Modeling the available bandwidth of a path using a known stochastic process is one possible method for estimating future available bandwidth along the path without explicit support from network routers. Our two hypotheses for the stochastic process are as follows. First, an autoregressive integrated moving-average process (ARIMA) is a suitable model for the available bandwidth over time of a path. Second, the available bandwidth over time of a path can be modeled as a self-similar process. We verify both hypotheses using R statistical software and available bandwidth data sets published by Stanford Linear Accelerator Center (SLAC). Our results indicate that the available bandwidth over time of an end-to-end path can be modeled as fractional Gaussian Noise (FGN) and seasonal fractional ARIMA (SFARIMA) processes. On the other hand, we found that an ARIMA process is not a good model for available bandwidth over time of an end-to-end path.