Unmanned aerial vehicles (UAVs) are envisioned to provide diverse services from the air. The service quality may rely on the wireless performance which is affected by the UAV's position. In this paper, we focus on the UAV placement problem in the Internet of Vehicles, where the UAV is deployed to monitor the road traffic and sends the monitored videos to vehicles. The studied problem is formulated as video resolution maximization by optimizing over the UAV's position. Moreover, we take into account the maximal transmission delay and impose a probabilistic constraint. To solve the formulated problem, we first leverage the techniques in extreme value theory (EVT) and Gaussian process regression (GPR) to characterize the influence of the UAV's position on the delay performance. Based on this characterization, we subsequently propose a proactive resolution selection and UAV placement approach, which adaptively places the UAV according to the geographic distribution of vehicles. Numerical results justify the joint usage of EVT and GPR for maximal delay characterization. Through investigating the maximal transmission delay, the proposed approach nearly achieves the optimal performance when vehicles are evenly distributed, and reduces 10% and 19% of the 999-th 1000-quantile over two baselines when vehicles are biased distributed.
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