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IMC '05, 2005 Internet Measurement Conference — Abstract

Pp. 173–186 of the Proceedings

Multi-Hop Probing Asymptotics in Available Bandwidth Estimation: Stochastic Analysis

Xiliang Liu, City University of New York; Kaliappa Ravindran, City College of New York; Dmitri Loguinov, Texas A&M University


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

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