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

TL;DR

This paper presents a unified analytical framework using closed queueing networks to evaluate and optimize the performance of large-scale bike sharing systems, addressing demand fluctuations and operational challenges.

Contribution

It introduces a novel product-form solution for steady state probabilities in bike sharing systems modeled as multi-class closed queueing networks.

Findings

Provides a mathematical performance analysis framework.

Derives steady state joint probabilities for queue lengths.

Offers insights for system optimization and demand management.

Abstract

During the last decade bike sharing systems have emerged as a public transport mode in urban short trips in more than 500 major cities around the world. For the mobility service mode, many challenges from its operations are not well addressed yet, for example, how to develop the bike sharing systems to be able to effectively satisfy the fluctuating demands both for bikes and for vacant lockers. To this end, it is a key to give performance analysis of the bike sharing systems. This paper first describes a large-scale bike sharing system. Then the bike sharing system is abstracted as a closed queueing network with multi-class customers, where the virtual customers and the virtual nodes are set up, and the service rates as well as the relative arrival rates are established. Finally, this paper gives a product-form solution to the steady state joint probabilities of queue lengths, and gives performance analysis of the bike sharing system. Therefore, this paper provides a unified framework for analyzing closed queueing networks in the study of bike sharing systems. We hope the methodology and results of this paper can be applicable in the study of more general bike sharing systems.