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Previously, the network must be congested by probing flow before the congestion-related parameters (such as background flow and available bandwidth) can be estimated, which lead to the inaccuracy and inefficiency of today's Internet. In this work, the authors study how to estimate network state without saturating the network. By introducing the queueing theory, this study proposes a novel packet time series analysis (PTSA) framework model, which can be used to estimate the congestion-related parameters without saturating the network. The accuracy and efficiency of PTSA are validated under NS-2 simulation environment. The performance of PTSA methodology is evaluated in Schooner test-bed with a special scenario. The analytical, simulative and experimental results show that PTSA framework is more efficient to estimate network state with less aggression and higher sensitivity than those methods that need to saturate the network.