Subexponential loss rates in a GI/G/1 queue with applications

Consider a simple server queue with i.i.d. arrival and service processes and a finite buffer. The queue content process is recursively defined. Under certain conditions, we show that the stationary expected loss rate for this queue has an explicit asymptotic characterization. For a fluid queue with capacity c, characterized by intermediately regularly varying on periods, which arrive with Poisson rate, we determine the average loss rate at which the fluid is arriving during an on period. Accuracy of the above asymptotic relations is verified with extensive numerical and simulation experiments. These explicit formulas have potential application in designing communication networks that will carry traffic with long-tailed characteristics, e.g. Internet data services.