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Abstract:
This paper proposes a novel mean-field matrix-analytic method in the study of bike sharing systems, in which a Markovian environment is constructed to express time-inhomogeneity and asymmetry of processes that customers rent and return bikes. To achieve effective computability of this mean-field method, this study provides a unified framework through the following three basic steps. The first one is to deal with a major challenge encountered in setting up mean-field block-structured equations in general bike sharing systems. Accordingly, we provide an effective technique to establish a necessary reference system, which is a time-inhomogeneous queue with block structures. The second one is to prove asymptotic independence (or propagation of chaos) in terms of martingale limits. Note that asymptotic independence ensures and supports that we can construct a nonlinear quasi-birth-and-death (QBD) process, such that the stationary probability of problematic stations can be computed under a unified nonlinear QBD framework. Lastly, in the third step, we use some numerical examples to show the effectiveness and computability of the mean-field matrix-analytic method, and also to provide valuable observation of the influence of some key parameters on system performance. We are optimistic that the methodology and results given in this paper are applicable in the study of general large-scale bike sharing systems.
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Source :
ANNALS OF OPERATIONS RESEARCH
ISSN: 0254-5330
Year: 2021
Issue: 2
Volume: 309
Page: 517-551
4 . 8 0 0
JCR@2022
ESI Discipline: ENGINEERING;
ESI HC Threshold:87
JCR Journal Grade:2
Cited Count:
WoS CC Cited Count: 0
SCOPUS Cited Count: 2
ESI Highly Cited Papers on the List: 0 Unfold All
WanFang Cited Count:
Chinese Cited Count:
30 Days PV: 1
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