A Stochastic Foundation of Available Bandwidth Estimation: Multi-Hop Analysis

This paper analyzes the asymptotic behavior of packet-train probing over a multi-hop network path P 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 P. We show that the real response curve Z is tightly lower-bounded by its multi-hop fluid counterpart F, obtained when every cross-traffic flow on P is hypothetically replaced with a constant-rate fluid flow of the same average intensity and routing pattern. The real curve Z asymptotically approaches its fluid counterpart F as probing packet size or packet train length increases. Most existing measurement techniques are based upon the single-hop fluid curve S associated with the bottleneck link in P. We note that the curve S coincides with F in a certain large-dispersion input range, but falls below F 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 Z from S using large packet size or long packet-trains. However, the bias is not completely removable for the techniques that use the portion of S that falls below F.