## 2 Theoretical Background of Bike-Sharing Systems  
### Bike-Sharing--History  
Bike-sharing, commonly referred to as public bicycle systems (PBS), has become an essential component of sustainable urban transportation strategies. Historically, the evolution of bike-sharing presents a fascinating path from grassroots initiatives to sophisticated technological frameworks, reflecting the broader trend of urban mobility progress. This progression can be divided into four unique generations, each marked by technological advancements and operational improvements that have gradually influenced the contemporary systems we observe today. The idea of bike-sharing began in the 1960s with the White Bicycle Plan in Amsterdam, the initial system that offered bicycles for public and communal access [29]. This innovative project sought to promote sustainable transportation and decrease dependence on automobiles in the city. However, the lack of systems to monitor or control bicycle usage caused significant problems, including widespread theft, misuse, and operational failures. Although the programme eventually did not succeed, it established the conceptual groundwork for future advancements by presenting the notion of shared urban mobility [3, 29]. The second wave of bike-sharing systems appeared in the 1990s, featuring notable enhancements to overcome the shortcomings of earlier versions. Copenhagen's Bycyklen initiative, introduced in 1995, served as a remarkable case. This system implemented coin-operated docking stations and specially designed bicycles to reduce theft and improve operational efficiency. The systematic, station-oriented model of Bycyklen represented a significant progress by offering a dependable and orderly means of access. Although these systems were devoid of digital technology and user tracking, they demonstrated the viability of bike sharing as a scalable service and laid the groundwork for future, more sophisticated systems [7]. A significant shift took place with the launch of the third generation of bike-sharing programmes in the late 1990s and early 2000s, fuelled by advancements in information and communication technologies (ICT). These systems incorporated innovations, such as GPS tracking, mobile apps, and electronic payment methods, turning bike sharing into a completely digital and user-friendly solution. Notable instances are Lyon's Velo'v system and Paris's Velib', both initiated in 2007. Velib' emerged as one of the initial large-scale systems to integrate real-time information on bike availability, available kiosks, and effortless payment methods. These characteristics not only enhanced the user experience but also allowed cities to track system performance and refine operations using data-informed decision making. The success of Velib' showcased the possibility for bike-sharing to grow quickly and function effectively in crowded urban environments, facilitating its worldwide acceptance [30]. The fourth wave of bike-sharing systems appeared in the mid-2010s, featuring dockless designs and cutting-edge technologies like electric-assist bicycles (e-bikes) and AI-enabled fleet management. Dockless systems removed the necessity for fixed docking stations, utilising GPS-enabled smart locks and mobile apps for users to find and unlock bikes. In China, companies, such as Mobike and Ofo, popularised this model, providing unparalleled flexibility and considerably reducing infrastructure costs for urban regions. Users were able to collect and leave bicycles almost anywhere inside a specified service zone. Nonetheless, the swift expansion of dockless systems has also brought about new difficulties, such as improper parking, urban congestion, and excessive fleet presence in specific metropolitan areas [31, 32]. To address these challenges, hybrid systems have developed as a progression of fourth-generation models, merging the adaptability of dockless systems with the organisationof station-based models.