Local ratio based distributed bike-dock pair allocation in public bike system

Public bike system (PBS) is widely deployed in the world because of relieving city last-mile problem and offering convenient short trip service. However, as PBS getting popular, the phenomenon of resources imbalance shows the trend of increasing gradually at recent years. This problem means that users will not able to rent or return bikes when they come to empty or full stations. Furthermore, this terrible problem is against to the PBS operators' targets---offering service to as much users as possible and saving users' trip time. We formulate above problem with two practical targets as a bike-dock pair allocation (BDA) problem. In this problem, we allocate bike-dock pair to users to fulfill above two targets. We design a BDA algorithm with the local ratio technique and prove that is 3-approximated for BDA problem. Furthermore, we propose the distributed version of the BDA algorithm. The real data experiment shows our distributed bike-dock pair allocation (DBDA) algorithm can save 29.44% of time for each trip in average and help 98.05% of users successfully use PBS service.