MATHEMATICAL ANALYSIS OF VEHICLE DELIVERY SCALE OF BIKE-SHARING RENTAL NODES

Abstract. Aiming at the lack of scientific and reasonable judgment of vehicles delivery scale and insufficient optimization of scheduling decision, based on features of the bike-sharing usage, this paper analyses the applicability of the discrete time and state of the Markov chain, and proves its properties to be irreducible, aperiodic and positive recurrent. Based on above analysis, the paper has reached to the conclusion that limit state (steady state) probability of the bike-sharing Markov chain only exists and is independent of the initial probability distribution. Then this paper analyses the difficulty of the transition probability matrix parameter statistics and the linear equations group solution in the traditional solving algorithm of the bike-sharing Markov chain. In order to improve the feasibility, this paper proposes a "virtual two-node vehicle scale solution" algorithm which considered the all the nodes beside the node to be solved as a virtual node, offered the transition probability matrix, steady state linear equations group and the computational methods related to the steady state scale, steady state arrival time and scheduling decision of the node to be solved. Finally, the paper evaluates the rationality and accuracy of the steady state probability of the proposed algorithm by comparing with the traditional algorithm. By solving the steady state scale of the nodes one by one, the proposed algorithm is proved to have strong feasibility because it lowers the level of computational difficulty and reduces the number of statistic, which will help the bike-sharing companies to optimize the scale and scheduling of nodes.