We consider a TCP/AQM system with large link capacity (NC) shared by many flows. The traditional rule-of-thumb suggests that the buffer size be chosen in proportion to the number of flows (N) for full link utilization, while recent research outcomes show that O( √N) buffer sizing is sufficient for high utilization and O(1) buffer sizing makes the system stable at the cost of reduced link utilization. In this paper, we consider a system where the AQM is scaled as O(Nα) with a buffer of size O(Nβ) (0 < α < β < 0.5). By capturing randomness both in packet arrivals and in packet markings, we develop a doubly-stochastic model for a TCP/AQM system with many flows. We prove that, under such a scale, the system always performs well in the sense that the link utilization goes to 100% and the loss ratio decreases to zero as the system size N increases. Our results assert that the system enjoys benefit of largeness with no tradeoff between full link utilization, zero packet loss, and small buffer size, at least asymptotically. This is in stark contrast to existing results showing that there always exists a tradeoff between full link utilization and the required buffer size. Extensive ns-2 simulation results under various configurations also confirm our theoretical findings. Our study illustrates that blind application of fluid modeling may result in strange results and exemplifies the importance of choosing a right modeling approach for different scaling regimes.