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The main drawback of traditional intrusion detection systems makes anomaly detection systems an active research area. In this paper we introduce a novel network-based anomaly detection approach using stochastic learning automata. The paper main objective is to construct a network-based statistical anomaly detection system capable of classifying the ensemble network broadcast traffic as normal or abnormal. For this purpose the approach constructs a learning automaton from time series data of purified network broadcast traffic in learning process. Time series data of observed network broadcast traffic are compared by the normal model and any deviation from it is marked as abnormal. This approach is novel in that apply stochastic learning automaton with a special reinforcement scheme to the problem of network anomaly detection and presents an online high precision network-based anomaly detection system using broadcast traffic time series data.