The Packet-pair dispersion techniques are the most common probing-based approach to measuring the bottleneck capacity of a path. In practice, the dispersion measurement, and therefore the bandwidth estimation, could be seriously distorted by the cross traffic queuing between or in front of the probe packet pair. Almost all the existing packet-pair techniques depend on heuristic filtering methods to find a final capacity estimate. In this paper, we take a different perspective to exploit the cross-traffic effect. We develop a queueing model to describe the output packet-pair dispersions interfered by the cross traffic, based on which a new measurement technique to estimate the available bandwidth is derived. Another important contribution is that we for the first time reveal that the statistics of the cross traffic, e.g. the marginal distribution and the autocovariance function of the arrival process, can also be inferred from the stochastic behavior of the output packet dispersions. Efficiency of the proposed available bandwidth estimation and traffic characterization techniques are demonstrated by computer simulations.