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

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Queueing Theory and Network Applications (QTNA 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10591))

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Abstract

As a favorite urban public transport mode, the bike sharing system is a large-scale and complicated system, and there exists a key requirement that a user and a bike should be matched sufficiently in time. Such matched behavior makes analysis of the bike sharing systems more difficult and challenging. To design a better bike sharing system, it is a key to analyze and compute the probabilities of the problematic (i.e., full or empty) stations. In fact, such a computation is established for some fairly complex stochastic systems. To do this, this paper considers a more general large-scale bike sharing system from two important views: (a) Bikes move in an irreducible path graph, which is related to geographical structure of the bike sharing system; and (b) Markovian arrival processes (MAPs) are applied to describe the non-Poisson and burst behavior of bike-user (abbreviated as user) arrivals, while the burstiness demonstrates that the user arrivals are time-inhomogeneous and space-heterogeneous in practice. For such a complicated bike sharing system, this paper establishes a multiclass closed queueing network by means of some virtual ideas, for example, bikes are abstracted as virtual customers; stations and roads are regarded as virtual nodes. Thus user arrivals are related to service times at station nodes; and users riding bikes on roads are viewed as service times at road nodes. Further, to deal with this multiclass closed queueing network, we provide a detailed observation practically on physical behavior of the bike sharing system in order to establish the routing matrix, which gives a nonlinear solution to compute the relative arrival rates in terms of the product-form solution to the steady-state probabilities of joint queue lengths at the virtual nodes. Based on this, we can compute the steady-state probability of problematic stations, and also deal with other interesting performance measures of the bike sharing system. We hope that the methodology and results of this paper can be applicable in the study of more general bike sharing systems through multiclass closed queueing networks.

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Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under grant Nos. 71671158 and 71471160; and by the Natural Science Foundation of Hebei province under grant No. G2017203277.

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Authors and Affiliations

  1. School of Economics and Management Sciences, Yanshan University, Qinhuangdao, 066004, China

    Quan-Lin Li, Rui-Na Fan & Zhi-Yong Qian

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  1. Quan-Lin Li
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  3. Zhi-Yong Qian
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Correspondence to Rui-Na Fan .

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Editors and Affiliations

  1. Konan University, Kobe, Japan

    Wuyi Yue

  2. Yanshan University, Qinhuangdao, China

    Quan-Lin Li

  3. Yanshan University, Qinhuangdao, China

    Shunfu Jin

  4. Yanshan University, Qinhuangdao, China

    Zhanyou Ma

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Li, QL., Fan, RN., Qian, ZY. (2017). A Nonlinear Solution to Closed Queueing Networks for Bike Sharing Systems with Markovian Arrival Processes and Under an Irreducible Path Graph. In: Yue, W., Li, QL., Jin, S., Ma, Z. (eds) Queueing Theory and Network Applications. QTNA 2017. Lecture Notes in Computer Science(), vol 10591. Springer, Cham. https://doi.org/10.1007/978-3-319-68520-5_8

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  • DOI: https://doi.org/10.1007/978-3-319-68520-5_8

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