Decision System Based on Markov Chains for Sizing the Rebalancing Fleet of Bike Sharing Stations

Abstract

Docked Bike Sharing Systems often experience load imbalances among bike stations, leading to uneven distribution of bicycles and to challenges in meeting users’ demand. To address the load imbalances, many docked Bike Sharing Systems employ rebalancing vehicles that actively redistribute bicycles across stations, ensuring a more equitable distribution and enhancing the availability of bikes for users. The determination of the number of rebalancing vehicles in docked Bike Sharing Systems is typically based on various criteria, such as the size of the system, the density of stations, the expected demand patterns, and the desired level of service quality. This is a determining factor, in order to increase the efficiency of customer service at a reasonable cost. To enable a cost-effective rebalancing, we have used a cluster-based approach, due to the large scale of the Bike Sharing Systems, and our model is based on Markov Chains, given their proven effectiveness in this domain. Degrees of subsystem load at station level were used for modeling purposes. Additionally, a quantization strategy around cluster load was developed, to avoid state space explosion. This allowed the computation of the probability of transitioning from one degree of system load to another. A new method was developed to determine the fleet size, based on the identified subsystem steady state, describing the rebalancing necessity. The model evaluation was performed on traffic data collected from the Citi Bike New York Bike Sharing System. Based on the evaluation results, the model transition rates were in accordance with the expected values, indicating that the rebalancing operations are efficient from the point of view of the fulfillment of on-time arrival constraints.