Fundamental calculus on generalized stochastically bounded bursty traffic for communication networks

Since many applications and networks do not require or provide deterministic service guarantees, stochastic service guarantee analysis is becoming increasingly important and has attracted a lot of research attention in recent years. For this, several stochastic versions of deterministic traffic models have been proposed in the literature. Unlike previous stochastic models that are based on the traffic amount property of an input process, we present another stochastic model, generalized Stochastically Bounded Burstiness (gSBB), which is based on the virtual backlog property of the input process. We show the advantages of this approach. We study the superposition of gSBB traffic, and set up the input–output relation. Under various service disciplines, we characterize the output process for each source and investigate probabilistic upper bound on delay. Finally, we introduce a stochastic ordering monotonicity property of gSBB. With this property, we show that many well-known traffic models can be readily represented using the proposed gSBB model. These results set up the basis for a network calculus for gSBB traffic.