The characterization of the Quality of Service (QoS) and the dimensioning of actual communications networks, namely those based on the IP protocol, are very complex tasks that are intimately related to the traffic that is offered to the network. This traffic has a highly varying behavior due to the fact that networks generally support a large diversity of applications, with different QoS demands, and to different mechanisms of traffic generation and control (that operates at different time scales). These facts have induced a set of peculiar behaviors in Internet traffic, like for example self-similarity, long-range dependence and multifractality, whose common characteristic is statistical invariance with time scale (known as scaling) and have a significant impact on network QoS.

The main focuses of this Thesis are the statistical characterization and modeling of the communications networks' traffic, and we can divide it in two major parts. The first part is dedicated to studying the influence that second order statistics of offered network traffic have in network performance, through the analysis of the so called Correlation Horizon that separates the relevant from the irrelevant part of the autocovariance function, from a performance point of view. The second part is dedicated to the proposal of new traffic models and their parameter inference procedures. Firstly, two new parameter inference methods are proposed for the two states Markov modulated Poisson process (2-MMPP) and their applicability conditions are verified. In a second phase, two novel traffic models based on the MMPP with an arbitrary number of states are proposed, together with their parameter inference procedures, having the ability to fit the traffic scaling characteristics. The building methodologies of these processes are intimately related to the notion of time scale: starting from a MMPP that is inferred in order to describe the largest time scale characteristics, the models are iteratively refined through the incorporation of characteristics belonging to successively finer time scales. In the first proposed model, a MMPP is inferred for each time scale and the equivalent traffic model is obtained by superposing all the MMPPs representative of each time scale. In the second proposed traffic model, each state of the MMPPs associated to each time scale leads to a new MMPP in the following time scale that gives a more detailed description of the traffic associated to that state; the equivalent traffic model is a MMPP corresponding to the tree structure that was built using this methodology. Finally, the third phase proposes a new traffic model based on the so called Lindenmayer systems, which were firstly proposed in the sixties to model plant growth; the proposed model has the ability to fit the traffic multifractal characteristics.

All the proposed traffic models were tested with real traffic and their efficiency was assessed by comparing the (i) first and second order statistics; (ii) scaling characteristics and (iii) queuing behavior of real traffic and traffic generated by simulating the models that were inferred from measured data.