]. Leveraging this understanding, optimal control strategies can be developed to enhance system performance, stability, and safety. By incorporating insights from the study of actual system behavior, a reliable and efficient control strategy can be formulated. For large systems, it is often impractical to comprehensively analyze the intricate behavior of the entire system, necessitating the adoption of reductionist approaches that enable the study of simplified subsystems or components, in order to gain insight and understanding. In this sense, clustering plays an important role in addressing challenges related to a BSS. By employing clustering techniques, valuable insights can be gained into the system's behavior, allowing for the grouping of similar bikes, stations, or users, based on various attributes, such as location [12; 13], usage patterns [14; 15], or user preferences [16; 17]. This enables the identification of user segments and the tailoring of services accordingly. Clustering also aids in optimizing bike allocation [18], station placement [19], and route planning [20], resulting in enhanced operational efficiency and improved user experience. Moreover, clustering facilitates anomaly detection [21], enabling the identification and resolution of issues, such as bike theft, vandalism, or system malfunctions. Overall, clustering techniques provide a powerful toolset for analyzing and understanding the complex dynamics of BSSs, enabling data-driven decision making and the development of innovative solutions to enhancing the sustainability and usability of BSSs. One common approach to performing clustering is utilizing feature descriptors. Feature descriptors provide a concise representation of the characteristics and attributes of bike sharing data, enabling efficient and effective clustering algorithms to be applied. The careful selection of feature descriptors is of the utmost importance in ensuring the accuracy and reliability of the clustering results. These descriptors should capture the relevant information that distinguishes different user behaviors and patterns. In the literature, descriptors such as bike demand [22], trip duration [23], or distance traveled [24] can provide insights into user preferences and usage patterns. Moreover, the proper usage of these feature descriptors is also of great importance. Techniques such as Principal Component Analysis (PCA) have been used in other studies, to reduce the dimensionality of the feature space, allowing for a more efficient clustering process. [PERSON] et al. [25] have shown that by extracting the most informative features, PCA helps to eliminate noise and redundancy, leading to more meaningful and interpretable clustering results. Feature descriptors play a vital role in uncovering hidden patterns and structures within bike sharing data. They enable the identification of distinct user groups, such as commuters, leisure riders, or occasional users, facilitating targeted interventions and improvements in BSS operations [26]. Additionally, other studies use feature descriptorsin anomaly detection, identifying unusual or abnormal user behaviors that may require further investigation [27]. In recent years, there has been a growing interest in the application of MCs for modeling and optimizing BSSs [28; 29; 30].