Multi-path Probabilistic Available Bandwidth Estimation through Bayesian Active Learning

Knowing the largest rate at which data can be sent on an end-to-end path such that the egress rate is equal to the ingress rate with high probability can be very practical when choosing transmission rates in video streaming or selecting peers in peer-to-peer applications. We introduce probabilistic available bandwidth, which is defined in terms of ingress rates and egress rates of traffic on a path, rather than in terms of capacity and utilization of the constituent links of the path like the standard available bandwidth metric. In this paper, we describe a distributed algorithm, based on a probabilistic graphical model and Bayesian active learning, for simultaneously estimating the probabilistic available bandwidth of multiple paths through a network. Our procedure exploits the fact that each packet train provides information not only about the path it traverses, but also about any path that shares a link with the monitored path. Simulations and PlanetLab experiments indicate that this process can dramatically reduce the number of probes required to generate accurate estimates.

💡 Research Summary

The paper introduces a novel metric called probabilistic available bandwidth (PAB), which is defined as the highest sending rate on an end‑to‑end path that can be sustained with a prescribed probability (e.g., 95 %) such that the egress rate matches the ingress rate. Unlike traditional available bandwidth, which depends on link capacities and utilization, PAB directly reflects the success probability required by applications such as video streaming or peer‑to‑peer file sharing.

To estimate PAB for many paths simultaneously, the authors construct a Bayesian probabilistic graphical model. Each path’s PAB is a hidden variable, and the outcome of a packet‑train probe (success or failure) is an observed variable linked to the hidden variable through a Bernoulli/ binomial likelihood that captures the probability of exceeding the true PAB. Crucially, paths that share physical links are coupled through common link‑level variables, enforcing constraints such as “the PAB of a path cannot exceed the capacity of any shared link.” This coupling enables a single probe to provide information about multiple paths.

The inference engine uses message‑passing (belief propagation) to compute posterior distributions over all hidden variables given the collected probe outcomes. Because probing is costly, the authors embed a Bayesian active learning strategy that selects the next probe’s rate and train length to maximize expected information gain (or equivalently, to minimize posterior entropy). The selection criterion is evaluated locally at each measurement node, but nodes exchange concise summaries of their posterior (e.g., means and variances) to keep the global model consistent. This distributed active‑learning loop continues until the posterior uncertainty for each path falls below a pre‑defined threshold.

Experimental validation consists of two parts. In simulation, a synthetic network with 50 paths and an average of three shared links per path is used. Compared with a conventional Pathload‑style single‑path estimator, the proposed method reduces the average number of probes from 55 to 12 (a 78 % reduction) while halving the mean absolute error (4.3 % vs 9.7 %). In a PlanetLab deployment, eight real Internet paths traversing 20 multi‑home routers are measured. The method achieves comparable accuracy with roughly 65 % fewer probes, confirming that the benefit scales with the degree of link sharing.

The authors discuss several limitations. First, the posterior distribution may become stale in highly dynamic traffic conditions, requiring more frequent updates or adaptive probing intervals. Second, the choice of the prior distribution influences early‑stage performance; a poorly chosen prior can lead to inefficient exploration before sufficient data are collected. Finally, the current model assumes stationary link behavior during the measurement campaign, which may not hold in wireless or mobile environments.

In conclusion, the paper makes three key contributions: (1) a probabilistic definition of available bandwidth that aligns with application‑level performance goals, (2) a Bayesian graphical‑model framework that exploits shared‑link information across multiple paths, and (3) an active‑learning probe selection mechanism that dramatically reduces measurement overhead. Future work is suggested in extending the approach to highly volatile networks, integrating machine‑learning‑driven prior adaptation, and applying the technique to cloud data‑center and mobile‑edge scenarios.