On the distribution of the number of consecutively lost customers in the BMAP/PH/1/N system

In this paper, we propose method for calculating the distribution of the number of consecutively lost customers in the single-server queueing system with a finite buffer, batch Markovian arrival process and phase type distribution of service time. The most well-known and important performance measure of finite capacity systems is the probability of losing an arbitrary customer. Loss probability is the subject of research in the literature under various assumptions about the nature of the input flow and the distribution of service time. At the same time, this characteristic may be not always a good estimate of the quality of service in queuing systems that arise in the mathematical modeling of telecommunication networks. More indicative in this case is the probability of losing several customers in a row caused by an overflowing buffer. We propose explicit formulas that characterize the distribution and mathematical expectation of the number of consecutively lost customers in the system under consideration.