Analysis of a self-similar traffic envelope for a trade-off of leaky bucket algorithm parameters

Numerous investigations have revealed that the packet network traffic is bursty and highly correlated. If many large bursts meet in a single queue an overflow is unavoidable even for a slightly loaded network, therefore shaping packet traffic becomes a crucial issue. One of the most commonly used traffic shaping algorithms is a leaky bucket. An important property of a leaky bucket algorithm is that one can find different pairs of leaky bucket parameters (r, b) for the same drop probability pd. The burstiness curve binds leaky bucket parameters (r, b) for the fixed drop probability pd. The basic goal of the analysis presented in the dissertation is computing a burstiness curve for the FARIMA traffic model with support of original results obtained for its envelope analysis; an FGN model has been used as a reference. The motivation for finding the burstiness curve is that trading r and b values for the same pd yields in changing traffic parameters without changing QoS. The reason for choosing the FARIMA model is that the FARIMA process can exhibit SRD and LRD structures independently and simultaneously and a distribution of a FARIMA process is known. The obtained results have been confirmed by a simulation study. An additional achievement of this dissertation is derivation of an envelope process for the three types of FARIMA models.