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A receding horizon routing controller for inventory replenishment agents in bike sharing systems with time-varying demand

A Bike Sharing System (BSS) may be modeled as a graph with two node types: stations with finite bike inventory subject to time-varying demand and intersections to represent the underlying transportation network. Mobile agents (replenishment trucks) travel on the arcs of the graph to reset station inventories and make routing decisions at intersections. One-way rides create inventory imbalances across the system. Inventory control via rebalancing trucks has two main facets: selecting the number of bikes to load/unload between the truck and a station and routing decisions for the truck based on daily demand patterns. This paper focuses on the latter and introduces a Receding Horizon Controller which minimizes a user dissatisfaction metric defined as the expected number of users unable to rent or return a bike due to a station being empty or full, respectively. We model stations as M/M/1/K queues subject to time-varying birth and death rates based on the time of day. The controller proceeds in an event-driven manner and determines at each event the optimal routes over a finite planning horizon, with the control applied over a shorter action horizon. The proposed controller is applied to a simulated BSS with station and demand parameters extracted from the data sets of Hubway, the BSS in Boston MA.