Dockless Bike-Sharing Systems with Unusable Bikes: Removing, Repair and Redistribution under Batch Policies

This paper discusses a large-scale dockless bike-sharing system (DBSS) with unusable bikes, which can be removed, repaired, redistributed and reused under two batch policies: One for removing the unusable bikes from each parking region to a maintenance shop, and the other for redistributing the repaired bikes from the maintenance shop to some suitable parking regions. For such a bike-sharing system, this paper proposes and develops a new computational method by applying the RG-factorizations of block-structured Markov processes in the closed queueing networks. Different from previous works in the literature of queueing networks, a key contribution of our computational method is to set up a new nonlinear matrix equation to determine the relative arrival rates, and to show that the nonlinearity comes from two different groups of processes: The failure and removing processes; and the repair and redistributing processes. Once the relative arrival rate is introduced to each node, these nodes are isolated from each other, so that the Markov processes of all the nodes are independent of each other, thus the Markov system of each node is described as an elegant block-structured Markov process whose stationary probabilities can be easily computed by the RG-factorizations. Based on this, this paper can establish a more general product-form solution of the closed queueing network, and provides performance analysis of the DBSS through a comprehensive discussion for the bikes' failure, removing, repair, redistributing and reuse processes under two batch policies. We hope that our method opens a new avenue to quantitative evaluation of more general DBSSs with unusable bikes.