Cell loss asymptotics in buffers fed with a large number of independent stationary sources

We derive asymptotically exact expressions for buffer overflow probabilities and cell loss probabilities for a finite buffer which is fed by a large number of independent and stationary sources. The technique is based on scaling, measure change and local limit theorems and extends the results of Courcoubetis and Weber (see J. Appl. Prob., vol.33, no.3, p.886-903, 1996) on buffer overflow asymptotics. We discuss the cases when the buffers are of the same order as the transmission bandwidth as well as the case of bufferless multiplexers. Moreover we show that the results hold for a wide variety of traffic sources including on/off sources with heavy-tailed distributed on periods which are typical candidates for so-called “self-similar” inputs showing that the asymptotic cell loss probability behaves in much the same manner for such sources as for Markovian type of sources which has important implications for statistical multiplexing. The paper concludes with comparison of the theoretical results with simulations