On the distribution of consecutive losses in a finite capacity queue

In this paper we study the connection between the overall loss ratio and the number of consecutive cells lost during one buffer overflow period in a finite capacity queue. The study includes detailed calculations of consecutive loss probabilities and loss ratios for ten sets of parameters of the queueing system. The results show that two queueing systems having exactly the same cell loss ratio may have quite different consecutive cell loss probabilities. In other words, in the first system the losses may have a tendency to occur in groups much more often than in the second one. This effect can be quite strong and may be observed even if the buffer capacities, traffic intensities or the distributions of the service time are equal in both systems.