Fleet Size and Rebalancing Analysis of Dockless Bike-Sharing Stations Based on Markov Chain

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.

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