Abstract
In order to improve the dynamic optimization of fleet size and standardized management of dockless bike-sharing, this paper focuses on using the Markov stochastic process and linear programming method to solve the problem of bike-sharing fleet size and rebalancing. Based on the analysis of characters of bike-sharing, which are irreducible, aperiodic and positive-recurrence, we prove that the probability limits the state (steady-state) of bike-sharing Markov chain only exists and is independent of the initial probability distribution. Then a new “Markov chain dockless bike-sharing fleet size solution” algorithm is proposed. The process includes three parts. Firstly, the irreducibility of the bike-sharing transition probability matrix is analyzed. Secondly, the rank-one updating method is used to construct the transition probability random prime matrix. Finally, an iterative method for solving the steady-state probability vector is therefore given and the convergence speed of the method is analyzed. Furthermore, we discuss the dynamic solution of the bike-sharing steady-state fleet size according to the time period, so as improving the practicality of the algorithm. To verify the efficiency of this algorithm, we adopt the linear programming method for bicycle rebalancing analysis. Experiment results show that the algorithm could be used to solve the disordered deployment of dockless bike-sharing.
Highlights
Geo-Inf. 2019, 8, 334 constructing the model based on the Markov decision process by combining the spatial elements, and the Hierarchical Reinforcement Pricing (HRP) algorithm is developed based on the depth deterministic strategy gradient algorithm to encourage users to rebalance the dockless bike-sharing
The traditional Markov chain steady-state probability vector solution method is improved, and the "Markov chain dockless bike-sharing fleet size solving method" is given. This method combines the actual application of bicycles to construct a transition probability sparse matrix
For the sparse matrix may be reducibility, the method of arguing irreducibility based on graph theory and the general iterative method for the steady-state fleet size are given
Summary
The concept of “bike-sharing” [1,2,3,4] was proposed the first time in Amsterdam in 1965. The bike-sharing deployed by merchants since 2016 are mainly dockless bicycles [10]. The dockless bike-sharing adopts the operation mode of “smart dockless”, “GPS positioning”, “network convenient payment” and “requesting on demand”. It has become a popular way for short-distance green travel in China. The problems of fleet size and rebalancing [13,14,15] of the dockless bike-sharing stations are mainly illustrated as follows:. The fleet size and rebalancing of dockless bike-sharing stations are in urgent need of scientific analysis. It is necessary to propose an algorithm to determine the number of shared bicycles rationally and quickly at each station to achieve the goal of standardized management
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