Network Multiplexer with Truncated Heavy-Tailed Arrival Streams

This pa.per investigates the asymptotic behavior of a single server queue with truncated heavy-tailed arrival sequences. 14'-e have discovered and explicitly asymptotically cha.ra.cterized a unique asymptotic behavior of t,he queue length distribution. Informally, this distribution on t,he log scale resembles a stair-wave function t h t lias steep drops a t specific buffer sizes. This has important8 design implications suggesting that negligible increa.ses of the buffer size in certain buffer regions can clecrea.se t.he overflow probabilities by order of magni t,u des. A problem of t,liis type arises quite frequently in practice when the arrival process distribution has a bounclecl support and inside that support it is nicely ma.t,ched wit,li a. hea.vy-hiled distribution (e.g. Pareto). However, our primary interest in this scenario is in its possible applic,a.t,ion to controlling heavy-tailed traffic flows. More precisely, one can imagine a network cont,rol procedure in which short network flows are separa.tec1 from long ones. If the distribution of flows is heavy-tailed t,liis procedure will yield truncated heavytailed clist,ribution for the short network flows. Intuit,ively, it, can be expected that with short flows one can obta.in iiiuch bet,ter multiplexing gains than with t,he original ones (before the separation). Indeed, our analysis confirms t,his expectation.