Modelling of Sharing Systems via Renewal Processes

This paper is devoted to the analysis of the possibilities of modelling of bike sharing systems using the methods of recovery theory. The first chapter analyzes the main academic papers and textbooks that reflect the fundamentals of the renewal theory, describe different ways of modelling bike sharing systems, and also offer a variety of different applications of renewal theory in other scientific spheres. In addition, this chapter describes the definitions of the renewal theory, as well as the development of an algorithm for modelling the expected number of bicycles based on them. The second chapter consists of a simulation study, during which the performance of the model is tested on the generated data. Also, this chapter confirms the hypothesis of the possibility of modelling bike sharing systems using renewal theory. The result of the simulation is an estimate of the expected number of bicycles at a single station during the day. The third chapter is devoted to the application of the developed algorithm on the real data of the bike sharing system “Divvy” in Chicago. As a result, an estimate of the expected number of bikes for a real bike-station is made, as well as several model flaws that can be corrected in subsequent studies. In the study, it was possible to develop a simple applied algorithm for modeling automatic bike sharing systems based on the renewal theory, to test the performance of the model on both generated and real data, as well as to identify the current flaws of the model, which can be corrected with further modification of the developed algorithm.