State-dependent Beneš Buffer Model with Fast Loading and Output Rates

We consider a state-dependent generalization of the exponential Beneš model of single-source buffer system in which the source process consists of alternating transmission and idle periods. Martingale methods are applied for analyzing limit non-stationary behavior of the buffer content process, when the buffer is loaded and depleted, with rates proportional to a large parameter N. Depending on traffic conditions, defined by parameters of the model, different types of approximations are established for the buffer content. We show that in heavy traffic the buffer content grows linearly in N , while the deviations of the order √ N from the deterministic limit are approximated by the Gaussian diffusion process. In the moderate traffic the buffer content grows as √ N , and the normalized buffer content is approximated by diffusion process with reflection at zero. In the case of normal traffic we show that the buffer utilization tends to the ratio of ”the input-to-output-rate”. Moreover, we show that the main contribution to the utilization comes from arbitrary small buffer content.