Long-tailed loss rates in a single server queue

In this paper we have considered several queueing systems with finite buffers and long-tailed arrivals. For these queueing systems we have derived explicit asymptotic formulas for approximating loss rates. The accuracy of the suggested approximate formulas is demonstrated on various numerical and simulation experiments. Overall, we expect that these approximate expressions, both for reasons of their explicit nature and accuracy, will be useful tools in designing modern communication networks that will be able to efficiently carry non-traditional long-tailed ("bursty") traffic.