Approximation of Throughput Rate of Docked Bike-Sharing System

Abstract

This paper proposes an approximation algorithm for the throughput rate of a docked bike-sharing system (DBSS) with stochastic user demands, routing matrix, and cycling times. A DBSS with a fixed number of cycling bikes is formulated as a closed service network with a buffered M/M/1 queue at each station. Accordingly, an approximation algorithm for the throughput rate of the DBSS is developed. The formulated 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 as well as determine the optimal number of bikes achieving the maximum throughput rate in the DBSS. This paper also proposes a method to determine whether a station is a bike surplus station or a bike deficient station, given user demands, routing matrix, cycling time matrix, and dock allocation. The approximation algorithm is verified in a real-world bike-sharing network. The throughput rate of the DBSS is found to increase trapezoidally with the bike input under an upper bound. Moreover, if the input exceeds the optimal number of bikes in the DBSS, the bikes are left idle, and the spatial distribution of bike surplus stations and bike deficient stations becomes constant.