Multi-Hop Probing Asymptotics in Available Bandwidth Estimation: Stochastic Analysis
This paper analyzes the asymptotic behavior of packet-train probing over a multi-hop network path carrying arbitrarily routed bursty cross-traffic flows. We examine the statistical mean of the packet-train output dispersions and its relationship to the input dispersion. We call this relationship the response curve of path . We show that the real response curve is tightly lower-bounded by its multi-hop fluid counterpart , obtained when every cross-traffic flow on is hypothetically replaced with a constant-rate fluid flow of the same average intensity and routing pattern. The real curve asymptotically approaches its fluid counterpart as probing packet size or packet train length increases. Most existing measurement techniques are based upon the single-hop fluid curve associated with the bottleneck link in . We note that the curve coincides with in a certain large-dispersion input range, but falls below in the remaining small-dispersion input ranges. As an implication of these findings, we show that bursty cross-traffic in multi-hop paths causes negative bias (asymptotic underestimation) to most existing techniques. This bias can be mitigated by reducing the deviation of from using large packet size or long packet-trains. However, the bias is not completely removable for the techniques that use the portion of that falls below .