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During the last decade bike sharing systems have emerged as a publictransport mode in urban short trips in more than 500 major cities around theworld. For the mobility service mode, many challenges from its operations arenot well addressed yet, for example, how to develop the bike sharing systems tobe able to effectively satisfy the fluctuating demands both for bikes and forvacant lockers. To this end, it is a key to give performance analysis of thebike sharing systems. This paper first describes a large-scale bike sharingsystem. Then the bike sharing system is abstracted as a closed queueing networkwith multi-class customers, where the virtual customers and the virtual nodesare set up, and the service rates as well as the relative arrival rates areestablished. Finally, this paper gives a product-form solution to the steadystate joint probabilities of queue lengths, and gives performance analysis ofthe bike sharing system. Therefore, this paper provides a unified framework foranalyzing closed queueing networks in the study of bike sharing systems. Wehope the methodology and results of this paper can be applicable in the studyof more general bike sharing systems.

A Unified Framework for Analyzing Closed Queueing Networks in Bike Sharing Systems