In this paper, we show that significant simplicities can arise in the analysis of a network when link capacities are large enough to carry many flows. In particular, we prove that, when an upstream queue serves a large number of regulated traffic sources, the queue-length of the downstream queue converges almost surely to the queue-length of a simplified queueing system (single queue) obtained by removing the upstream queue. We provide similar results (convergence of the queue-length in

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... tion) for general (including non-regulated) traffic arrivals. In both cases, the convergence of the overflow probability is uniform and at least exponentially fast. Through an extensive numerical investigation, we demonstrate several aspects and implications of our results in simplifying network analysis. * In general, Γ does not have to be a fixed subset for the results to hold. However, the results are more meaningful in the case when Γ constitutes a fixed set of flows (see Remark 1 in Section III-A).