On the structure of data losses induced by an overflowed buffer - Chydzinski, Andrzej (Applied mathematics and computation, 2022)
•The autocorrelation of the interarrival times of a stream of packets has a deep impact on the structure of losses induced by an overflowed buffer.•The burst ratio parameter can be effectively computed for an autocorrelated stream using the Markov-modulated Poisson process (MMPP) model.•The autocorrelation makes the dependence of the burst ratio on the system load to be complicated, with muliple local extrema.•For small or moderate buffers, the burst ratio in an uncorrelated model can be higher than in its autocorrelated counterpart.•The burst ratio depends severely on the service time distribution, no matter if arrivals are positively autocorrelated, or not. We deal with the statistical structure of data losses, when packetized data are transmitted through a channel with a buffering mechanism and may be subject to losses due to the buffer overflow. The main contribution is an explicit formula for the burst ratio parameter, which reflects the tendency of losses to cluster together, in long series. A general model of the arrival stream is used, which enables arbitrary shaping of the interarrival time distribution and the autocorrelation function of interarrival times. In numerical examples, the dependence of the burst ratio on various model parameters is shown, with a special attention to the impact of the autocorrelation of the arrival process. Some unexpected, counterintuitive observations are made.