English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

As a favorite urban public transport mode, the bike sharing system is alarge-scale and complicated system, and there exists a key requirement that auser and a bike should be matched sufficiently in time. Such matched behaviormakes analysis of the bike sharing systems more difficult and challenging. Thispaper considers a more general large-scale bike sharing system from twoimportant views: (a) Bikes move in an irreducible path graph, which is relatedto geographical structure of the bike sharing system; and (b) Markovian arrivalprocesses (MAPs) are applied to describe the non-Poisson and burst behavior ofbike-user (abbreviated as user) arrivals, while the burstiness demonstratesthat the user arrivals are time-inhomogeneous and space-heterogeneous inpractice. For such a complicated bike sharing system, this paper establishes amulticlass closed queueing network by means of some virtual ideas, for example,bikes are abstracted as virtual customers; stations and roads are regarded asvirtual nodes. Thus user arrivals are related to service times at stationnodes; and users riding bikes on roads are viewed as service times at roadnodes. Further, to deal with this multiclass closed queueing network, weprovide a detailed observation practically on physical behavior of the bikesharing system in order to establish the routing matrix, which gives anonlinear solution to compute the relative arrival rates in terms of theproduct-form solution to the steady-state probabilities of joint queue lengthsat the virtual nodes. Based on this, we can compute the steady-stateprobability of problematic stations, and also deal with other interestingperformance measures of the bike sharing system. We hope that the methodologyand results of this paper can be applicable in the study of more general bikesharing systems through multiclass closed queueing networks.

A Nonlinear Solution to Closed Queueing Networks for Bike Sharing Systems with Markovian Arrival Processes and under an Irreducible Path Graph