A novel model for simulating aggregate network traffic is proposed. Our model, besides reflecting self-similarity and long-range dependence, it is able to capture the appropriate level of burstiness of different types of traffic by selecting the proper parameters. Different types of self-similar traffic traces (LAN/WAN, WWW, VBR video) are analyzed by estimating their self-similarity coefficient H, as well as the parameters of their marginal distributions. When comparing the real traces with our artificial traces, the agreement, which was evaluated both qualitatively (visually) and quantitatively (by means of the marginal PDF and the periodogram), is better than the achieved with previously models. By analyzing different types of traffic traces, the model is shown to be flexible enough to be applied to simulate a variety of communications scenarios. A queue with our proposed traffic as input is analyzed. A proof of convergence of aggregate traffic to alpha-stable processes is also included, as well as the conditions under which the Gaussian assumption is appropriate.