Capacity regions for network multiplexers with heavy-tailed fluid on-off sources

Consider a network multiplexer with a finite buffer fed by a superposition of independent heterogeneous on-off sources. An on-off source consists of a sequence of alternating independent activity and silence periods. During its activity period a source produces fluid with constant rate. For this system, under the assumption that the residual activity periods are intermediately regularly varying, we derive explicit and asymptotically exact formulas for approximating the stationary overflow probability and loss rate. The derived asymptotic formulas, in addition to their analytical tractability, exhibit excellent quantitative accuracy, which is illustrated by a number of simulation experiments. We demonstrate through examples how these results can be used for efficient computation of capacity regions for network switching elements. Furthermore, the results provide important insight into qualitative tradeoffs between the overflow probability, offered traffic load, available capacity, and buffer space. Overall, they provide a new set of tools for designing and provisioning of networks with heavy-tailed traffic streams.