Analysis on generalized stochastically bounded bursty traffic for communication networks

We introduce the concept of generalized stochastically bounded burstiness (gSBB) for Internet traffic, the tail distribution of whose burstiness can be bounded by a decreasing function in a function class with few restrictions. This new concept extends the concept of stochastically bounded burstiness (SBB) introduced by previous researchers to a much larger extent - while the SBB model can apply to Gaussian self-similar input processes, such as fractional Brownian motion, gSBB traffic contains non-Gaussian self-similar input processes, such as α-stable self-similar processes, which are not SBB in general. We develop a network calculus for gSBB traffic. We characterize gSBB traffic by the distribution of its queue size. We explore the property of sums of gSBB traffic and the relation of input and output processes. We apply this calculus to a work-conserving system shared by a number of gSBB sources, to analyze the behavior of output traffic for each source and to estimate the probabilistic bounds for delays. We expect this new calculus to be of particular interest in the implementation of services with statistical qualitative guarantees.