In this paper we develop a novel model-based technique, the Delphi algorithm, for inferring the instantaneous volume of competing cross-traffic across an end-to-end path. By using only end-to-end measurements, Delphi avoids the need for data collection within the Internet. Unique to the algorithm is an efficient exponentially spaced probing packet train and a parsimonious multifractal parametric model for the cross-traffic that captures its multiscale statistical properties (including long-range dependence) and queuing behavior. The algorithm is adaptive; it requires no a priori traffic statistics and effectively tracks changes in network conditions. NS (network simulator) experiments reveal that Delphi gives accurate ross-traffic estimates for higher link utilization levels while at lower utilizations it over-estimates the cross-traffic. Also, when Delphi's single bottleneck assumption does not hold it over-estimates the cross-traffic.