Estimating the reliability of an end-to-end network path is critically important for applications that support remote real-time task execution. Available bandwidth defined as a minimum spare capacity of links constituting a network path is an important QoS characteristic of the path. In this work we demonstrate a new approach to modeling available bandwidth behavior from a time-series analysis prospective. In particular, we introduce a notion of crossing probability - the probability that the available bandwidth drops below the QoS critical threshold for the period of time required for the real-time task execution. We estimate the ''crossing probability'' by an application of the ARCH^2 (AutoRegressive Conditional Heteroscedasticity) model to the available bandwidth behavior. We characterize the network path by model coefficients @b0 and @b1, which may be evaluated and updated dynamically. We use these coefficients to quickly output the ''crossing probability'' for arbitrary values of the threshold and length of the real-time task. The model was evaluated on real bandwidth measurements across multiple network paths.