For more accurate multiple-period real-time monitoring of road traffic, this paper investigates the unmanned aerial vehicle scheduling problem with uncertain demands. A mixed integer programming model is designed for this problem by combining the capacitated arc routing problem with the inventory routing problem. A local branching based solution method is developed to solve the model. A case study which applies this model to the road traffic in Shanghai is performed. In addition, numerical experiments are conducted to validate the effectiveness of the proposed model and the efficiency of the proposed solution method.