Fluid and Diffusion Limits for Bike Sharing Systems

TL;DR

This paper develops fluid and diffusion limit models for large-scale bike sharing systems using heavy traffic approximations of multiclass queueing networks, providing new insights into system performance.

Contribution

It introduces a general framework for analyzing large-scale bike sharing systems via fluid and diffusion limits, including convergence to semimartingale reflecting Brownian motion.

Findings

Convergence of scaled bike counts to SRBM in high-dimensional space

Establishment of fluid and diffusion limit theorems for bike sharing systems

Enhanced understanding of system performance under heavy traffic conditions

Abstract

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.