Some New Makovian Models for Traffic and Performance Evaluation in Telecommunication Networks

A number of models are being developed for the traffic, service and queuing in the emerging telecommunication networks. The task is rather difficult because the traffic is bursty and correlated. These models include the compound Poisson process (CPP), the Markov modulated Poisson process (MMPP) and self-similar traffic models such as the Fractional Brownian Motion (FBM). The CPP and the ∑K k=1 CPPk traffic models often give a good representation of the burstiness (batch size distribution) of the traffic from one or more sources, but not the auto-correlations of the inter-arrival time observed in real traffic. Conversely, the MMPP models can capture the auto-correlations but not the burstiness. Self-similar traffic models such as the FBM can represent both burstiness and auto-correlations, but they are analytically intractable in a queuing context. The traffic arriving to a node