Abstract:

In this paper, an approximate model and algorithm for the throughput rate are established by studying a docked bike-sharing system (DBSS) using stochastic user demands, routing matrix, and cycling times. A DBSS with a fixed number of bikes can be considered a closed queuing network with a buffered M/M/1 queue at each station, thus establishing an approximate model and algorithm for the throughput rate of DBSS. This algorithm can calculate the average number of bikes on roads and at stations. Moreover, it can estimate the average cycling time on roads and bike dwell time at stations and further determine the optimal number of bikes achieving the maximum throughput rate in the DBSS. Additionally, this paper proposes a method to determine whether a station is a bike surplus station or a bike deficient station under given user demands, routing matrix, cycling time matrix, and dock allocation. Finally, the approximate algorithm is verified in a real-world DBSS. The results show that the throughput rate of the DBSS increases in a step-wise manner with the increasing bike input under an superior limit. When the number of bike inputs exceeds the optimal quantity, there will be idle bikes, and the spatial distribution of bike surplus stations and bike deficient stations will remain unchanged.

Key words: docked bike-sharing system, operational efficiency, closed queuing network, system throughput rate, bike surplus and deficient stations, bike input