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In this paper a study on the buffer overflow period in a finite-buffer queue is presented. A special attention is paid to the autocorrelation and batch arrivals, which are supposed to mimic the properties of real arrival processes. Using the batch Markovian arrival process, formulas for the duration of the first, subsequent and stationary overflow periods, as well as formulas for the distribution of the number of consecutive losses during the overflow period are shown. Moreover, analytical results are illustrated via numerical examples. In particular, the influence of the autocorrelation and batch arrivals on the duration of the overflow period is demonstrated.

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