Research On Fluid Limit And Diffusion Limit For A Large-scale Bike Sharing Systems

Recently,with the intensification of environmental problems such as urban traffic and smog,green city and transportation is rising up.Bike sharing system with the advantages of its own energy saving,green and convenience has been rapidly developed in many countries and cities.However,with the gradual increase of the scale of the public bicycle system and the gradual increase of the use frequency,the problem of "rent / return bicycle" is widespread in the system operation.So far performance analysis of bike sharing systems always exists many difficulties and challenges under some more general factors.First of all,we propose a more general large-scale bike sharing system having renewal arrival processes of bike users and general travel times,and establish a multiclass closed queueing network from the practical factors of the bike-sharing systema.The queue length process of this multiclass closed queueing network is established by means of the numbers of bikes both at the stations and on the roads.Appling the functional strong law of large numbers to establish the fluid limit theorem of the key performance indexes under the heavy traffic conditions,and to obtain the limit of the fulid model for bike sharing system.Secondly,base on the fulid limit,we set up the diffusion scaled processes of the arriving processes and routing processes of this bike sharing system.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 box state space,and also the diffusion limit theorem of the bike sharing system is obtained.Furthermore,providing a numerical example to analyze performance index and the probability of the problematic stations of the bike sharing system,at the same time,the numerical example is also a good demonstration for the method provided in this paper.Finally,this paper applies the results to the bike sharing system of Haidian district of Beijing city,and analyzes the key performance indexes and probability of the problematic stations of the bike sharing system under the steady-state operation.And we also raise the feasible suggestions to make sure that the operating efficiency and customer satisfaction can be increased.Thus the results and methodology of this paper provide new highlight in the study of more general large-scale bike sharing systems,and it is a very important and challenging research in the field of bike sharing system.