Vehicle platooning is a promising technology that can lead to significant fuel savings and emission reduction. However, the macroscopic impact of vehicle platoons on highway traffic is not yet well understood. In this article, we propose a new fluid queuing model to study the macroscopic interaction between randomly arriving vehicle platoons and the background traffic at highway bottlenecks. This model, viewed as a stochastic switched system, is analyzed for two practically relevant priority rules: proportional (or mixed) and segmented priority. We provide intuitive stability conditions, and obtain bounds on the long-run average length and variance of queues for both priority rules. We use these results to study how platoon-induced congestion varies with the fraction of platooned vehicles, and their characteristics such as intra-platoon spacing and arrival rate. Our analysis reveals a basic tradeoff between congestion induced by the randomness of platoon arrivals, and efficiency gain due to a tighter intra-platoon spacing. This naturally leads to conditions under which the proportional priority is preferred over segmented priority. Somewhat surprisingly, our analytical results are in agreement with the simulation results based on a more sophisticated two-class cell transmission model.