Network multiplexer with truncated heavy-tailed arrival streams

This paper investigates the asymptotic behavior of a single server queue with truncated heavy-tailed arrival sequences. We have discovered and explicitly asymptotically characterized a unique asymptotic behavior of the queue length distribution. Informally, this distribution on the log scale resembles a stair-wave function that has steep drops at specific buffer sizes. This has important design implications suggesting that negligible increases of the buffer size in certain buffer regions can decrease the overflow probabilities by order of magnitudes. A problem of this type arises quite frequently in practice when the arrival process distribution has a bounded support and inside that support it is nicely matched with a heavy-tailed distribution (e.g. Pareto). However, the primary interest in this scenario is in its possible application to controlling heavy-tailed traffic flows. More precisely, one can imagine a network control procedure in which short network flows are separated from long ones. If the distribution of flows is heavy-tailed this procedure will yield a truncated heavy-tailed distribution for the short network flows. Intuitively, it can be expected that with short flows one can obtain much better multiplexing gains than with the original ones (before the separation). Indeed, the analysis confirms this expectation.