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We propose and estimate an alternating renewal model describing the propagation of anomalies in a backbone internet network in the United States. Internet anomalies, either caused by equipment malfunction, news events or malicious attacks, have been a focus of research in network engineering since the advent of the internet over 30 years ago. This article contributes to the understanding of statistical properties of the times between the arrivals of the anomalies, their duration and stochastic structure. Anomalous, or active, time periods are modelled as periods containing clusters or 1s, where 1 indicates a presence of an anomaly. The inactive periods consisting entirely of 0s dominate the 0–1 time series in every link. Since the active periods contain 0s, a separation parameter is introduced and estimated jointly with all other parameters of the model. Our statistical analysis shows that the integer-valued separation parameter and five other non-negative, scalar parameters satisfactorily describe all statistical properties of the observed 0–1 series.