  Bike sharing systems have rapidly developed around the world, and they are
served as a promising strategy to improve urban traffic congestion and to
decrease polluting gas emissions. So far performance analysis of bike sharing
systems always exists many difficulties and challenges under some more general
factors. In this paper, a more general large-scale bike sharing system is
discussed by means of heavy traffic approximation of multiclass closed queueing
networks with non-exponential factors. Based on this, the fluid scaled
equations and the diffusion scaled equations are established by means of the
numbers of bikes both at the stations and on the roads, respectively.
Furthermore, the scaling processes for the numbers of bikes both at the
stations and on the roads are proved to converge in distribution to a
semimartingale reflecting Brownian motion (SRBM) in a $N^{2}$-dimensional box,
and also the fluid and diffusion limit theorems are obtained. Furthermore,
performance analysis of the bike sharing system is provided. Thus the results
and methodology of this paper provide new highlight in the study of more
general large-scale bike sharing systems.
