The imbalanced distribution of shared bikes in the dockless bike-sharing system (a typical example of the resource-sharing system), which may lead to potential customer churn and lost profit, gradually becomes a vital problem for bike-sharing firms and their users. To resolve the problem, we first formulate the bike-sharing system as a Markovian queueing network with higher-demand nodes and lower-demand nodes, which can provide steady-state probabilities of having a certain number of bikes at one node. A model reduction method is then designed to reduce the complexity of the proposed model. Subsequently, we adopt an operator-based relocation strategy to optimize the reduced network. The objective of the optimization model is to maximize the total profit and act as a decision-making tool for operators to determine the optimal relocation frequency. The results reveal that it is possible for most of the shared bikes to gather at one low-demand node eventually in the long run under the influence of the various arrival rates at different nodes. However, the decrease of the number of bikes at the high-demand nodes is more sensitive to the unequal demands, especially when the size of the network and the number of bikes in the system are large. It may cause a significant loss for operators, to which they should pay attention. Meanwhile, different estimated values of parameters related with revenue and cost affect the optimization results differently.
Although the dockless bike-sharing system, which can be regarded as a typical example of the resource-sharing system, has been increasingly popular for years with people especially in China, the imbalanced distribution of shared bikes gradually becomes a major problem for both bike-sharing companies and their customers. To solve the imbalance problem, we aim to investigate the long-term performance of a system under the influence of some key factors (with an emphasis on the unequal demand between different nodes), which can guide us to discover the causes of the problem and offer several valuable suggestions to the operators. According to the fundamental principle of a dockless bike-sharing system, we propose a model reduction method to reduce the complexity of the theoretical network models, which are developed based on the Markovian queueing theory with the consideration of higher-demand nodes and lower-demand nodes. The theoretical network models provide us with steady-state probabilities of having a certain number of bikes at one node, which are used as an important part of the optimization model for solving the imbalance problem by carrying out an operator-based relocation strategy. The objective of the optimization model is to maximize the total profit and determine the optimal relocation frequency. It is found that most of the shared bikes are possible to gather at one low-demand node eventually in the long run under the influence of the different arrival rates at different nodes, but the decrease of the number of bikes at the high-demand nodes is more sensitive to the unequal demands and may cause a great loss for operators, which should be payed attention to especially when solving the relocation problems.
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