Swarming systems, such as BitTorrent, are one of the most common solutions for scalable, robust and inexpensive content distribution. Although the service capacity of swarming systems has been studied for decades through modeling and analysis, there is a lack of experimental evidence about how the throughput of such systems behaves in under-provisioned regimes. The aim of this paper is to fill this gap. In this paper, we consider a closed-loop model to assess the throughput of peer-to-peer systems. Then, we show through controlled experiments using BitTorrent clients that some analytical findings recently reported in the literature, such as the missing piece syndrome, occur in practice. In particular, we indicate that when seeds have a small effective service capacity, or when seeds are intermittent, the throughput saturates as the population size grows. Finally, we discuss the implications of such findings on the modeling and design of swarming systems.