Traffic modeling has an increasing importance in the management and dimensioning of telecommunications networks. Traffic models are used, for example, in the dimensioning of links and buffers while considering the effects of statistical multiplexing and in network performance analysis. In the Internet, the complexity associated with the generation and traffic control mechanisms, as well as the diversity of applications and services, introduced a set of peculiar traffic characteristics, such as self-similarity, long range dependence and multifractality. These characteristics have a strong impact on the network performance and, therefore, need to be properly modeled. This Thesis proposes a set of traffic models, which are able to describe these peculiar behaviors, and that can be classified in two classes: Markovian models and models based on Lindenmayer systems. In both cases, we propose models for traffic with fixed and variable packet size.

In the first part of the Thesis we propose two Markovian models and the respective parameter inference procedures. The first model is a Markov modulated Poisson process in discrete time (dMMPP) which characterizes the packet arrivals. It is obtained by superposing a memoryless dMMPP with an arbitrary number of states ($M$-dMMPP) and a set of dMMPPs with two states (2-dMMPPs). In order to infer the parameters, the 2-dMMPPs are used to fit the empirical autocovariance function and the $M$-dMPPP is used to fit the empirical probability mass function considering the restrictions imposed by the 2-dMMPPs. The number of states of the process can be adjusted according to the traffic characteristics. The second model is a batch Markovian arrival process in discrete time (dBMAP). It extends the first model by allowing the modeling of the packet size. In this process the packet arrivals occur according to a dMMPP and the packet sizes have a general distribution which depends on the phase of the subjacent dMMPP. The inference procedure of the first model is used to infer the parameters of the subjacent dMMPP. 

In the second part of the Thesis we propose traffic models based on Lindenmayer systems (L-Systems) and the respective parameter inference procedures. L-Systems were introduced in 1968 by A. Lindenmayer as a method to model plant growth. Starting from an initial symbol, an L-System generates iteratively progressively longer sequences of symbols, by successive application of production rules. In order to define traffic models based on L-Systems, the symbols are interpreted as arrival rates or mean packet sizes and each iteration is associated with a time scale of the traffic. We proposed one model to characterize the packet arrivals and three models to characterize simultaneously the packet arrivals and the packet sizes with different levels of detail. These models are able to capture the multiscaling and multifractal characteristics of the traffic.

The proposed models were tested using measured traffic and were evaluated by comparing (i) the first and second order statistics, (ii) the queuing behavior and (iii) scaling characteristics, of the measured traffic and of synthetic traffic generated according to the inferred models. The obtained results show that the proposed models are, in general, able to reproduce rigorously the main traffic characteristics.