Estimates on the packet loss ratio via queue tail probabilities

In this paper we consider the connection between the packet loss ratio (PLR) in a switch with a finite buffer of size L and the tail distribution of the corresponding infinite buffer queue Q. In the literature the PLR is often approximated with the tail probability P(Q > L), and in practice the latter is often a good conservative estimate on the PLR. Therefore, efforts have mainly focused on finding bounds and asymptotic expressions concerning the tail probabilities of the infinite queue. However, our first result shows that the ratio PLR/P(Q > L) can be arbitrary, in particular the PLR can be larger than the tail probability. We also determine an upper bound on this ratio yielding an upper bound on the PLR using the tail distribution of the infinite queue. The bound is fairly tight for certain traffic patterns. In many situations it clearly improves the estimation with the tail probability, and it is rarely significantly larger than the estimate P(Q > L), while it is an upper bound. On the other hand, if the PLR is much smaller than P(Q > L), then our bound is usually loose. For this case a practically good approximation on their ratio is proposed.